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is to your immediate right, forcing you to act ahead of everyone else, you must tighten up considerably. It is extremely important that you fold almost all marginal hands in this position. The possibility of a raise behind you plus the chance of a reraise from the original bettor is Position 159 devastating. Furthermore, you can frequently count on being in the same unpleasant position — not accidentally called under the gun — for the remainder of the hand. If you constantly call bets with marginal hands in this position, you will have to fold so many of them — either later in the same round when the bet is raised or on the next round when the bet is repeated — that you will lose an enormous amount relative to the occasional pots you might win by staying in. Thus, in five-card draw, if a player to your immediate right in early position opens, you should throw away two aces in most cases. In the same position in lowball, you'd usually have to throw away a one-card draw to a 7,6 and possibly a 7,5, even though these are hands you'd gladly play if you were sure there would be no raises behind you. In seven-card stud if the player to your right raises the opener on third street, you should fold most middle-sized pairs when there are several people behind you who might reraise. With any of these hands you'd almost certainly call in last position, a fact that underlines another of that position's advantages: You can play more hands. You no longer need to fear a raise from players who have not acted, and in most instances you will probably remain last on future betting rounds as well. Even in seven-card stud, when the bettor to your left happens not to be high on board and thus first to act, the other players will usually check around to that bettor on the following round. Strong Hand, Bettor to the Left Another significant advantage to last position is that when you make a strong handr you have more opportunity to win a big pot. You can sit there innocently with your monster hand and let the bettor to your left drive the other players around to you. That opponent bets, two or three players ahead of you call, and now bang, you raise. You get at least a single bet from opponents who told after you raise, and you get a double bet from those who call. You're also making it more expensive for them to try to draw out 160 Chapter Seventeen on you when there are more cards to come. (Notice, in this situation, the problems faced by players in first and middle positions. Those callers in the middle always risk a raise from a player behind them.) Strong Hand, Bettor to the Right If you had the same strong hand but the bettor were to your right, you would not be able to play the hand in the same way. If you raised, you would be requiring

players behind you to call a double bet to continue. Thus, you'd get fewer callers (if any) than you would if you raised in last position after they had committed themselves by calling the first bet. On the other hand, by just calling in first position, the best you can hope for is to collect some single bets from players behind you. At the same time, when there are more cards to come, you're making it relatively cheap for the callers to draw out on you. So with more cards to come, you have to decide whether your hand can stand competition or whether you should raise to drive players out. How Position Affects Play To show how differently you have to play in first and last positions, let's say I'm dealt in no-limit hold 'em (where position remains fixed throughout the hand). If the opponent on my left raised a moderate amount and got three calls, I would also call as long as most of the players had a decent amount of money in front of them. Were I to flop three Position 161 6s (the odds against it are about 8-to-l), I'd anticipate winning a big pot. However, were the player on my right to raise the same amount, I'd have to fold my pair of 6s even if I thought there would be some calls but no raises behind me. My bad position is what makes the difference. It changes things enough on future rounds to turn a call into a fold. If I were to flop three 6s in last position, that 6 on board would look pretty innocuous. The original bettor would probably bet again, maybe get called, and then I could put in a big raise — or perhaps slowplay and wait to raise on fourth street. However, if the bettor were to my right, I couldn't immediately raise with three 6s and hope to be called by players behind me whether on the flop or on fourth street. Thus, when I'm directly behind the bettor, my implied odds are reduced so much that it's not worth calling that bettor's first raise before the flop. Position Vis-A-Vis Other Players in the Game Position is important in relation to the playing style of the other players in the game. You prefer having the loose, aggressive player in the game sitting to your right and the tight, conservative player to your left. Then you can usually decide how to play your hand after the aggressive player has acted, while you don't have to worry about many surprises from the conservative player behind you. You are also in a better position to control the aggressive player and indeed to trap him into mistakes. Similarly, if there are players in the game who tip off whether or not they are playing a hand, you'd like them to your left so you can use that information when deciding whether to call the first bet yourself. Summary In sum, while in a horse race you like being first, in a poker game

you like being last. Chapter Eighteen Bluffing The 1978 no-limit hold 'em world championship at the Horseshoe in Las Vegas came down to a battle between owlish Bobby Baldwin of Tulsa, Oklahoma, and sartorial real-estate magnate Crandall Addington of San Antonio, Texas. An hour before the championship ended. Addington had $275,000, and Baldwin, about half as much — $145,000. Among the gamblers along the rail Addington was the clear favorite, but then came the hand that turned everything around. Acting first, Baldwin bet before the flop, and Addington called. The flop came: Baldwin pushed in another $30,000 worth of chips, perhaps chasing a straight or a diamond flush. Then again he might have had a pair of queens. But Addington promptly called the $30,000. Obviously he had a good hand himself. On fourth street the ace of diamonds fell — a scary-looking card — and by that time there was $92,000 in the pot. Slowly and deliberately Baldwin pushed in one $10,000 stack of chips, then another and another, until there were nine stacks in the center of the table. Finally, with something of a flourish, Baldwin placed a short stack of $5,000 on top of the others. He was making a $95,000 bet, leaving himself almost broke. Addington deliberated for a long time. He glanced at the stack of chips, and then at Baldwin for some clue. Was the kid bluffing? If Addington called the bet and won, Baldwin would be 163 164 Chapter Eighteen just about tapped out. If he called the bet and lost, Baldwin would take a commanding lead. Was the kid bluffing or not? Addington decided he wasn't and threw away his hand. As Baldwin raked in the $92,000 pot, he made sure to flash his two hole cards in Addington's direction. They were the: Worthless. Baldwin had indeed been bluffing. Addington seemed to get rattled, and an hour later Baldwin won all the chips and became the 1978 poker champion of the world. The Myth of Bluffing Successful bluffs, particularly in a high-stakes game, have great drama. Furthermore, people who do not play much poker often think that bluffing is the central element of the game. When Stu Ungar appeared on the Merv Griffin Show the day after he won the 1980 world poker championship, the first question Griffin asked him was, "Did you bluff very much?" Many occasional players who visit Las Vegas are constantly bluffing in the small $ 1 -$3 and $ 1 -$4 games, and they pay dearly for their foolishness. It's true bluffing is an important aspect of poker, but it is only one part of the game, certainly no more important than playing your legitimate hands correctly. Though a player who never bluffs cannot expect to win as much money as someone who bluffs with the proper frequency, most average players tend to bluff too much, particularly in limit games. When it costs an opponent only one more bet to see your hand, it is difficult to get away with a bluff, for with any kind of hand your opponent

is usually getting sufficient pot odds to call your bet — especially if he has seen you trying to bluff several times already. Bluffing 165 The Reality of Bluffing With this proviso, it must be repeated that from a theoretical point of view, bluffing is an extremely important aspect of poker. As a deceptive weapon, it is at least as important as slowplaying. Whereas slowplaying suggests weakness when you have strength, bluffing announces strength when you are weak. Recollect the Fundamental Theorem of Poker: Any time an opponent plays his hand incorrectly based on what you have, you have gained; and any time he plays his hand correctly based on what you have, you have lost. An opponent who knows you never bluff is much less likely to play his hand incorrectly. Any time you bet, he will know you are betting for value. He will play only when he figures he has a better hand than yours or when he is getting sufficient pot odds to call with more cards to come. Bluffing, then, or the possibility that you might be bluffing, is another way of keeping your opponents guessing. Your occasional bluffs disguise not just the hands with which you are in fact bluffing but also your legitimate hands, with which your opponents know you might be bluffing. To see how important bluffing is, imagine that you are up against an opponent who on the last round bets $20 into a $100 pot. You are getting 6-to-1 from the pot if you call. However, you know you can only win, as is often the case, if your opponent is bluffing. Let's say you know three opponents well. The first never bluffs in this spot, so your response to that player's bet is easy: You fold with the full knowledge that you have not cost yourself any money. The second opponent frequently bluffs. Once again your response is easy: You call, knowing you are going to win that last bet so often that calling must result in a long-run profit. The third player is the problem. He bets in such a way that the odds are about 6-to-1 against his bluffing. In fact, he can tell you in advance that if he bets, he will be bluffing once in seven times. Now you have a tough decision. You must choose between two equally upsetting alternatives. You are getting 6-to-1 from a Pot you can win only if your opponent is bluffing, and the odds 166 Chapter Eighteen against your opponent's bluffing are 6-to-1. If you fold, you know there's a chance your opponent stole the pot from you; but if you call, you know that six times out of seven you are simply donating your money to your opponent. Thus, a person who bluffs with approximately the right frequency — and also, of course, in a random way — is a much better poker player and will win much more money in the long run than a person who virtually never bluffs or a person who bluffs too much. The person

who never bluffs will never get much action. The person who always bluffs will get all the action he wants until he runs out of money. But the person who bluffs correctly keeps his true holdings disguised and is constantly forcing his opponents into tough decisions, some of which are bound to be wrong. Optimum Bluffing Frequency What is the right bluffing frequency? It is a frequency that makes it impossible for your opponents to know whether to call or fold. Mathematically, optimal bluffing strategy is to bluff in such a way that the chances against your bluffing are identical to the pot odds your opponent is getting. Thus, if, as in the example just given, an opponent is getting 6-to-1 from the pot, the chances against your bluffing should be 6-to-1. Then that opponent would break even on the last bet by calling every time and also by folding every time. If he called, he would lose $20 six times and win $120 once; if he folded, he would win nothing and lose nothing. Regardless of what your opponent does, you average winning an extra $100 every seven hands. However, mathematically optimal bluffing strategy isn't necessarily the best strategy. It is much better if you are able to judge when to try a bluff and when not to in order to show a bigger overall profit. To make sure we agree on what is meant by a bluff, we will define it as a bet or a raise with a hand which you do not think is the best hand. Bluffing can be separated into a couple of different categories. There is bluffing when there are more cards to come and when there are no more cardsto come. Secondly, within each Bluffing 167 of these categories, there is intuitive bluffing, which is the subject of this chapter, and mathematical bluffing, which will be discussed in the next chapter. Bluffs When There are More Cards to Come When there are more cards to come, your bluffs should rarely be pure bluffs — that is to say, bets or raises that have little or no chance of winning if you are called, even taking into account the cards you may get on future rounds. Instead your early-round bets should be semi-bluffs, those powerful, deceptive plays we looked at in detail in Chapters Eleven and Twelve. It is important to bluff occasionally on early rounds to keep your opponents off-balance. But why do it when you have only one or two ways of winning? For a pure bluff to work, your opponent or opponents must generally fold immediately. However, as we saw in Chapter Eleven, a semi-bluff has three ways of winning. It may win because your opponent folds immediately, and it may also win either because you catch a scare card that causes your opponent to fold on a later round or because you make the best hand. Nevertheless, while you should usually restrict your early-round bluffs to semi-bluffs, there is still nothing to prevent you from trying a pure bluff if you

feel there's a good chance of getting away with it. If you think your chances of getting away with it are greater than the pot odds you are getting, then you should go ahead and try it. You may recall in the chapter on ante structure we mentioned playing in a game where certain players played too tight for the ante. There was $10 in antes, and if these players were the only ones in the pot, I knew I could bet $7 with absolutely nothing and have a good chance of stealing that $10. My pot odds in that instance were less than 11 /2-to-l, but I knew I could get away with the bluff about 60 percent of the time. So it was a profitable play. 168 Chapter Eighteen If you do make a pure bluff on an early round and someone raises you, don't try to tough it out. You've been caught. Since you have no out, you don't even have to think about continuing. Give it up, and get on with the next hand. When you bluff with more cards to come, you often get called, and then you are faced with deciding whether or not to continue the bluff on the next round. Thus, when you bluff with a hand that probably can't improve to the best hand, you need to compare your chances of getting away with it to your effective odds if you are planning to continue betting on future rounds even when you don't improve. For instance, if there is $100 in the pot in a $10-$20 game with two cards to come, you may have to bluff twice. If you think you will bluff twice, you are risking $40 to win $120 — the $100 in the pot plus the $20 your opponent calls on the first round. So when you make that first $20 bet, you cannot think you are getting 5-to-1 from the pot. Rather you are getting 3-to-1 ($120-to-$40). For the play to be profitable, there must be a better than 3-to-1 chance your opponent will fold after the second bet. This is especially true of pure bluffs where you have no way of winning by improving to the best hand. Deciding whether to continue with a semi-bluff really depends on how the next card affects your chances and how your opponent's card seems to have affected his. Each individual round should be evaluated separately. Suppose you make a semi-bluff raise in seven-card stud with: You get called by a 9. Whether you should give up the bluff on the next round depends on what you catch, what your opponent catches, and also what kind of player your opponent is. If with Bluffing 169 your A,K,5 you proceed to catch a queen suited with the king and your opponent catches a deuce, you ought to bet again; but if your opponent catches, let's say, an 8 suited with the 9 and you catch a 3, give it up. Check, and if your opponent bets, throw the hand away. Your chances

have not improved, and it looks as if your opponent's have. He may have a flush draw, a straight draw, or simply a pair of 9s, but whatever he has, he looks like too much of a favorite for you to call when he bets. It takes experience to know when to give up on a bluff and when to pursue it. When your first bet is called, presumably your opponent has something. If you sense he's getting stronger and you don't improve, give it up. If you sense he's weak and staying weak and if you think he thinks you're strong, continue the bluff and hope to drive him out. Bluffs When All the Cards are Out When all the cards are out, you obviously can no longer semi-bluff. You have either made your hand or you haven't. So all bluffs on the end are pure bluffs. They are bets or raises that you do not expect to win if you are called. When you are sitting there knowing you have the worst hand, knowing you cannot win by checking, knowing you cannot win by calling your opponent's bet, the only question is whether or not to try to bluff. You should not if you think the chances your opponent will call are too great in relation to the pot odds you are getting. You should if you think your opponent will fold often enough for a bluff to show a profit. If there is $100 in the pot, you should make a $20 bluff if you think your opponent will fold more than once in six times. If there is $60 in the pot, you must assume your opponent will fold more than once in four times before you try to bluff. If there is $ 140 in the pot, your opponent needs to fold more than once in eight times. But, of course, the larger the pot, 170 Chapter Eighteen the better pot odds your opponent is getting to call your bet and the more likely it is he will call with any kind of a fair hand. Accurate assessment of your chances of pulling off a bluff comes, like so many advanced poker plays, only with experience. You must first be able to read hands. You are obviously not going to bluff out an opponent with a lock or any sort of big hand. In general, the weaker you think your opponent's hand is, the higher the chances your bluff will succeed. Second, you must be able to read opponents. It's generally easier to bluff out a timid opponent than a loose opponent, and it's generally easier to bluff out a tough opponent than a weak one who looks for any reason to call, including the possibility that you might be bluffing. In essence, you must consider your specific opponent in each situation before deciding whether to try a bluff. Even the way in which play developed in previous hands can have a bearing on whether a bluff is now right or not. Bluffing and Position Your position

can also affect the chances of a bluff's success. In most games with tough players, I've found it easier to bluff if I'm first than if I'm second and my opponent has checked. There are two reasons for this. If my opponent has checked to me, he knows he has shown weakness with his check, and when I bet, he suspects I am trying to take advantage of his weakness. So he's likely to call with any kind of hand. And, if he has a really bad hand, he might very well have tried to bluff himself. Since he checked instead, the chances are good he has a calling hand, and when I bet out on a bluff, he's likely to call, even if he thinks he's a small underdog. So in situations on the end where your hand can't win by checking but where you have reason to believe your opponent may be weak, a bluff in first position is more likely to succeed than a bluff in second position. Bluffing 171 Bluffing Against Come Hands Sometimes both you and your opponent have been drawing to a flush or a straight. You don't make your hand, but there's a good chance your opponent didn't make his either. Because of earlier bets on the come, there may be a fair amount in the pot — say, $ 100 in a $ 10-$20 game. Now let's say you are first, and you end up with an AJ high. You think there's a 55 percent chance your opponent made a legitimate hand, and there's a 15 percent chance he has you beat "by mistake" with something like an A,K or an A,Q high. In this spot you should bet because by betting you are likely to make your opponent throw away the A,K and A,Q high, thus improving your chances of winning from 30 percent to 45 percent. In contrast, when you have a busted hand and you suspect your opponent does, too, you may not want to bluff if you end up making something like a small pair. If you bet, your opponent will call with a legitimate hand, and he will fold without one. But if you check and then call, your opponent may bet his busted hands as well as his legitimate ones. Thus, with your small pair you beat his bluffs, which you could not do if you came out betting yourself. Either way, of course, you lose to his legitimate hands. Bluffing Against Two or More Opponents It is rarely correct to try to bluff out two or more people when all the cards are out; your chances of success decrease geometrically with each additional player in the pot. Paradoxically you might have a profitable bluffing opportunity against each of two opponents individually, but not against both of them as a group. Suppose, for example, you are heads-up on the end in a $10-$20 game. There is $80 in the pot, and you think you can get away with a bluff one out of three times. Clearly this is

an extremely profitable bluffing situation. Once you will win $80, 172 Chapter Eighteen and twice you will lose $20 for a net profit of $40 or an average profit of $13.33 per bet. Now suppose you are in the identical situation except that you are up against two players instead of one. We'll assume each player has put $40 in the pot to expand it to $120, and you think, as in the former case, that each opponent will fold one time out of three. You are now getting 6-to-1 instead of 4-to-1 from the pot. Nevertheless, an attempt at a bluff is no longer profitable because the probability that both of your opponents will fold is 1 /3 X 1 /3, which equals 1/9. In other words, eight times out of nine one or the other of your opponents will call on average. So you stand to lose $20 eight times for a total of $ 160 and to win $ 120 once. Your net loss is $40 or $4.44 per bet. Thus, opposing each individual player by himself results in a profitable bluffing situation, but if they're both in against you, you have gone from a profitable situation to an unprofitable one. (It should be pointed out that in most bluffing situations against more than one player the probabilities that each player will fold are not independent. The player in the middle will frequently fold a hand that he would call with if he was last, and sometimes the player who is last will call with a hand he would have folded without hesitation had he been in the middle, expecting the player behind him to call. Nevertheless, the general principle still holds that it is usually more profitable to try to bluff one player out of a pot containing 2X dollars than to bluff two players out of a pot containing 3X dollars.) Bluffing and Betting for Value The number of poker hands anyone can have is comparatively limited, but in addition to the hands themselves there are so many other variables that rarely if ever is a particular play always right or always wrong. Your play is affected by the size of the pot, your position, the opponent or opponents you are facing, the way they have been playing, the amount of money they have and you have, the flow of the game, and other, more subtle Bluffing 173 factors. This point is particularly applicable to questions of bluffing and betting fair hands for value on the end. Here are some general principles that usually apply. When you bluff, you are rooting for your opponent to fold because that is the only way you can win the pot. When you bet for value, you are rooting for your opponent to call because you want your legitimate hand to win one more bet from him. It is important to realize that it may be right to bet a fair hand for value, and it may also be right to bluff, but it is almost never right to do neither.

If you decide you can't get away with a bluff on the end when you miss your hand, then you should bet for value when you do make your hand. (The only exception to this principle would occur in games like hold 'em and five-card stud, where your opponent can see your last card and might often have a good sense of whether it made your hand. In those cases, if you bet a hand for value, you are likely to get called — or raised — only by a hand that has you beat.) Similarly, when you don't think a value bet is justified with a fair hand, since your opponent will only call if he has you beat, then if you miss your hand, you should usually bluff. For when you bluff, it is possible your opponent will throw away his fair hands. Sometimes it may be correct both to bluff and to bet a fair hand for value on the end. Suppose you are up against one player and decide, before you see your last card, that you will come out betting if you don't improve. In seven-card stud, let's say on sixth street you have: Notice that in addition to your A,Q high four-flush you hold a small pair. When you pick up your last card, you find that you 174 Chapter Eighteen didn't make the flush, but you don't have a bad hand either. You caught another queen and so now have queens up. Should you bet this hand for value? Many professional players say no. They contend that if you were so sure you should bluff if you missed, then you should not bet a fair hand for value since you will only be called if your opponent has you beat. However, both plays may be right, especially if the pot is large. Let's say there's an 80 percent chance your queens up are the best hand, and there's a 30 percent chance your opponent will fold if you bet. That means that if you bet your queens up for value, 30 percent of the time your opponent will fold and not pay you off. Nevertheless, you are still a 5-to-2 favorite when that player calls your bet. You will win that extra bet 50 percent of the time, while you will lose it only the 20 percent of the time your opponent has your queens up beat. Clearly, then, you should bet with your two pair since you have a 5/7 chance of winning if you are called. On the other hand, if you miss making even two pair, there is still a 30 percent chance your opponent will fold what may be the best hand if you bet. Therefore, a bluff will also be profitable in the long run, so long as your bet is less than 3/7 of the pot. A similar situation comes up in hold 'em when I am heads-up against a good player. I raise before the flop in last position, and my opponent calls. The flop comes something like:

My opponent checks. I check. He now suspects I have A,K; A,Q; or K,Q; and he is right. He is ready to call with any pair if a high card doesn't come, but if one does, he will consider folding. I know all this. Therefore, I am going to bet when an ace, king, or queen comes, even though only two of those cards pair me. My Bluffing 175 opponent should call me often enough with the worst hand to make a value bet correct, yet I suspect he will fold with enough frequency to make a bluff profitable too. Bluffing According to Your Opponent You must, of course, consider your opponent when deciding whether to bet a fair hand for value or to bluff. Against a perpetual caller, obviously you should rarely bluff. However, against such a player you should bet any hand that you figure is a reasonable favorite to be the best hand. In contrast, against a tough player capable of tough folds, you can get away with bluffs more often, but you should be more reluctant to bet your fair hands for value. A tough opponent is not likely to pay you off with his worse hands, and when he does call, he's likely to show down a hand that beats you. Here is a typical situation showing when a bluff is right and when it is not. Let's say in draw poker you draw three cards to a pair of jacks, and your opponent draws three to what you suspect is a pair of aces. First, we'll assume your opponent is the type of player who will almost always fold if his hand doesn't improve. In this instance, your play is to bluff if you don't improve since you may make your opponent throw away his pair of aces. However, if you make jacks up, you should check rather than bet for value since you are a big underdog if you bet and get called. If your opponent calls, he is likely to have made aces up. Now let's assume your opponent is the type who almost never folds. Against this player you cannot bluff with one pair because he will almost certainly call you with his bigger pair. However, if you make jacks up against him, then you should bet for value since your two pair are almost a 5-to-2 favorite to be the best hand when you get called. The difference is that this opponent will call with one pair of aces as well as with aces up, 176 Chapter Eighteen whereasthe first opponent would most likely not have called with only a pair of aces. Bluffing as Advertising When you get caught bluffing, you of course lose. However, you may not mind being caught and losing early in a session because you are considering your image for future hands. You may even make an ill advised bluff early so that you will get a lot more calls on your legitimate hands the rest of the night. (Similarly, an early ill-advised call against tough players

may keep them from bluffing against you the rest of the night because they fear you're likely to call their bluffs.) Creating an image that you almost never bluff can also be advantageous. I am generally considered a tight player, and I sometimes pass up an early, marginally profitable bluffing situation to enhance this image. What that does is allow me to steal some pots in the future with complete impunity. No one imagines I am daring to bluff. When you are up against even average players, they are constantly studying the way you play. So considering the effect of any play on future hands should be an important part of your game, especially in no-limit and pot-limit poker and especially when you are playing against the same people all night or from one night to the next or one week to the next. Some players go so far as to argue that bluffs should show a loss because those losses will be repaid with interest when they get a lot of action on their legitimate hands. Game theory, as we shall see in the next chapter, suggests that when you employ optimal bluffing strategy, you should break even on your bluffs. However, there is no reason not to develop a sense of your opponents and of betting situations so your bluffs show a profit. A successful bluff wins the whole pot, and it takes a lot of extra calls of your legitimate hands to make up for one pot. Therefore, against all but very tight players, you should bluff slightly less than optimally so your bluffs show a profit. The greater your Bluffing 177 reputation as a tight player, the more you will be able to get away with bluffs. At the same time, you will still get caught often enough to get paid off when you do have a good hand. Summary A bluff is a bet or raise with a hand you do not think is the best hand. With more cards to come, you should generally restrict yourself to semi-bluffs with handsthat may become the best hand. When deciding whether to make a pure bluff, you estimate whether your chances of getting away with it are better than the pot odds you are getting. However, if there are more cards to come and you plan to continue to bluff, you must take into account your effective odds. On the end you should usually bluff with a busted hand when you think your opponent is weak. Against a tough player, the bluff tends to work more often in first position. However, if you have a hand with some value, don't bet when you are first so that you can snap off your opponent's bluffs. If you are in second position and your opponent checks, show down these same hands since they have little chance of winning if you bet and get called. The odds against a bluffs working increase almost geometrically with each extra person in a pot. Therefore, it is rarely correct to try to bluff out two

or more players, especially on the end. When to bluff and when to bet a fair hand for value is a difficult problem of judgment and experience. In general, if you do not think you could get away with a bluff, you should bet your fair hands for value; if a fair hand cannot be a profitable bet, then a bluff should be. Bluffs are another tool of the well-rounded poker player. In my opinion, they should show a long-run profit the same as any other poker play. Even if you get caught only occasionally, you can still expect to get paid off when you do have a hand. Chapter Nineteen Game Theory and Bluffing Game theory sounds like a theory about games, but it is actually a branch of mathematics dealing with the decision-making process. While it applies to games, as we shall see, it also applies to such disciplines as economics, international relations, social science, and military science. Essentially game theory attempts to discover mathematically the best strategies against someone also using the best strategies. Against an opponent you think is weaker than you are — and it can be in any game whatsoever — you would usually rely on your judgment rather than on game theory. However, against an opponent you think is better than you or against an opponent you don't know, game theory can sometimes enable you to overcome the other's judgmental edge. To show how game theory can work in this regard, we'll employ the children's game of odds and evens. Each of two players puts out one or two fingers. If the total is even, one player wins; if the total is odd, his opponent wins. Now mathematically this is an absolutely even game. However, over a long series it is possible for one person to gain an edge by outwitting the other, by deciding whether to put out one or two fingers on the basis of what the other person put out in the previous round or rounds, by picking up patterns — in a word, by figuring out what his opponent is thinking and then putting out one or two fingers in order to foil him. 8 Figuring out what the other person is thinking is, of course, a crucial aspect of poker. See Chapter Twenty-three, "The Psychology of Poker." 179 180 Chapter Nineteen Suppose someone challenges you to this game. Feeling confident about his judgment and ability to outguess you, he is willing to lay you $101 to $100 per play. We'll assume you too feel your challenger has the best of it in terms of judgment. Nevertheless, by employing game theory, you can gladly accept the proposition with the assurance that you have the best of it. All you have to do is flip a coin to decide whether to put out one or two fingers. If the coin comes up say, heads, you put out one finger; if it comes up tails, you put out two fingers. What has this procedure done? It has completely destroyed your opponent's ability to

outguess you. The chances of your putting out one or two fingers are 50-50. The chances of a coin coming up heads or tails are 50-50. However, instead of your thinking about whether to put out one or two fingers, the coin is making the decisions for you, and most importantly it is randomizing the decisions. Your opponent might be able to outguess you, but you are forcing him to outguess an inanimate object, which is impossible. One might as well try to guess whether a roulette ball is going to land on the red or the black. Since your opponent is laying you $101 to $100, by using game theory you have assured yourself of an 0.5 percent mathematical advantage (or a 50-cent positive expectation per bet). You have removed whatever advantage your opponent might have had in out-thinking you and given yourself an insuperable edge over the long run. Only if you thought you could out think your opponent would you be better off using your judgment instead of a coin flip. Using Game Theory to Bluff In this chapter we are mainly concerned with how game theory can be applied to the art of bluffing and calling possible bluffs in poker. For this purpose we will talk about mixed strategy, a strategy in which you make a certain play — specifically a bluff or a call of a possible bluff— a predetermined Game Theory and Bluffing 181 percentage of the time, but you introduce a random element so that your opponent cannot know when you are making the play and when you are not. You will recall from the last chapter that, everything else being equal, the player who never bluffs and the player who bluffs too much are at a decided disadvantage against a player who bluffs correctly. To illustrate this point and to show how game theory can be used to decide correctly when to bluff, we'll set up a proposition. We are playing draw lowball with no joker, and I give you a pat: You stand pat, and I must draw one card. If I catch a five, a six, a seven, an eight, or a nine, I beat you with a better low than yours. If I catch any other card, you win. That means that of the 42 cards remaining in the deck, I have 18 winners (4 fives, 4 sixes, 4 sevens, 3 eights, and 3 nines) and 24 losers, which makes me a 24-to-18 or 4-to-3 underdog. We each ante $100, but after the draw — which you do not see — I can bet $100. Suppose I said I'm going to bet $ 100 every time. Clearly you would call every time because you would stand to win $200 the 24 times I'm bluffing and lose $200 the 18 times I have the best I take a: 182 Chapter Nineteen hand for a net profit of $1,200. On the other hand, suppose I said I will never bluff; I will only bet when I have your 9,8 low beat. Then you

would fold every time I bet, and once again you would win 24 times (when I don't bet) and lose 18 times (when I do) for a net profit of $600 since you win or lose $100 in each of these hands. So with either of these variations of the proposition, you definitely have the best of it. However, if I only bluff some of the time, the situation is much different. Suppose I were to bluff only when I caught the king of spades. In other words, I would bet whenever I caught any of my 18 good cards and also when I caught the king of spades. If I bluffed this infrequently, your proper play would still be to fold when I bet because the odds against my bluffing are 18-to-l. But notice how this improves my position. Bluffing when I catch the king of spades still doesn't give me a profit, but it allows me to win 19 times instead of 18 and lose only 23 times instead of 24. That single bluff once out of 19 times has begun to close the gap between your status as a favorite and mine as an underdog. Notice too that you have no way of knowing when I am bluffing since I am randomizing my bluffs by using a card, an object as inanimate as the coin in the odds-evens game, to make my bluffing decision for me. If bluffing with one card makes me less of an underdog than never bluffing at all, suppose I choose two — say, the king of spades and the jack of spades. Once again your correct play is to fold when I bet. But now you win only 22 times when I don't bet, and I win 20 times when I do. Assuming you have no way of knowing when I'm bluffing and when I'm not, my using just two key cards to bluff, in addition to my 18 good cards, has reduced you from 24-to-18 favorite to a 22-to-20 favorite — that is, from a 4-to-3 favorite to an 1 l-to-10 favorite. This bluffing seems to have possibilities. Suppose instead of two cards, I picked five key cards — the king of spades and all four jacks. That means I would be betting 23 times — 18 times with the best hand and five times on a bluff. Now all of a sudden you are in a bad situation with your pat 9,8 because you have to Game Theory and Bluffing 183 guess whether I'm bluffing when I bet. I could even tell you precisely the strategy I am using, but you would still have to lose your money. What would happen? You know there are 18 cards that will make me my hand and five other cards I will bluff with. Thus, the odds are 18-to-5 or 3.6-to-1 against my bluffing. With the $200 in antes and my $100 bet, the pot is $300. So you are getting 3-to-1 odds from the pot. You cannot profitably call a 3.6-to-1 shot when you

stand to win only 3-to-1 for your money. Lo and behold, by using five cards to bluff with, I win that pot from you 23 out of 42 times, and you win it only 19 times. I make a profit of $400. Thus, my occasional random bluffing has swung a hand that is a 24- to-18 underdog into a 23-to-19 favorite. To assure yourself there is no arithmetical sleight of hand here, you can work out what happens if you call every time I bet. You will win $200 from me the five times I am bluffing and $ 100 from me the 19 times I don't bet, for a total of $2,900. But you will lose $200 to me the 18 times I have the best hand for a total of $3,600. Your net loss when you call is $700, which is $300 more than you lose if you simply fold when I bet. Had I picked seven cards to bluff with instead of five, the odds would then be 18-to-7 against my bluffing, and since the pot odds you're getting are 3-to-1, you would be forced to call when I bet. However, you would still end up losing! Seven times, when I'm bluffing, you would win $200 from me for a total of $1,400 and the 17 times I don't bet at all you would win $100 from me for a total of $1,700. Your wins after 42 hands would total $3,100. But I would win $200 from you the 18 times I bet with my good cards for a total of $3,600, giving me a net profit and you a net loss of $500 after 42 hands. It should be pointed out — once again to make it clear there are no tricks to this arithmetic — that you would lose even more money if you folded every time I bet with my 18 good cards and seven bluffing cards. You would win $100 from me the 17 times I don't bet, while I would win $100 from you the 25 times I do. Your net loss would now be $800 instead of $500. 184 Chapter Nineteen Optimum Bluffing Strategy Let's say I choose specifically 6 key cards to bluff with. That means I will bet 24 times. 18 of those times I have the best hand, and 6 of those times I am bluffing. Therefore, the odds against my bluffing are exactly 3-to-1. The pot is $200, and when I bet, there is $300 in the pot. Thus, your pot odds are also 3-to-1. You are calling $ 100 to win $300. Now when the odds against my bluffing are identical to the odds you are getting from the pot, it makes absolutely no difference whether you call or fold. Furthermore, whatever you do, you will still lose exactly $600 after 42 hands. If you were to fold every time I bet, I would beat you out of $ 100 24 times when I bet and lose $100 to you 18 times, when I don't bet, for a

profit of $600. If you were to call me every time, you would beat me out of $200 six times when I'm bluffing and $ 100 18 times, when I don't bet, for a total of $3,000; but I would beat you out of $200 18 times when I bet with my good hands for a total of $3,600. Once again my profit is $600. So other than being a psychic, there is no way in the world you can prevent me from winning that $600 per 42 hands, giving me a positive expectation of $14.29 per hand. Bluffing exactly 6 times out of 24 has turned a hand that was a 4-to-3 underdog when I didn't bluff at all into a 4-to-3 favorite — no matter what strategy you use against me. We can now move to the heart of game theory and bluffing. Notice first that the percentage of bluffing I did was predetermined — one time every 19 bets or 5 times every 23 bets or 7 times every 25 bets. Notice secondly that my bluffing was completely random; it was based on certain key cards I caught, which my opponent could never see. He could never know whether the card I drew was one of my 18 good cards or a bluff card. Finally, notice what happened when I bluffed with precisely six cards — which made the odds against my bluffing in this particular instance identical to the pot odds my opponent was getting. In this unique case my opponent stood to lose exactly the same amount by calling or folding. Game Theory and Bluffing 185 This is optimum bluffing strategy — it makes no difference how your opponent plays. We can say, then, that if you come up with a bluffing strategy that makes your opponent do equally badly no matter how he plays, then you have an optimum strategy. And this optimum strategy is to bluff in such a way that the odds against your bluffing are identical to the odds your opponent is getting from the pot. In the situation we have been discussing, I had 18 good cards, and when I bet my $100, creating a $300 pot, my opponent was getting 3-to-1 odds from the pot. Therefore, my optimum strategy was to bluff with six additional cards, making the odds against my bluffing 3-to-1, identical to the pot odds my opponent was getting. Let's say the pot was $500 instead of $200 before I bet. Once again I had 18 winning cards, and my opponent could only beat a bluff. The bet is $100, and so my opponent would be getting $600-to-$ 100 pot odds when he called. Now my optimum strategy would be to bluff with 3 cards. With 18 good cards and 3 bluffing cards, the odds against my bluffing would be 6-to-1, identical to the pot odds my opponent would be getting to call my bet. If the pot were $ 100 and I bet $ 100, I'd have to bluff with 9 cards when I had 18 good

cards, making the odds against my bluffing identical to the 2-to-l odds my opponent would be getting from the pot. It is important to realize that when the results are the same whether your opponent calls or folds, you will still average the same no matter how that opponent mixes up his calls and folds. Returning to the initial optimum strategy example, where I make a $100 bluff with 6 cards and bet 18 good cards into a $200 pot, I will still average $600 in profits per 42 hands in the long run whether my opponent calls 12 times and folds 12 times or calls 6 times and folds 18 times, or whatever. The inability of a player to find any response to offset his disadvantage is the key to game theory problems, though most game theory books don't put it in thisform. Bluffing on the basis of game theory can also be described in terms of percentages. Suppose you have a 25 percent chance of 186 Chapter Nineteen making your hand, the pot is $100, and the bet is $100. Thus, if you bet, your opponent is getting 2-to-l odds from the pot. Since there is a 25 percent chance of making your hand, there should be a 12 1 /2 percent chance you are bluffing to create the 2-to-l odds against your bluffing, which is the optimum strategy. For example, in draw lowball there are 48 cards you do not see when you draw one card, and we'll assume 12 of them (25 percent) will make your hand. So you should pick 6 other cards (12 1 /2 percent) out of the 48 to use for a bluff. You pick cards, of course, to randomize your bets. Without the random factor, the good opponents against whom you use game theory to bluff would quickly pick up your pattern and destroy you. The beautiful thing about game theory is that even if your opponent knows you are using it, there is nothing he can do about it. Game Theory and Bluffing Frequency According to Your Opponents In actual poker situations, optimum strategy based on game theory is not always the best strategy. Obviously if you are up against an opponent who almost always calls you, then you shouldn't bluff at all. By the same token, if you are up against someone who folds too much, you should bluff with some frequency. Game theory bears out these shifts in strategy. Notice in the first part of this chapter that if you bluffed with five cards instead of six — that is, slightly less than optimally — you would win $300 more per 42 hands if your opponent called rather than folded every time. However, if you bluffed with seven cards instead of six, you would win $300 more if your opponent folded rather than called every time. Here is where a player's judgment supersedes optimum game theory strategy: He would bluff a little less against Game Theory and Bluffing 187 opponents who call too much and a little more against opponents

who fold too much. Good, intuitive players understand this concept. If they notice they have folded on the end a few hands in a row, they are ready to call next time. Otherwise players will start bluffing them. And they use similar considerations in deciding whether to bluff themselves. It is against such expert players, whose calling and folding are right on target, or whose judgment is as good as or better than yours, that game theory becomes the perfect tool. When you use it, there is no way they can outplay you. Summary of Game Theory as a Tool for Bluffing When using game theory to decide whether to bluff, you must first determine your chances of making your hand. You must then determine the odds your opponent is getting on that bet. Then you must randomly bluff in such a way that the odds against your bluffing are identical to your opponent's pot odds. Here's one more example. Suppose you have a 20 percent chance of making your hand, there's $100 in the pot, and the bet is $25. Your opponent is then getting $125-to-$25 or 5-to-1 odds if you bet. The ratio of your good hands to your bluffs should, therefore, be 5-to-1. Since you have a 20 percent chance of making your hand, you should randomly bluff 4 percent of the time. (20 percent-to-4 percent equals 5-to-1.) When you bluff in this fashion, you take optimum advantage of the situation. A good, convenient way to randomize your bluffs, as we have seen, is to pick cards from among those you haven't seen. If, for example, ten cards make your hand and you need a 5-to-1 bluffing ratio, then you should pick two additional cards to bluff with. Here is another example. You draw one card to a spade flush in draw poker, and your opponent draws three cards. Therefore, the chances are enormous that your opponent will not be able to beat a flush, only a bluff. The pot contains $20. The bet is $10. If 188 Chapter Nineteen you bet, your opponent is getting $30-to-$10 or 9-to-3 odds from the pot. Since nine unseen spades make your flush, you should pick three additional cards to bluff with, such as the two red 4s and the 4 of clubs. You now bet with twelve cards creating a 9- to-3 ratio between your good hands and your bluffs. It is not always possible to use cards to arrive at exactly the ratio you need to bluff optimally. However, as long as you are close, you can still expect to gain. You recall that choosing six cards to bluff with in the draw lowball example created exactly the right proportion vis-a-vis the pot odds my opponent was getting; nevertheless, I still ended up with a profit when I bluffed with five or with seven cards whether my opponent called or folded. Of course, the closer you are to the exact ratio, the better, in terms of game theory. Using Game Theory to Call Possible Bluffs Just as you can use

game theory to bluff, you can also use it to call possible bluffs. Usually when your hand can beat only a bluff, you use your experience and judgment to determine the chances your opponent is bluffing. If your hand can beat some of your opponent's legitimate hands, then you do a standard comparison of your chances of having the best hand plus the chances your opponent is bluffing against the pot odds you are getting. However, against an opponent whose judgment is as good as or better than yours, or one who is capable of using game theory to bluff, you in your turn can use game theory to thwart that player or at least minimize his profits. Suppose the pot is $ 100, and your opponent assumes you will fold one out of three times rather than call a $20 bet. It then becomes profitable for that opponent to come out bluffing $20 to win $ 100 because he figures to lose $20 twice but steal $ 100 once for a net profit of $60 and an expectation of $20 per bet. By the same token, if your opponent thinks you will never fold in this Game Theory and Bluffing 189 situation, he will never bluff. Therefore, it behooves you to have an opponent think you might sometimes fold, but you should call sufficiently often to catch his bluffs. When you use game theory to decide whether to call a possible bluff, you make calculations similar to those you make when deciding whether to employ a bluff yourself — and you randomize your calls just as you randomize your bluffs. You figure out what odds your opponent is getting on his possible bluff, and you make the ratio of your calls to your folds exactly the same as the ratio of the pot to your opponent's bet. If your opponent bets $20 to win $100, he is getting 5-to-1 on a bluff. Therefore, you make the odds 5-to-1 against your folding. That is, you must call five times and fold once. You can use key cards to randomize again — for example, if you catch certain unseen cards, you fold. Otherwise, you call. In contrast to using game theory to bluff, using game theory to decide whether to call doesn't turn an unprofitable situation into a profitable one. All it does is prevent your opponent from outwitting you — just as using a coin in the odds-evens game prevents your opponent from outwitting you there. If your opponent is using optimum game theory strategy to bluff, there is still nothing you can do to get the best of him. Summary Game theory cannot replace sound judgment. It should only be used when you think your opponent's judgment is as good as or better than yours or when you simply don't know your opponent. Furthermore, game theory can be used accurately to bluff or call a possible bluff only in a situation where the bettor obviously either has the best hand or is bluffing — for example, a player in seven-card stud

betting into your pair of aces with an obvious flush draw. However, if the bettor may be betting a legitimate hand that is not the best hand, then the concepts in Chapter Twenty-one, "Heads-Up On The End," would apply. 190 Chapter Nineteen When using game theory to decide whether to bluff, you must determine the pot odds your opponent is getting if you bet and then randomly bluff in such a way that the odds against your bluffing are identical to or almost identical to your opponent's pot odds. If your opponent is getting 5-to-1, the odds against your bluffing should be 5-to-1. By playing this way, you give your opponent no correct decision. He does just as well — or badly — in the long run by calling or folding. When using game theory to decide whether to call a possible bluff— assuming your hand can beat only a bluff and assuming your judgment doesn't give you a hint — you must determine the odds your opponent is getting on a bluff. Make the ratio of your calls to your folds the same as those odds. If your opponent is getting 4-to-1 odds on a bluff, you must call randomly four out of five times to make that bluffing unprofitable. Chapter Twenty Inducing and Stopping Bluffs The two preceding chapters demonstrated how, with sound judgment or game theory, a player who bluffs correctly gains a tremendous edge over his opponents. In fact, given two games — one with otherwise poor players who bluff approximately correctly and another with solid players who do not bluff— you do better to play in the solid game. When I started playing draw poker for a living in Gardena, California, I intuitively suspected I was better off playing in games with the typically tight Gardena players than in the looser games with players who played too many hands. I realize now what the difference was. The tight players never bluffed, which was profitable for me, whereasin the looser games players were bluffing more or less correctly — and that hurt me. Good bluffing strategy is such a powerful weapon that it is important to develop tactics to keep your opponents from bluffing correctly. Naturally you are not concerned about changing the habits of opponents who almost never bluff or bluff far too much. But when you find yourself up against a player whose occasional bluffing keeps you on the defensive, you want to try to lead that opponent away from correct bluffing strategy. You want to induce him to bluff more than he should or stop him from bluffing as often as he should. Whether you try to induce a bluff or to stop a bluff depends upon your opponent. If you are playing against a relatively tight player who nevertheless seems to be winning too many hands without getting called, suggesting he may be stealing some pots, you want to stop him from bluffing. That is, you want to push him away from optimum bluffing strategy to the point where he is afraid to bluff

you at all. On the other hand, you want to push an aggressive player who may be bluffing slightly more than 191 192 Chapter Twenty optimally into bluffing even more. In other words, against an opponent who seems to bluff a little more than is correct, induce a bluff and make that player bluff more. Against an opponent who tends to bluff less than is correct, stop him and make him bluff even less. In either case, you are stopping bluffs or inducing bluffs to make your opponents bluff incorrectly. Most professional players are aware of the power of correct bluffing strategy, so they often try to induce bluffs or stop bluffs. However, they sometimes forget an important principle: If you are trying to induce a player to bluff and that player bets, then you must call. This principle is obvious, yet many go against it. If you try to induce a bluff and still fold when your opponent bets, all you may have succeeded in doing is helping that player bluff you out of even more pots than he otherwise would have. Similarly, if you do something to stop a bluff and then call when your opponent bets, you would do better and catch more bluffs if you didn't try to stop his bluffing in the first place. In other words, if you think your hand is worth a call after having tried to stop a bluff, it is crazy to have tried to stop the bluff. You simply reduce the possible hands your opponent might have bet with and therefore the number of hands he might have that you can beat when you call. These two principles regarding inducing and stopping bluffs should be self-evident. When you try to induce a bluff, you will always call if your opponent bets. When you try to stop a bluff, you will always fold if your opponent bets. To do otherwise is completely counterproductive, and it would be better not to try to induce or stop a bluff in the first place. Artificial Techniques There are two basic kinds of techniques to induce and stop bluffs — strategic techniques and artificial techniques. Artificial techniques are easier to understand. They can be used only against average to slightly-above-average players, for they rarely work against tough opponents, who are likely to see through them fast. Inducing and Stopping Bluffs 193 An obvious ploy to stop a bluff is to reach for your chips as though you're anxious to call. If your opponent still comes out betting, fully expecting you to call, you throw away your hand. Of course, you have to use this play against the right player. An experienced player who sees you reaching for chips and suspects what you are up to is all the more likely to come out bluffing, fully expecting you to fold. A ploy to induce a bluff is to give the impression you intend to fold your hand. Now if your opponent bets, you call. But once again an experienced player who sees through the ploy might not

bet without a good hand; realizing a bluff won't work, that player saves money when he or she has nothing. There are several other artificial ploys — feigning disinterest in the hand to induce a bluff, feigning tremendous interest to stop a bluff — but they will not succeed often against top players. Against such players you must use strategic tactics. Strategic Techniques StoppingBluffs Essentially the strategy to stop bluffs is to represent more strength than you actually have. Your opponent will not try to bluff, thinking you have at least a calling hand and perhaps better. Let's say you are playing draw poker, jacks or better to open, against someone you want to stop from bluffing. As the dealer in last position, you open with a pair of aces. After having originally checked in a very deep position, the potential bluffer now calls you. There is no chance that player has something like two pair, since in that case he would have opened himself. Instead he must be on the come. Drawing first, he takes one card, which either makes his hand or doesn't. Now you stand pat! Even when you check after the draw, your opponent will almost never bet unless he actually made his hand. He certainly will not try a bluff in the hope that you will throw away a pat hand. He probably won't 194 Chapter Twenty even bet a small straight. If he does bet, he's made his hand, and you fold, knowing you have not cost yourself any money — that is, knowing your opponent did not steal the pot from you. To stop a bluff in this spot, some players would draw one card, representing two pair, and many players would draw two, representing three-of-a-kind. But in either case, their opponent may still bluff, and he will probably be bluffing approximately correctly. By standing pat, you are stopping the bluff almost completely at almost no cost to yourself. Since you have two aces, there is no chance your opponent can catch a bigger pair than yours, and the odds are approximately 500-to-l that you would make a full house by drawing three cards at the same time that your opponent makes a straight or flush. By stopping a bluff in this fashion, you have reduced your opponent's chances of winning money from you to a minimum. Let's assume the opponent who draws one card makes the hand 20 percent of the time. When that opponent never bluffs — and by standing pat you have pretty well forced him not to bluff— you win the pot 80 percent of the time. Given the pot's size, your opponent's proper bluffing frequency, according to game theory, is about 7 percent. However, as long as your opponent bluffs anywhere from 1 percent to 20 percent of the time, he does better than if he doesn't bluff at all. If, for instance, he bluffs only 2 percent of the time, you still shouldn't call when he bets, and now he wins 22 percent of the pots rather than 20

percent. If he bluffs 10 percent of the time, he is still a 2-to-l favorite to have his hand made when he bets. Since the pot is giving you better than 3-to-1 odds with the antes, you are forced to call, but you will lose that last bet two times out of three. So you clearly fare better when this opponent never bluffs (or, of course, bluffs way too much) than when he bluffs anywhere near correctly. Inducing and Stopping Bluffs 195 Suppose you are up against an opponent who usually bluffs correctly in hold 'em, and the following hand develops: Opponent Your opponent is first to act and he bets. You are worried about a flush or a straight, as well as other hands, but you are also worried about a possible bluff. Therefore, after he bets, you should raise with your two small pair. If he calls with, say, a pair of kings or a four-flush, he will certainly not try to bluff you out on the end. On the other hand, if he reraises or calls and then bets on the end, you should usually throw your hand away. You know you are beat since your opponent would be afraid to bluff you after you have suggested so much strength. You Board 196 Chapter Twenty Inducing and Stopping Bluffs 197 Inducing Bluffs When you are up against a player who bluffs too much, rather than stop his bluffs, you should usually induce one. Let's take an example similar to the draw poker example earlier. Once again as the dealer you open with two aces or even two queens, and an aggressive player who originally checked now calls. This player takes one card, and you're sure he's on the come. Since you want this player to bluff, you should go out of your way to take three cards, making it clear you're starting off with only one pair. Now if he bets, you call. Even if you've succeeded in increasing the player's tendency to bluff only slightly, you have gained by inducing a bluff. You have given yourself more winning chances when you call that last bet than you would have otherwise had. Just as you try to stop a bluff by representing strength, you try to induce a bluff by representing weakness. Let's say you have a high pair in the hole in hold 'em, and on fourth street the board is something like: You should check behind an opponent who checks if you want to induce him to bluff on the end. The only dangerous thing about this play is that you are giving your opponent a free card. If he has an ace, any ace on the end gives him the best hand. However, if he has a small pair, the odds are a long 21-to-l that he will improve to three-of-a-kind. Of course, if your opponent is slowplaying three 9s, you are already beat, and you save a bet. The question you must ask yourself is whether you want to bet on fourth street to avoid

giving a free card or whether it's worth trying to induce a bluff on the end. Opponent You have the best possible first four cards. Yet you should frequently check and call if your opponent bets. Besides disguising your hand, you are inducing a bluff on a future betting round. When you are inducing opponents to bluff, it isn't necessary to lure them so far away from correct bluffing strategy that they are favorites to be bluffing when they bet. All you want to do is lead them to bluff significantly more than the correct frequency. Clearly you should never stop bluffs by people who bluff way too much. However, it may be correct to induce bluffs from people who rarely bluff if you can induce them to bluff more often than their chances of making the hand. Summary Players who bluff with approximately the correct frequency are dangerous opponents because they often force you into the Sometimes inducing a bluff is nearly the same as slowplaying. Take this hand from seven-card razz: You 198 Chapter Twenty position of making an incorrect play. Therefore, it is important to try to stop or induce bluffs to lead opponents away from correct bluffing strategy. You should normally induce a bluff against players who already bluff too much and stop bluffs against players who already bluff too little. In the first case, you are in a situation where you would have to call if your opponent bets. By inducing a bluff, you increase your chances of winning that last bet since your opponent will bet more hands — including his bluffs — that you can beat than he otherwise would. In the second case, against someone who bluffs too little, you feel you would have to fold if that opponent bets, even though there is some chance he might be bluffing. By stopping his bluffs, you reduce the opponent's chances of winning since he will bet only when he has made his hand, and you can comfortably fold. Besides artificial means, you try to induce a bluff by showing weakness on an earlier round; you stop a bluff by showing strength on an earlier round. Thus, inducing a bluff is something akin to slowplaying, and stopping a bluff is something akin to semi-bluffing. When you induce a bluff, you plan to call if your opponent bets since you have increased the chances he is bluffing. When you stop a bluff, you plan to fold if your opponent bets since you have reduced or even completely eliminated the chances he is bluffing. Chapter Twenty-one Heads-Up On The End Most of the concepts we have discussed up to now apply to situations in which there are more cards to come and in which there may be more than two players in the pot. However, if the war that is a poker hand continues from the struggle for the antes to the final showdown, it eventually reaches a last round of betting, most often between two players. And in this last round, after all the cards are out,

you must sometimes apply concepts totally different from those that were operative in earlier betting rounds. In this chapter we will discuss these concepts. They apply to any one-winner limit game (thus excluding high-low split) when two players are heads-up on the end. Bluffing On The End There are two basic conditions that determine how you act when you are heads-up on the end — whether or not you have made a legitimate hand and whether you are in first position or last position. Without a legitimate hand against an opponent with a legitimate hand, you cannot win except on a bluff— a bet or a raise that causes your opponent to fold. You cannot hope to win by checking or by calling. Determining whether or not to try a bluff on the end is based on the same logic as any other bet. You have to decide whether the attempt has positive expectation. If the pot is $100 and you bet $20 with nothing, you have to believe your opponent will fold more than once in six times in order to expect a profit. Thus, if your opponent folds once in five times, you will lose $20 four times, but you will win $100 once on average for a net profit of $20 or an average profit of $4 per hand. However, if your opponent folds once in seven times, you will 199 200 Chapter Twenty-one lose $20 six times and win $100 once for a net loss of $20 or an average loss of $2.86 per hand. Whether a bluff works often enough to be profitable depends, like most plays on the end, upon an accurate assessment of what your opponent is likely to do. While it's tough to get away with a bluff on the end, it's much tougher to get away with a bluff raise. Your opponent needs to fold more often for a bluff raise to show a profit because you are putting in a double bet. Suppose, as in the last case, there is $100 in the pot, and your opponent bets $20. You now call his $20 and raise another $20 on a bluff. With your opponent's $20 bet, the pot has increased to $120, but you are making a $40 investment in the hope your opponent will fold. Since you are now getting only 3-to-1 for your money, your opponent must no longer fold more than once in six times but more than once in four times for you to show a profit. Yet when calling your bluff raise, your opponent is getting 8-to-l for his money. The $100 already in the pot, plus your opponent's original $20 bet, plus your $40 call and raise adds up to a total of $160 in exchange for the opponent's $20. So as we noted in the chapter on raising, it takes a very tough opponent, capable of super-tough folds, to throw away a legitimate hand in this situation. Average players will almost always call. The only time a bluff raise might work against them is when

you suspect correctly that they have nothing themselves. Most of the time, though, when your opponent bets and you have nothing, your best play is to fold. Let us now consider betting strategy heads-up on the end when you have a legitimate hand. You are going to be either first or last to act, and as we have noted, strategy changes according to your position. We'll begin by looking at strategy in last position, which is not quite so tricky as in first position. Heads-Up On The End 201 Last Position Play Last Position Play After Your Opponent Has Checked When you are in last position, your opponent will have either checked or bet. First, what should you do when your opponent checks? Some might reply that you should bet if you think you have the best hand. But this is not at all the case. Your chances of having the best hand might be as high as 90 percent or better, but still you should not necessarily bet. Take the following hand from seven-card stud: 9 Opponent With four jacks your chances of having the best hand are enormous, but in either first or second position you cannot Though you are not in last position in this example, I use it becouse it illustrates the principle so succinctly. You 202 Chapter Twenty-one possibly bet the hand on the end for the simple reason that your bet has absolutely no positive expectation. Since your four jacks are exposed for the world to see, your opponent will fold every hand he can have except four queens or a straight flush in hearts. With either of those hands, he will raise. So your bet has nothing to gain and everything to lose. This very obvious situation points toward the key distinction between play in the final round of betting and in earlier rounds. With one card to come, you would most certainly bet the four jacks to avoid giving your opponent a free card to outdraw you. Your bet forces him either to fold and thus give up any chance to outdraw you or to call and pay for that slim chance. However, when all the cards are out, betting to avoid giving a free card no longer applies. So if you now still decide to bet your hand, you no longer ask what your chances are of having the best hand but rather what the chances are of winning the last bet when you are called. This distinction may seem like hair-splitting, but it is most assuredly not. In fact, it is crucial to successful play — that is, to winning or saving extra bets — when you are heads-up on the end. To take a very common situation, let's say you have threeof-a-kind in seven-card stud, and you know your opponent is drawing to a flush and has nothing else. The odds against that opponent's making the flush on the last card are, we'll assume, 4- to-1, which means you are an 80 percent favorite to have the best hand. However, if

your opponent checks, you certainly should not bet because, as in the case of the four open jacks, a bet has no positive expectation. Your opponent will fold if he didn't make the flush, and he will call or possibly raise if he did. So even though you are an 80 percent favorite to have the best hand, you become an underdog if you bet and get called. To repeat, then, the decision to bet a legitimate hand for value on the end should be based not on your chances of having the best hand but on your chances of winning the last bet when you are called. When you bet for value on the end after your opponent has checked, you must figure your hand has better than a 50-50 Heads-Up On The End 203 chance of winning when you are called. In fact, you have to figure it has at least about a 55 percent chance of winning to compensate for those times when your opponent is planning to check-raise. With three-of-a-kind against a flush draw, you are certainly the favorite, but you are not the favorite if your opponent calls. Yet to show a profit on your last round bets, clearly you must be the favorite even when your opponent calls. At the same time, you should not carry this principle to such an extreme that you bet only when you have a lock, because then you will not win a lot of final bets you should win. To bet on the end after your opponent has checked, it is only necessary that you are the favorite when your opponent calls. Thus, if you figure you are only a 60 percent favorite when called, you should certainly bet even though you know there's a 40 percent chance your opponent will beat you if he calls. Your bet still has positive expectation. After ten such bets you will have won six and lost four on average for a net profit of two bets. Even if one of those four losses is a check-raise which you call, you still win six bets while losing five for a one-bet profit. To give a concrete example of such relatively close decisions, let's say you are playing draw poker, and your opponent stands pat and then checks to you when you draw one. Since your opponent stood pat, you are quite sure you are facing a straight, a flush, or a full house. Yet your opponent checked to you. You know he will call with just about any of his hands. Therefore, you should bet an ace-high straight or even a queen-high straight, because your opponent probably would have come out betting himself with a tiny flush or better. Chances are, then, he has a straight smaller than yours. It's true you may lose in the showdown, but you are enough of a favorite with a queen-high straight to warrant a bet. 204 Chapter Twenty-one Last Position Play After Your Opponent Has Bet Let us now consider your options in last position when your

opponent does not give you a free call but comes out betting. When he bets, you can either fold, call, or raise. Deciding whether to fold or call is relatively straightforward. The question is: Are your chances of winning the pot better than the odds you are getting from the pot, either because your hand is better than your opponent's or because your opponent is bluffing? If you think your chances are better, you call. If not, you fold. If you are thinking of raising after your opponent bets, you must ask the same question you would have asked before betting had your opponent checked: What are the chances of winning that extra bet when you are called? You should not raise unless you figure you are at least a 55 percent favorite, since you also face the possibility of a reraise. In fact, one way of looking at raising an opponent on the end without the nuts is that you are laying almost 2-to-l odds on that last bet, especially if your opponent is capable of bluffing on a reraise. When you raise and your opponent raises back, you usually lose two bets, but if he calls, you only gain one bet. Of course, this consideration does not apply against a player who will never bluff on a reraise. If such a player raises you back, you can just throw your hand away, knowing you are beat. Before raising on the end, you must also consider the overall ability of your opponent. Once he puts in an initial bet, an average player will call your raise almost every time. Therefore, you certainly should not try a bluff raise. However, you should raise with any hand you consider a reasonable favorite to win the last bet because you can be pretty sure of getting paid off. Tough players, on the other hand, will frequently come out betting, but they are capable of folding and not paying you off if you raise. Therefore, a bluff raise has some chance against them. However, when you are raising for value against tough players, you should Heads-Up On The End 205 have a better hand than you need against average players, because when the former are willing to call your raise and thus pay you off, they are likely to show down a strong hand. On close decisions you should not raise tough players on the end as often as you would weak or average players because you don't win that extra bet often enough to make the play profitable. Tough players either throw away a hand you would beat or call with a hand you might not be able to beat. Ironically, though, a raise may sometimes be correct against a world-class player when you have a hand that is only fairly good. The key factor is whether a raise will make your opponent throw away some hands that are better than yours. Let's say you have a hand that you figure has a 52 percent chance of winning if you call, but little chance

of winning if you raise and get called. Nevertheless, it would be correct to raise if you think your opponent will then throw away some hands that beat you. If your analysis is correct, a raise might lift you from a 52 percent favorite to a 65-70 percent favorite, and if the pot is big enough, that added 13-18 percent gives the raise positive expectation. Remember, though, that this play is worth considering only against superstars. Against average and good players — and also against superstars most of the time — the basic formula for raising on the end remains the same: Raise only if you are favored to win that extra bet when your opponent calls. To summarize play in last position after your opponent has bet, you have three options — fold, call, or raise. You should generally fold when the chances of winning are less than the pot odds you are getting. Thus, if your hand has only a 15 percent chance of winning and the pot is $80, you cannot call a $20 bet. However, your chances of winning do not have to be over 50 Percent to justify a call. All that's necessary is that the pot odds you're getting are better than your chances of winning in the showdown. Thus, if you think you have a 30 percent chance and the pot is $80,you would be right to call a $20 bet because the pot o dds you're getting are greater than the odds against yourshowing down the best hand. Even when you decide you can or cannot call 206 Chapter Twenty-one with your underdog hand, you have not necessarily eliminated the option of raising. Against a very, very good player, you might consider raising with some mediocre hands if a raise has greater expectation than a fold or a call — that is, if it will make your opponent throw away enough hands that would be better than yours. Anytime you are last and your opponent bets, you always have the three alternatives of folding, calling, or raising. The one that becomes right is the one that gives you the highest mathematical expectation. First Position Play When you are first to act with a legitimate hand, you have four options. One is to check with the intention of raising if your opponent bets. Another is to come out betting. The third is to check with the intention of calling if your opponent bets. And the fourth is to check and fold if your opponent bets. Check-Raising in First Position With very strong hands your options are to try a check-raise or to come out betting. The key factors in deciding whether to check-raise are: 1.The chances your opponent will bet if you check. 2.The chances your opponent will call your raise. The second factor is just as important as the first, because if there were no chance your opponent would call your raise, it would usually be wrong to check since you'd risk not winning even a single bet when your opponent checks behind you.

However, all but very tough players will generally call your raise after you have checked and they have put in an initial bet. They might grumble as they do it, but they'll do it. In limit games the decision to check-raise or come out betting can be determined by a precise formula. To simplify, we'll Heads-Up On The End 207 assume you know for sure you have the best hand. First, determine what percentage of times your opponent will call if you bet. That's one side of the equation. Next determine what percentage of times your opponent will bet if you check but then fold when you raise. Finally, determine what percentage of times your opponent will bet if you check and then call your raise. Now double this last percentage. If the sum of the last two percentages is greater than the first, it is correct to try a check-raise. This formula may sound overly complicated, but it really is not. Let's say you think there is a 70 percent chance your opponent will call if you bet. But you also think there is a 40 percent chance he will bet if you check and call your raise, thus rewarding you with a double bet; and perhaps there's another 10 percent chance he'll bet if you check but fold when you raise. Because you'll win two bets 40 percent of the times that you check, you double that figure to 80 and add the remaining 10 percent chance your opponent will bet and fold when you raise. That adds up to 90, and since 90 is greater than the 70 percent chance that your opponent will call your bet, it is right to checkraise. Another way of looking at the problem is in terms of expectation. Let's say you bet 100 times, and you check with the intention of raising 100 times. In the former case, you'll win 70 bets; in the latter you'll win 80 bets when your opponent bets and calls your raise and 10 more when he bets and folds, for a total of 0 bets. You win 20 bets more by check-raising, and so checkraising has greater expectation than betting out. Most players do not check-raise enough on the end. They'd rather go for the single bet in the hopes of getting called. However, it is worth taking a little chance of losing one bet if there is a good chance of gaining two bets. Since most players will automatically call a rais,e when you check-raise, you can simplify the above formula. In general, you should check with the intention of raising if you believe the chances of your opponent's betting when you check are at least half as good as the chance of hi s calling when you bet. Nor should you get discouraged if you 208 Chapter Twenty-one occasionally check and your opponent checks behind you. Checkraising is a long-run gamble like everything else in poker. If you know you should win two bets in a particular situation more than half as often as you

would win one bet, then you made the right play by checking even if it didn't happen to work. Sometimes you also gain an added benefit when a check-raise doesn't work. Since your opponents noticed you checked a good hand once, they may become a little timid about betting behind you on future hands, thus saving you some bets on second-best hands with which you were planning to call if they bet. Check-raising on the end works best against average-to-good players. You should try it less often against weak players and tough players. Weak players tend to call so much on the end when you bet that you have to be pretty certain they will bet for a check-raise to be profitable. If, for example, you are sure your opponent will call if you come out betting, you have to be over 50 percent sure he will bet if you check before you consider checkraising. Even 50 percent isn't good enough unless you are also sure your opponent will call when you raise (which, of course, a weak player will most likely do). Against tough players you would check-raise less often because tough players tend not to bet as many hands on the end as they call you with, and they frequently throw away their hands when you raise. Thus, the chances of winning a double bet with a check-raise decrease. There is one major time to deviate from the general check-raise formula, and that is when you think you can win three bets by betting, getting raised, and then reraising. A classic example of such a situation against an average player in seven-card stud occurs when you look like a straight on board but have a hidden full house, and your opponent may have a flush. You bet your apparent straight, your opponent raises with his flush, and you lift him out of his seat by reraising. Heads-Up On The End 209 Playing Fair-to-Good Hands in First Position as a Favorite In first position, with fair-to-good hands that are not strong enough to try a check-raise, you have three options — to bet, to check and call when your opponent bets, and to check and fold when your opponent bets. Which play you try in any given situation depends not so much upon the strength of your hand but upon your mathematical expectation for each play. And your expectation depends upon your ability to assess your opponent's style of play and what he is likely to do in a given situation. Some players bet with more hands than they call with; others call with more hands than they bet with; and still other, very tight players bet only when they are sure they have you beat. Thus, how you act in first position depends upon your knowledge of your opponent. Here are the general rules for each play. If your hand is worth a call or almost worth a call had you checked and your opponent bet, you should bet when your opponent is one who will call with more hands

than he will bet, a habit which is typical of the majority of players. 10 If your hand is worth a call, you should check and call when your opponent is one who will bet with more hands than he will call. As we shall see, this player is usually the type who may try to bluff after you have checked in first position. You should check and fold when you are not the favorite if called and when your opponent is one who will almost always bet only with a hand that beats yours. This player may call with a few hands worse than yours. However, since this type will only bet with a hand that clearly beats you, the bets you save by folding after he bets are greater than the few bets you might pick up by betting and getting called by his worse hands. The key factor in deciding whether to check-raise, bet, check and call, or check and fold in first position is, as we have seen, 10 See pages 213-214 for an exception to the rule. 210 Chapter Twenty-one which of the plays has the greatest positive expectation or the least negative expectation. Let's say that on a scale of 0 to 100 you have hand 80, a good hand but not a great hand. Your opponent could have anything from 0 to 100, with each hand equally likely. That would seem to make you a 4-to-1 favorite if you bet, but that's not at all the case. The question is, which hands will your opponent call with? If he will call only with hands 75 and upward, you are clearly an underdog if you bet — specifically a 4-to-1 underdog since you will lose to 20 of your opponent's hands and beat only five. We'll assume you know your opponent will call with hands 57 and upward. (We are, of course, being very hypothetical here since no player could know his opponent so precisely.) If your opponent will call with hands 57 and upward, that means that if you bet, you will win 23 times — when your opponent has hands 57-79 — and lose 20 times — when he has hands 81-100. Thus you are a 23-to-20 favorite when you bet. However, that does not mean the correct play is to bet. You still do not have enough information. You must also know what hands your opponent will bet if you check. Suppose your opponent will bet hands 62 and up if you check (which means you blow a bet if he has hands 57-61), but he will also bet with hands 0-10. That is, there are eleven hands your opponent will bluff with. Once again there are 20 hands you will lose to (hands 81- 100), but now, instead of 23, there are 29 hands you will beat — hands 0-10 and hands 62-79. Thus, if you check and call when your opponent bets, you are a 29-to-20 favorite to show down the best hand. Clearly it is better to play the last

round of betting as a 29-to-20 favorite than as a 23-to-20 favorite, and so the correct play here is to check and call. This is the point of the rule: Check and call when your opponent will bet with more hands than he will call. By checking against such an opponent, you increase your chances of winning one last bet. Suppose you are still a small favorite if you bet. Once again you have hand 80, and your new opponent will call with hands 57 and up. But this opponent is much more timid than the other, and Heads-Up On The End 211 you know he will bet only with hands 81 and upward. How should you play? It might at first seem correct to check and fold if your opponent bets, since any time he bets behind you he has you beat. However, when you check, you give up an even-money bet as a 23-to-20 favorite, which cannot be correct. That's more than the vigorish that keeps bookmakers in business. After making that bet 43 times, you will be ahead 3 units on average. Under no circumstances, then, can it be correct to check and fold if you are favored to win when your opponent calls you. As a 23-to-20 favorite, the correct play here is to bet. The only time it might be correct to check is when you're not sure whether you're the favorite and when you're also worried about a raise that you will have to call. Playing Fair-to-Good Hands in First Position as an Underdog In cases where you think you're the underdog if called, the decision to bet or check becomes even more ticklish. Let's say there's $60 in the pot in a $ 10-$20 game, and again you have hand 80. But this time you know your opponent will call only with hands 65 and up. Thus, you are a 20-to-15 underdog if your opponent calls. You also know that if you check, your opponent will bet with hands 70 and up. How should you play? As an underdog, you might think you should check. But what will you do if your opponent bets after you check? Since there's $60 in the pot plus your opponent's $20, you're getting $80-to- $20 or 4-to-1 odds from the pot, and we said your opponent will bet with hands 70-100. You have hand 80, and so you'll lose to 20 hands and beat 10 hands. Since you are getting 4-to-1 from the pot and are only a 2-to-l underdog, clearly you must call when your opponent bets. Look again at what happens when you bet. Your opponent will call with hands 65-100. By betting you've added five wins — when your opponent has hands 65-69 — to your possibilities. 212 Chapter Twenty-one Instead of going in as a 20-to-10 underdog, which you would be doing if you checked, you're going in as a 20-to-15 underdog since you'll still lose to 20 hands, but now you will beat 15 hands instead of 10. So the correct play is to

bet because betting here makes you less of an underdog than checking. Your hand is worth a call, and your opponent will call with more hands than he'll bet. (This play is something like splitting 8s in blackjack against the dealer's 10. You are still an underdog, but you are less of an underdog than if you had simply hit.) Suppose with $60 in the pot you again have hand 80, and your opponent will again call with hands 65 and up. But this opponent will bet only with hands 82 and up. How should you play? In the previous case you really didn't like your situation. You bet as a 20-to-15 underdog only because you would have had to call as a 20-to-10 underdog. But in the present case, in which you are still a 20-to-15 underdog if you bet, you don't have to worry about calling. Any time your opponent bets, you know he has you beat since he will only bet with hands 82 and up. You certainly don't want to bet as an underdog when you don't have to, so the correct play in this instance is to check and fold if your opponent bets. You blow a bet 15 times, when your opponent has hands 65-79 and checks behind you, but you save a bet 20 times, when he has hands 81-100. You save more bets than you sacrifice. Checking and folding has greater expectation than betting as a 20-to-15 underdog. A curious situation develops, though, when you are an underdog when called and your opponent will bet if you check with only a few hands you can beat. It would seem that the correct play is to check and fold if your opponent bets. However, it often works out that the play with the greatest expectation is to bet your own underdog hands even though, if you checked, you could not call when your opponent bet. Depending upon the size of the pot, this situation occurs when your opponent will call with many hands you can beat but will bet with only a few hands you can beat. Heads-Up On The End 213 Let's say there's $60 in the pot, and you have hand 80. You know your opponent will call with hands 65 and up (remember, we are being completely hypothetical here for the purposes of illustration), but he will bet only with hands 76 and up. Thus, if you check with hand 80 and your opponent bets, you will be a 20-to-4 or a 5-to-1 underdog. Since you're only getting $80- to-$20 or 4-to-1 odds from the pot, you cannot call. However, when you yourself bet, you add 11 wins to your possibilities — when your opponent has hands 65-75 — thus creating a situation where you are getting favorable odds from the pot. Here's how this situation works out mathematically. Remember that we know your opponent will call with hands 65 and up but he will bet only with hands 76 and up. All the hands are equally likely. Thus if you check

and fold when he bets then in 100 times you will win $60 76 times when he has hands 0-75) for a total of $4,560. However if you bet you will win $60 65 times and $80 15 times while losing $20 20 times. This works out to $4,700 which is $140 more than you would have won by checking and folding if your opponent bet. Consequently, even though as an underdog you would not call if your opponent bet on the end, it may sometimes be right for you to bet, depending upon the size of the pot and the number of second-best hands you think your opponent will call with. Finally, there are some unusual situations, when the pot is fairly large and your opponent is somewhat timid, where it may be correct to check and call even though your opponent would call you with more hands than he would bet himself. This is the exception we referred to earlier to the general rule that you should bet when your opponent will call with more hands than he would bet. Suppose you have hand 80. You're playing in a $10-$20 game, and there's $200 in the pot. You know your opponent will call only with hands 75 and up; so you're a 4-to-1 underdog if you bet But you'd be getting at least 10-to-l from the pot, so a bet could be right. However, you also know your opponent is afraid tо bet for value on many handsthat beat you — say, hands 81 -90 . 214 Chapter Twenty-one This opponent will bet hands 91-100 and he may occasionally bluff— say, with hands 1-4. Even though this opponent will bet with fewer hands than he would call with, and even though the pot odds you're getting make your hand worth a call, it nevertheless becomes correct to check in this instance. The reason is that ten times — in the cases where your opponent has hands 81-90 — you save $20 when he checks the best hand behind you. Furthermore, when your opponent does bet and you call, you're only a 10-to-4 or 2!/2-to-l underdog instead of the 20-to-5 or 4- to-1 underdog you would be if you came out betting. You've also eliminated the possibility of getting raised in a situation where, given the size of the pot, you would almost have to call. It becomes correct to check and call, though you know your opponent would call with more hands than he would bet, if when you are an underdog you think your opponent will check some better hands behind you and if you fear a raise. Remember, though, that the last two situations we have described are unusual. The general rules still apply the majority of the time. If your hand is worth a call, you should bet when your opponent will call with more hands than he will bet, and you should check and call when your opponent will bet with more hands than he will check. In other words, you should make the play that

gives you the greatest number of wins and the smallest number of losses. First Position Play in Practice Let us now see how first-position play heads-up on the end works in practice. Suppose in draw poker you draw three cards in first position and make aces up. Your opponent draws one card. He may have two pair, or he may be drawing to a straight or a flush. You feel that this type of player will call with two pair if you bet but will bet them for value if you check. How should you play? There's no mystery here. Clearly you should check and call. By checking and calling, you may save a bet in one situation and Heads-Up On The End 215 gain a bet in another. With two pair, your opponent will call if you bet and bet if you check. So you win either way. If your opponent was drawing to a flush or a straight and makes it, he will of course bet if you check, but he will call, or probably raise, if you bet — which will cost you an extra bet if you call the raise. With a busted hand, your opponent will not call if you bet, so you gain nothing by betting. However, your opponent might bet on a bluff if you check. In this single instance you win an extra bet by checking and calling. So checking and calling has greater expectation than betting. And to repeat: The object of poker is not to win pots but to win money; it is with these extra bets won or saved that you win money. Here is another draw poker situation. You draw one card to two small pair, and your opponent draws three. You don't improve. You know your opponent suspects you were drawing to a flush or a straight, and you also know this player's a pay station, the type who will call "to keep you honest." How should you play? You should bet. Assuming your opponent was drawing three to a big pair, you're about a 71 percent favorite to have the best hand. Any time you're even a small favorite against someone you know is going to call virtually every time, you should bet. In this case you're wagering even money as a 71 percent or 5-to-2 favorite. Clearly that's a wager with positive expectation even though you expect to lose 29 percent of the time. Suppose in hold 'em you have (Notice that there is no flush possibility.) You are first to act. How should you play? You should probably come out betting. If you are up against something like A, 10 or K,10 or J,10, you lose either way. If you check, your opponent will surely bet, and you will call. If your opponent has Q, 10, you may lose a double bet by betting out since your opponent will raise. On the other hand, if your opponent has hands like 10,8 or 10,7 or 10,6, you win either way; if you check, your opponent will most

likely bet. However, two very possible hands your opponent might have are A,Q and K,Q which he may very well not bet if you check but with which he will probably call if you bet. Since you are likely to gain a bet more frequently than you lose one (when your opponent raises), betting has greater expectation than checking and calling. Put in terms of the rules given earlier, in this situation your opponent will call with more hands than he will bet. A final set of examples from draw lowball should demonstrate how your play on the end in first position varies directly in terms of your opponent. Both players in the pot draw one card, and you are first to act: Heads-Up On The End 217 You are up against a player who doesn't bluff but is always afraid everyone else does. How should you act? You should bet. Your opponent will probably call with a queen-low or better, while only a seven-low or better will beat you. Therefore your opponent will call with many hands that you will beat and a relative few that will beat you. On the other hand, if you checked, your opponent would not bet most of those losing hands. Thus, you stand to win more often by betting than by checking. Suppose you have the same hand in draw lowball against an aggressive, tough player, and you're first. How should you play? In this case, you should check and call because your opponent is likely to bet more hands than he calls with. Besides beating your opponent's rough 8s, you also snap off his bluffs, which you could not do if you came out betting. Ordinarily, if you bet, your opponent would give up the idea of bluffing. In general, a player who bets with more hands than he calls with is the type of player who not only bets for value but also bluffs perhaps more often than is correct. Thus, when you check, your opponent's bluffing hands are added to those he bets for value. Now suppose instead of a perfect eight-low, you have the following hand: You You Once again you're up against that player who never bluffs but worries that everyone else does. You're first. How should you play? Here you should check and fold if your opponent bets. Since your hand beats only queen-,Jack-, and tenlows(the losing hands 216 Chapter Twenty-one and the board at the end is 218 Chapter Twenty-one with which your opponent would call), it is no longer worth a bet for value, because you get beat with his nine-lows and better. And since this opponent never bets on a bluff, you should fold in the face of a bet. The odds that you are beat are overwhelming. Against the aggressive player, you would also check, but you would call a bet since there are many hands this opponent might be betting that you can beat. In other words, a call against this type of player would have positive expectation. First Position Play in Terms of

the Strength of Your Hand We'll wrap up play in first position by summarizing it according to the strength of your hand. If your hand is a cinch or a near cinch, you have two options. One is to bet, and one is to check-raise. You would decide which to do according to the check-raise formula presented earlier. However, if you are sure you have the best hand but suspect your opponent will raise if you bet, you should bet out in an attempt to win three bets when your opponent raises and you reraise. If your hand figures to be a favorite when called but is not good enough to check-raise, you have two options — to bet or to check and then call. Basically you bet if your opponent will call with more hands than he'll bet with and you check and call if he'll bet with more hands than he'll call with. If your hand is an underdog when called, you have three options. One is to bet, a second is to check and call, and the third is to check and fold. (A bluff check-raise is a remote possibility against very tough players who are capable of very tough folds.) You should check and call if your opponent will bet more hands than he will call with, including some hands you can beat. You should also check and call when your opponent will check many hands that will beat you but might come out bluffing with some hands you can beat. And you should come out betting if you have Heads-Up On The End 219 a calling hand but your opponent will call with more hands than he will bet. Finally, if you have virtually no chance of winning if you check and your opponent bets and you are an underdog if you bet and he calls, then the proper play is to check and fold if he bets. Summary The concepts in this long chapter are important and slippery enough to warrant a final framing in an outline summary. The essence of each play is a judgment of its expectation. I. Last Position Play A. If you are second to act when all the cards are out and your opponent bets: 1.Call if your hand is not worth a raise but has a better chance of winning than the pot odds you are getting. Your chances of winning are the sum of the chancesthat your opponent is bluffing, plus the chances that your hand can beat his legitimate hand. 2.Raise if your opponent will still be the underdog after calling your raise. Raise also as a bluff if you think it will work often enough to have positive expectation. Also consider raising with what appears to be a calling hand if your opponent is capable of throwing away a better hand than yours for one more bet. B. If you are second to act when all the cards are out and your opponent checks: 1.Bluff if you think it will work often enough, remembering that a bluff

does not tend to work as often in second position as it might in first position. 2.Bet your hand for value if you are a favorite to have the best hand, even when your opponent calls your bet. Don't bet in close situations to avoid a check-raise. 220 Chapter Twenty-one II. First Position Play A. If you are first to act when all the cards are out and have a very strong hand: 1.Try to check-raise if your opponent will bet and call your raise more than half as often as he will call you when you bet. 2.Come out betting if you don't think a check-raise will work often enough to be profitable or if you think you can win three bets when your opponent raises and you reraise. B. If you are first to act and have a bad hand: 1.Bluff if you can get away with it often enough for the play to have positive expectation. 2.Otherwise check and fold if your opponent bets. С If you are first to act and have a hand that is a favorite to win if called but not strong enough for you to try a check-raise: 1.Bet if your opponent will call with more hands than he will bet with if you check. 2.Check and call if your opponent will bet with more hands than he will call with. 3.Never check and fold. D. If you are first to act and have a hand that is a small underdog to win when your bet is called: 1.Bet if your opponent will call with more hands than he will bet, aslong assome of the hands he would have bet, had you checked, would be worse than yours. Check and call if you think your opponent will check behind you with a significant number of hands better than yours but might still bluff with some hands you can beat. 2.Check and call if your opponent will bet with more hands than he will call with, as long as your pot odds make it worth calling when he does bet. 3.Check and fold if your opponent will almost never bet a hand worse than yours. Chapter Twenty-two Reading Hands The ability to read hands may be the most important weapon a poker player can have. As the Fundamental Theorem of Poker suggests, the key mistake in poker is to play your hand differently from the way you would play it if you knew what your opponent had. The more often you play your hand correctly on the basis of what your opponent has the less you give up and the more you gain. If you somehow knew what your opponent had every time, you almost couldn't lose because you would always play correctly. It follows, then, that the better you are at reading your opponents' hands, the closer you come to perfect play, and the closer you come to perfect play, the less you lose and the more you win. Reading hands is both an art and a science. It is an art because you

must know your opponents. Before you can technically analyze what your opponents might have, you must have played with them for a considerable length of time, seen how they play their hands against you, and most importantly, watched them play hands in which you are not involved. Even when you are not in a hand, you should not relax your concentration. You want to discover how your opponents tend to play the various hands they might have. Will a particular opponent raise with strong hands in early position, or will he slowplay? Will he raise on a draw? How does he play his big hands from one round of betting to the next? How often does he bluff? The more you know about an opponent's general playing habits, the less difficulty you will have reading what he might be holding in a specific situation. Ironically, it is not as hard to read good players as it is to read a bunch of incompetents. When a good player makes a play, there is a sensible reason for it, and your job is to find the reason and Put that player on a hand. But there is no pattern to the play of a 221 222 Chapter Twenty-two weak player, and so you must do a great deal of tentative guesswork to put him on a hand. Nevertheless, by playing solidly against weak, unpredictable players, you have to win eventually. Sooner or later a sound, logical poker player must beat someone playing by the seat of his pants. The latter may get lucky for a while, catching the inside straights he draws to, winning with two small pair when you raised with aces on third street, but percentages are bound to catch up with him. Many good players get upset when a sucker draws out on them. While it's never pleasant to lose a pot you were favored to win, you should nevertheless welcome these beats. Congratulate such players on hanging in there to make their hands. Encourage them so they play even more sloppily. It shouldn't be long before you have their money. The more you play against average-to-good players, the easier it becomes to read your opponents' hands because they tend to check, bet, and raise for logical reasons and with a certain consistency to their play. However, as your opponents get tougher and tougher, your ability to read hands starts to fall off because tough players disguise their hands and they are sometimes intentionally inconsistent. They make tricky, ambiguous plays like semi-bluffing, like raising with the second-best hand, like slowplaying right to the end and then check-raising you. They may even play a hand as it would normally be played, which can sometimes be the most deceptive play of all. In a word, they do all the sorts of things we have been discussing in this book. They are trying as hard to deceive you about what they have as you are trying to discover what they have. And of course, you are presumably playing your hands equally hard against them,

even as you are trying to read their hands. Reading Hands 223 Reading Hands on the Basis of Your Opponents' Play and Exposed Cards There are two universally applicable techniques for reading hands in all poker games and one more for open-handed games like seven-card stud, razz, and hold 'em. Most commonly you analyze the meaning of an opponent's check, bet, or raise, and in open-handed games you look at his exposed cards and try to judge from them what his entire hand might be. You then combine the plays he has made throughout the hand with his exposed cards and come to a determination about his most likely hand. Here is a simple problem in reading hands that should make this point clear. The game is seven-card stud, and your opponents are decent players: Player A Player В You Player A with the pair of aces showing bets; Player В with the pair of kings showing calls; and Player С with the pair of queens showing calls. There are no raises. You are last to act. How should you play your three 7s? If you combine what you see on board with what your opponents have done, there should be no doubt in your mind that you must fold; your three 7s have no chance whatsoever. The crucial factor is that the pair of queens overcalled. Player A may be betting with aces alone. But when Player В calls him, Player В must have at least kings up. Being a decent player, Player С knows this. Therefore, С could not call without having kings up beat. What are C's possible hands? Well, С cannot have aces and queens or kings and queens because there's a third ace and a third king out, making it impossible for С to have two of either. So, he must have three queens or better, and while your three 7s might beat the first two hands, they cannot beat C's three queens or better. Therefore, you fold. Here is a good example of this kind of hand reading, which to my chagrin cost me half a pot. I was playing five-card stud high-low split with a replace on the end. With an ace and an 8 Reading Hands 225 showing, I called the maximum raises on third street even though two other players each had a 6 and a 5 showing. There was another player in the pot with an obvious pair of kings. When it got down to the last card, I had A,8,6,3 showing. One 6,5 had folded, but despite the strength of my board, the other stayed with a ragged 6,5,10,Q showing. And of course, the pair of kings stayed. Now I was betting and raising, hoping the Q, 10 low would get out. But that player read me too well. He didn't even take the opportunity to replace one of his cards. What I was trying to do was win the whole pot, the high and the low, from the two kings, but the Q, 10 low was clever enough to figure

out my hand. He said to himself, "Sklansky is representing an 8 low, but could he have an 8 low? No, he couldn't. Why? Because he would never have called all those raises on third street with three cards to an 8 low when there were two other players in the pot who looked as if they had three cards to a 6 low. Therefore, he must have another ace in the hole." He was, of course, absolutely right. I won the high with my two aces, beating the two kings, but the Q,10 low was rewarded for his accurate reading with the low half of the pot (which I would have won against the two kings with my two aces counting also as a low pair). The player with the Q,10 low considered the way I played the hand not just at the end, but from the beginning, and he combined my play with the cards showing to arrive at the correct conclusion about what I was holding. He also analyzed the order in which I received my upcards. He knew I started with A,8 and then caught the 6 and the 3. If he had not known that — if, for example, he had not been sure whether I started with A,8 or A,6 - it would have been impossible for him to conclude with such certainty that I had a pair of aces. It is in this way that you use logic to read hands. You interpret your opponents' plays on each round, and in open-handed games you note the cardsthey catch on each round, Paying close attention to the order in which they catch them. You then put these two pieces of evidence together — the plays and Player С 224 Chapter Twenty-two 226 Chapter Twenty-two the upcards — to draw a conclusion about an opponent's most likely hand. In that high-low split hand, the Q,10 low was able to put me on a specific hand quite early. However, it is generally a mistake to put someone on a specific hand early and then stick to your initial conclusion no matter how things develop. A player who raises on third street in seven-card stud with a king showing may have two kings, but he may also have a small pair in the hole with the king kicker or a three-flush or a J,Q,K or a number of other hands as well. Drawing a narrow, irreversible conclusion early can lead to costly mistakes later, either because you fold with the best hand or because you stay in as a big underdog. What you do in a game like seven-card stud or hold 'em or razz is to put an opponent on a variety of hands at the start of play, and as the hand continues, you eliminate some of those hands based on his later play and on the cards he catches. Through this process of elimination, you should have a good idea of what that opponent has (or is drawing to.) when the last card is dealt. Suppose,

for instance, in seven-card stud a player starts with a queen of spades, then catches the deuce of spades, then the 7 of spades, then the 5 of hearts, and he's betting all the way. You have a pair of 10s which does not improve. Your opponent bets on the end, and clearly you can beat only a bluff. The question is — might your opponent be bluffing? With something like a fourflush and a small pair, he would probably have played the hand exactly the same way — semi-bluffing right to the end, assuming you didn't catch any dangerous-looking cards. Therefore, while your opponent may, in fact, have a pair of queens or queens up, there's also a chance he has a busted hand. Very possibly you should call his final bet, given the pot odds you're getting — but realizing at the same time that he may indeed have been semibluffing yet still caught his hand on the last card. Suppose, on the other hand, your seven-stud opponent started with that same queen of spades and you with that same pair of 10s. Once again your opponent is betting all the way. But this time he catches the 7 of diamonds, then the 4 of clubs, then the Reading Hands 227 jack of hearts. Now when he bets on the end, you should almost certainly fold your two unimproved 10s because when he caught the and but continued betting, you had to eliminate the flush draw as one of his possible hands. Therefore, he is almost certainly betting on the end for value with at least a pair of queens ___more likely two pair. Ironically, it can sometimes occur that because your opponent's hand looks less dangerous on board it is more of a threat to have you beat when your opponent bets on the end, because nothing showing suggests he might have been semi-bluffing as the hand progressed. At the end of a hand it becomes especially crucial to have a good idea of what your opponent has. The more accurately you can read hands on the end, the better you can decide whether you have, for example, a 20 percent chance of having your opponent beat or a 60 percent chance or whatever. You use your ability to read hands to come up with these percentages and then decide how to play your own hand. In practice, most players don't arrive at exact figures like 20 percent or 60 percent, but at the very least they try to decide whether their opponent has a bad hand, a mediocre hand, a good hand, or a great hand. Let's say your opponent bets on the end. Usually when a person bets, it represents either a bluff, a good hand, or a great hand, but not a mediocre hand. If your opponent had a mediocre hand, he would probably check. If you have only a mediocre hand yourself, you have to decide what the chances are that your opponent is bluffing and whether those chances warrant a call in relation to

the pot odds. If you have a very good hand, you must decide whether your opponent has a good hand or a great hand. If you think the chances are high he has only a good hand, you would raise. But if you think he may very well have a great hand, you would just call. If you are virtually certain he has a great hand, you might even fold your very good hand, depending upon the size of the pot. You ask yourself two questions: What does it look like my opponent is representing? Could he have the hand he's representing and have played it the way he did? Once aw your conclusions about your opponent's hand on the 228 Chapter Twenty-two basis of his play and his upcards, you decide on the basis of your own holding and the size of the pot whether to bet, check, call, raise, or whatever. We have seen that in open-handed games one way to read hands is to start by considering a variety of possible hands an opponent might have and then eliminate some of those possibilities as the hand develops. A second or, more accurately, a complementary way to read hands is to work backward. It is that sort of thing my high-low split opponent did. If, for instance, the last card in hold 'em is a deuce and an opponent who'd been quiet from the start suddenly bets, you think back on his play in earlier rounds. If there was betting on the flop or on fourth street, that player would not have called with nothing but two 2s in the hole. So he is betting now either as a bluff or because he has something other than three 2s. If, on the other hand, everyone checked on the flop and on fourth street, it's very possible the player caught three 2s on the end. Every step of the way you must work forward and backward to zero in on your opponent's most likely hand. Using Mathematics to Read Hands When you can't actually put a person on a hand but have reduced his possible hands to a limited number, you try to use mathematics to determine the chances of his having certain hands rather than others. Then you decide what kind of hand you must have to continue playing. Using mathematics is particularly important in draw poker, where your main clue to what an opponent might have is what you know about his opening, calling, and raising requirements. If, for example, you know an opponent will raise you with three 2s or better before the draw, you can resort to mathematics to determine what hand is favored to have him beat. It works out to something like three queens. Obviously, then, if you have three 3s, it's not worth calling that opponent's raise on the chance that he has specifically three 2s. But if you have something like three 5s or three 6s, the pot odds make it correct to call because now not Reading Hands 229 only might you

draw out on a better hand by making a full house or four-of-a-kind, but there are a few hands your opponent could have which you already have beat. Sometimes you can use a mathematical procedure based on Bayes' Theorem to determine the chances an opponent has one or another hand. After deciding upon the kinds of hands your opponent would be betting in a particular situation, you determine the probability of his holding each of those hands. Then you compare those probabilities. If, for instance, in draw poker you know a particular player will open either with three-of-a-kind or two pair but will not open with one pair and will check as a slowplay with a pat hand, then it is 5-to-2 against that player's having trips when he does open. Why is this so? On average, according to draw poker distribution, a player will be dealt two pair 5 percent of the time and trips 2 percent of the time. When you compare these two percentages, you arrive at a ratio of 5-to-2. Therefore, the player is a 5-to-2 favorite to have two pair. Let's say in hold 'em an opponent puts in a big raise before the flop, and you read him for the type of player who will raise only with two aces, two kings, or ace, king. The probability that a player gets two aces on the first two cards is 0.45 percent. The probability of his getting two kings is also 0.45 percent. So he will get two aces or two kings 0.9 percent of the time on average. The probability of his getting an ace, king is 1.2 percent. By comparing these two probabilities — 1.2 percent and .9 percent— you deduce that the chances are 4-to-3 in favor of your opponent's having ace, king rather than two aces or two kings. Of course, knowing your opponent is a 4-to-3 favorite to have ace, king is not enough by itself to justify calling his raise with, say, two queens. You are a small favorite if he does have ace, king, but you're a big underdog if he has two aces or two kings. Nevertheless, the more you know about the chances of an opponent's having one hand rather than another when he bets or raises, the easier it is for you to decide whether to fold, call, or raise. Earlier in this chapter we talked about a player in seven-card stud raising on third street with a king showing, and we pointed 230 Chapter Twenty-two out that he might have two kings, but he might also have a small pair or a three-flush or something like J,Q,K. To simplify, we'll assume you know this particular player will raise only with a pair of kings or a three-flush. You have a pair of queens. The probability is about 11 percent before the raise that your opponent has another king in the hole to make a pair of kings, and it's about 5 percent that he has three of the same suit. This is simply the mathematical probability

based on card distribution and has nothing to do with any action the player takes. Therefore, when your opponent raises, which now limits his possible hands on the basis of what you know about him to either two kings or a threeflush, he is an ll-to-5 favorite to have the two kings, and you would probably fold your two queens. However, another king showing somewhere on the table radically reduces the mathematical probability of your opponent's having two kings before he raises because there are only two kings instead of three among the unseen cards. The probability of your opponent's having two kings is cut to about ТА percent. A raise now makes it about 40 percent that your opponent has a three-flush rather than two kings. Depending upon your position, your queens may be strong enough to justify a call. In this case you read your opponent's hand not just on the basis of what you know about him, the action he takes, and the exposed card you see, but also on the basis of a mathematical comparison of his possible hands. It does not, of course, take a mathematical genius to realize that another king on the table decreases the chances of an opponent's having two kings before he raises, so using math to read hands does not always require the precise knowledge of card-distribution probabilities presented here. Furthermore, you need to complement mathematical conclusions with what you know about a player. For example, in a relatively small-ante game, some players might not raise with two kings when there is no other king showing in hopes of making a big hand, but they will raise with two kings when there is a king showing to try to win the pot right there. They decide to go for the pot right away precisely because of the presence of that other king, which Reading Hands 231 reducestheir chances of improving. When you are up against such players, the presence of another king might actually increase the probability of their having two kings after they raise — not on the basis of mathematics but on the basis of the action they have taken and what you know about the way they play. Reading Handsin Multi-Way Pots Another factor in reading hands and deciding how to play your own is the number of players in the pot. Any time someone bets and someone else calls, you are in a more precarious position than when it is just up to you to call. In general, a caller ahead of you makes it necessary for you to tighten up significantly because you no longer have the extra equity that the bettor may be bluffing. Whether he is bluffing or not, the second player must have something to call. Therefore, when your hand is barely worth a call in a heads-up situation because of the extra chance of catching a bluff, it is not worth an overcall when someone else has called ahead of you. Here is an example of such a situation that came up in

a small ante razz game I was playing. On the first three cards I had an: A decent hand but not a great one. The high card brought it in, and a player called with a 5 showing. I was prepared to call or possibly raise. However, a player ahead of me, who was playing tight, raised with a 4 showing. Had the first player with the 5 showing not called the initial bet, I would have called the raiser with my 8,5,2 because, though the raiser was playing tight, there would have been a chance he was semi-bluffing. But since the raiser raised another low card that had already called, it was 232 Chapter Twenty-two almost a certainty he had a better hand than I did; and there was also the probability the first caller had a good hand. Therefore, given the small ante, my hand was no longer worth a call. The same sort of thinking must be employed when deciding whether to call a raise cold. With very few exceptions, you need a better hand to call a raise cold than you would need to raise yourself. The simple logic of this principle can be set forth through an example from draw poker. Let's say in the game you are playing you decide to raise before the draw with aces up or better. You look at your hand and find you have three 2s. You're prepared to raise, but all of a sudden the player to your right, who will also raise with aces up or better, puts in a raise. Now instead of raising, you can't even call. You must fold because the chances are too good that the raiser has you beat. This principle applies to any game. When you have a minimum or near-minimum raising hand and the player to your right, who has the same standards as yours, raises ahead of you, then his hand is probably better than yours, and your correct play is to fold. Summary Reading hands well is a powerful poker weapon because it allows you to play correctly more often, according to the Fundamental Theorem of Poker. The better you read your opponents' hands, the less likely you are to play your hand differently from the way you would play it if you could actually see what your opponents had. Weak players are difficult to read because there is little pattern to their play. Good players are easier because there is logic to their play. However, very tough players are more difficult to read because of their ability to disguise their hands. One way to read hands is to put opponents on a variety of possible hands and eliminate some of them on the basis of their play and the cards they catch from one round to the next, keeping track of the order in which they catch their cards. A second, Reading Hands 233 complementary way is to work backward, looking at an opponent's later plays in terms of how he played his hand in earlier rounds. You can

also read hands by using mathematics, by comparing possible hands on the basis of Bayes' Theorem. If you know an opponent will bet only certain hands, you form a ratio based on the probability of that opponent being dealt each of those hands. To simplify, you can divide his possible hands between those you can beat and those you can't beat. The ratio tells you which of the hands he is favored to have. Finally, when reading hands you must consider the number of people in the pot. When there is a caller ahead of you, the caller and the original bettor cannot both be bluffing, so you must play on the assumption that you are up against at least one legitimate hand. When there is a raiser ahead of you with the same standards as yours, you should have more than your minimum raising hand to call that raiser because you have to figure your minimal raising hand is beat. Throughout this chapter it has been implicitly suggested that a significant aspect of reading hands is knowing your opponents. Which leads us to the next chapter, "The Psychology of Poker." Chapter Twenty-three The Psychology of Poker Psychological Plays The late John Crawford was one of the great game players and gamblers of all time. His best games were bridge and backgammon, but he was also an excellent gin rummy player. He and the legendary games expert Oswald Jacoby used to play gin rummy against each other constantly. They were close in ability, but there was no question Crawford had the psychological edge. He would needle Jacoby, taunt him, even laugh at his play, until Jacoby sometimes became so enraged he could hardly see the cardsin front of him. Along the same lines, Los Angeles backgammon pro Gaby Horowitz is well-known for his glib, sometimes disparaging talk during a game, which is calculated to put his opponents on tilt. Seven-card stud poker pro Danny Robinson is equally famous for his nonstop patter during a hand, which is used to distract and confuse his opponents. These are all psychological ploys, and there are an endless number of such ploys. Some people approve of them. Some don't. While they have a definite place in poker, they are not what we mean by the psychology of poker. They are psychological devices that apply to all games or, for that matter, to all forms of competition. Chess champion Bobby Fischer used them in his famous match against Soviet master Boris Spassky. Managers like Earl Weaver and Billy Martin use them on the baseball diamond. And the late Soviet Premier Nikita Khrushchev was notorious for using them as tactics of cold war diplomacy. 235 236 Chapter Twenty-three The Thought Processes of Poker What we mean by the psychology of poker is getting into your opponents' heads, analyzing how they think, figuring out what they think you think, and even determining what they think you think they think. In this sense the psychology of poker is an extension of reading opponents' hands, and it is also an extension

of using deception in the way you play your own hand. Recently, while I was working on this book, a friend ran up to me and said, "I made a great play in seven-stud last night at the Castaways." We had recently been talking about using deception by betting a second-best hand to make an opponent think you are stronger than you really are in hopes he will fold if you improve. "Low card brought it in, and I called with a pair of kings," my friend began. "One of the kings was showing. Behind me a guy who was steaming and almost all-in called with an ace showing. He could have anything. Another guy, A.D., the best player in the game, raised with an ace showing. We all called. "On fourth street I catch a 5.1 have a king, 5 showing — still only a pair of kings. The guy who's steaming has ace, 10, and he bets. Maybe he has a small pair. The good player calls. Now I know for sure the good player has aces because he would never call another ace unless he had aces himself, especially with me sitting behind him with, maybe, two kings. He's played with me a lot, and he knows how I play." "So you folded your pair of kings." "No, I raised!" "That's pretty dangerous in that spot," I said. "Well, I knew A.D. had aces," My friend continued, "and I knew he knew I knew he had aces. So when I raise, he has to figure that since I know he has aces, I must have made kings up. The guy who's steaming calls, and A.D. reluctantly calls. Then I get lucky. I make an open pair of 5s on fifth street, and I bet out. The guy who's steaming goes all-in, but A.D. shakes his head and folds his two aces because now he's worried I've made a full house — 5s full of kings. I end up winning the hand with kings The Psychology of Poker 237 and 5s against a pair of 10s. A.D. grumbled afterward that he's the one who should have been raising." My friend did get lucky when he paired the 5s. However, in claying the hand he demonstrated the kind of thought processes that are the principal subject of this chapter. He went three steps beyond what he saw on the board. First, he thought about what his opponents might have. He tentatively put the steamer on a small pair, and with more assurance he put A.D. on a pair of aces. Then he went one step further. He thought about what A.D. thought he had — namely, a pair of kings. Then he went a step beyond that. He thought about what A.D. thought he thought A.D. had — and he knew A.D. knew that he thought A.D. had two aces. It was only after reaching this third level that he decided to raise with a pair of kings to make A.D. think he had kings up. Of course, it was also

important that A.D. was a good enough player to think on a second and third level himself. Otherwise the play would make no sense. Just as you can't put a weak player on a hand, you can't put him on a thought either. A weak player might reraise with two aces, without analyzing the possibility that the other man might have kings up. Very sophisticated poker play can go considerably beyond the third level. An instance of such play came up at the Sahara in Las Vegas in a tough seven-card stud game. One player had: The pair of 6s bet on the end; the A,K raised with aces and kings; and the pair of 6s called with 6s up. On the surface it may seem as if the 6s up made a sucker play in betting, that the aces and kings took a big chance in raising a possible flush or trips, and that the 6s up made another sucker play in calling the raise. In a typical game, the two small pair would no doubt check on the end, and the aces and kings might very well check behind him to avoid a check-raise. However, the thinking of the two players in this game was much more complicated. First, the was betting all the way; that player knew, therefore, that his opponent put him on a four-flush. So with two small pair he bet for value on the end because he knew his opponent thought he had a four-flush, and he figured the opponent would call with one pair to snap off a bluff. The A,K took it a step further. He thought the pair of 6s might in fact be betting two pair for value because he knew the man with the two 6s thought he put him on a four-flush and that therefore the man with two 6s would bet two pair to get a call from one pair. So the A,K raised for value, thinking his opponent might think he was raising with only one pair. The man with the 6s up was hoping exactly that, and given the size of the pot, he felt his hand had enough of a chance to justify calling the raise. If the pair of 6s' first two up-cards had not been the same suit, the aces and kings would never have considered raising the bet on the end. At best, he would only have had a crying call because with two small pair the other player would probably have checked since he couldn't represent a flush draw. But with those diamonds showing each opponent was trying to outwit the other, and the aces and kings ended up getting the The Psychology of Poker 239 best of the situation. The 6s up didn't reraise, of course, representing a flush, because he knew that at that point the pot was so large his opponent would certainly call with something like aces up. At the expert level of poker, the dialectic of trying to outwit your opponent can sometimes extend to so many

levels that you must finally abandon psychology altogether and rely on game theory. It is precisely when judgment fails that game theory becomes so useful. However, in ordinary play against good players, you should think at least up to the third level. First, think about what your opponent has. Second, think about what your opponent thinks you have. And third, think about what your opponent thinks you think he has. Only when you are playing against weak players, who might not bother to think about what you have and who almost certainly don't think about what you think they have, does it not necessarily pay to go through such thought processes. Against all others it is crucial to successful play, especially when deception is a big part of the game. Calling on the Basis of What Your Opponent Thinks There is a very important principle based on thinking about what your opponent thinks you have, and it is this: When an opponent bets in a situation where he is sure you are going to call, he is not bluffing. This point is obvious, yet many players overlook it. What it means is if you create the impression — by the way you have played your hand, by the look of your board, by the action you have put in the pot, or even by artificial means — that you are going to call a bet, an opponent who bets is betting value. He figures to have you beat because he knows you are going to call. Therefore, you should fold if he bets unless your hand warrants a call on the value of the hand. You should certainly fold a mediocre hand that can beat only a bluff; clearly 238 Chapter Twenty-three Another had: 240 Chapter Twenty-three no one but an idiot would bluff when he is sure he's going to get called. A prime example of such a situation arises when you bet on the end and a player raises you. It is very rare to find an opponent who is capable of raising on the end as a bluff. It is even rarer to find an opponent who would raise on a bluff when you have been betting all the way and have, therefore, given every indication of paying off a raise. So against all but very tough players capable of such a bluff raise, you should fold a routine hand because your opponent wouldn't raise without a good hand. Similarly, if you raise on the end and your opponent reraises, you should usually fold unless your hand can beat some of the legitimate hands with which he might be reraising. 11 In sum, when deciding whether to call a bet or a raise, it is important to think about what your opponent thinks you're going to do. An opponent who is sure you're going to call will not be bluffing when he bets or raises. A corollary to this principle is if your opponent bets when there appears to be a good chance you will fold, that opponent may

very well be bluffing. What this means in practice is that if your opponent bets in a situation where he thinks he might be able to get away with a bluff, you have to give more consideration to calling him even with a mediocre hand. Astute readers will have noticed that this principle and corollary are the bases of stopping and inducing bluffs, which were discussed in Chapter Twenty. When you show strength, especially more strength than you really have, to stop a bluff, you must be prepared to fold when your opponent bets into you because that opponent is expecting you to call; therefore he has a hand. Conversely, when you have shown more weakness than you really have, you must automatically call a player who bets on the end because you have induced a bluff: That player may be betting because he thinks you will fold. 11 These suggestions violate the precepts of Game Theory but they are valid for all but the wildest or toughest games. The Psychology of Poker 241 Betting on the Basis of What Your Opponent Thinks In deciding whether to bet, it is equally important to think about what your opponent thinks you have. If you know your opponent suspects you have a strong hand, you would tend to bluff more with a weak hand because the chances are good your opponent will fold. However, you should not bet a fair hand for value in this situation. Your opponent's fear of your strong hand will probably make him fold all the hands he might have except those which have you beat. Conversely, if you know your opponent suspects you are weak, you should not try to bluff because you'll get caught, but you should bet your fair handsfor value because he'll pay you off. Psychology and Future Impressions Varying your play and making an "incorrect" play intentionally are also part of the psychology of poker because you are trying to affect the thinking of your opponents for future hands. To take a simple example, you might make three-of-a-kind on fourth street in seven-card stud with two of the cards showing and check your open pair on a slowplay. Assuming your opponents saw your hand in a showdown, if you make a similar three-of-a-kind later in the session, you might bet it then. Since you checked three-of-a-kind before, your opponents are now likely to think you do not have three-of-a-kind, but something like two small pair or one pair and a three-flush. In other words, you are taking advantage of the impression you created earlier to get paid off later when you bet. By the same token, let's say you make an open pair on fourth street, but this time that's all you have. You check. Now your opponents will be suspicious that you may have three-of-a-kind. 242 Chapter Twenty-three They may give you a free card, and if one of them bets, you can be fairly certain that player has a good hand. In general, you should evaluate any play you make on its merits

alone — that is, on its expectation in a given situation. However, as we suggested in the chapter on bluffing, you might occasionally want to do something that is theoretically incorrect, especially in a no-limit game. You might either bluff a hand when you are almost sure you won't get away with it or fold a legitimate hand when you think you are getting bluffed and then show the hand. What you are trying to do is create an impression for the future. You are making a bad play so that it sticks in everybody's mind. Once you have opponents thinking one way, you take advantage of that thinking later. These types of plays will work against players who are good enough to try to take advantage of their new-found knowledge but who are not good enough to realize that you know they are going to try to take advantage of it and that they should therefore ignore it. Once again it comes down to knowing your opponents. You have to know how they think and whether they are capable of thinking on the level you are giving them credit for. If they think on a still higher level, you have to step up to that level too. Summary The psychology of poker is an important aspect of the game. You should think not only about what your opponents have, but about what they think you have and about what they think you think they have. You must go through such thought processes against good players in particular, but the better they are, the more difficult it is to figure them out. When you get to the expert level, the process sometimes becomes so complex and tenuous that you have to fall back on game theory. On the other hand, these thought processes can be costly against weak players — as we saw in Chapter Eight — because your opponents are not thinking on such an advanced level. The Psychology of Poker 243 Against weak players the best strategy is to play your cards in a basic, straightforward way. Thinking about what your opponent is thinking will improve your calling and betting strategy. If an opponent is sure you will call his bet, he is not bluffing; if he thinks you will fold, he may be bluffing. By the same token, if an opponent thinks you are strong, you may be able to bluff, but you should not bet a fair hand for value. If an opponent thinks you are weak, you can't bluff, but you can bet your fair hands for value. Ordinarily you evaluate a poker play solely on its own merits, but you can occasionally make a bad play for psychological effect — to create an impression for the future. The psychology of poker is an extension of reading hands and using deception in the play of your own hands, and thus it is an extension of the Fundamental Theorem of Poker. Chapter Twenty-four Analysis at the Table Like any other gambling game, poker is a game of risks

versus rewards. Any decision you make at the poker table can be thought of as a comparison of the risk involved in a particular play and the possible reward for the play. There are three questions involved in arriving at a decision: How great is the risk? How great is the reward? Is the reward great enough to justify the risk? When deciding whether to bluff, your risk is a bet. Your reward is the pot (as well as advertising value if you show the bluff). When deciding whether to bet a mediocre hand before all the cards are out, you risk a bet. If successful, your reward (when your opponent doesn't simply fold) is that you didn't give a lesser hand a free card to outdraw you. When you check a big hand, you risk losing a bet on that round as well as losing the pot to a hand that would have folded if you bet. Your reward is a check-raise or future bets on later rounds. When deciding whether to call, your risk is a bet, and your reward is the pot. Any poker decision can be put into these terms. What do you have to gain (including future benefits on subsequent hands) by making a particular play? What do you have to lose? The ability to evaluate properly the risk-reward ratio for any poker decision is the ultimate test on the road to becoming a champion poker player. The trouble is that unlike chess and many other games, poker is a game of speed. Every once in a while you are allowed to think about a hand, but in general you have to make decisions in a few seconds. You can't sit there for two minutes calculating odds, trying to read your opponents' hands, trying to figure out what they are thinking, and then deciding upon your best play. For one thing the other players at the table wouldn't tolerate your dawdling. For another, you would be giving away information about your hand, since any time you paused unduly long to 245 246 Chapter Twenty-four reflect, your opponents would know you had some kind of problem. (Consequently, when you find, despite your best efforts, you have to pause often when you're playing, you should also pause when you have no reason, to throw your opponents off.) Poker tends to be a game for quick-thinking people. Some geniuses are plodding thinkers, unable to come to quick decisions, and they can never become great poker players. On the other hand, some of the best poker players in the world are not super minds, but they are super-quick minds and can remember any mistake they and their opponents make. Some combination of quick thinking and instant recall has to be developed if you want to become a poker champion. Analysis in Theory One of the most difficult things for the average poker player to do is to make accurate decisions at the game in the heat of a hand. Many good and bad players alike simply decide what they think their

opponent has and then go on to determine their best play on the assumption that their opponent has the hand they're assuming he has. However, as we saw in the chapter on reading hands, this is a bad and potentially costly way of going about the business of decision-making. There is a better way, which is employed by most good players. They ask, "What are the various hands my opponent could have, and what are the chances he has each of them?" They determine the best play for each of the possible hands, and they usually choose the best play against their opponent's most likely hand or hands. Sometimes it works out that no matter what your opponent has, you wind up with the same best play. This is especially true in the relatively easy decisions — for example, deciding to fold when you have nothing in seven-card stud, the pot is small, and your opponent with an open pair of aces bets on the end. If, on the other hand, the pot were large — hence the reward would be large — you might want to determine the chances of a bluff raise working if your opponent has nothing but two aces. Analysis at the Table 247 And, of course, those chances depend upon the chances that your opponent has in fact only aces. Frequently, then, a different play becomes correct depending upon what your opponent has. For example, a bluff raise might have a reasonable chance of working if your opponent has nothing but two aces. It has less chance of working if that opponent has aces up. It has little to no chance of working if he's made a straight and no chance whatsoever against aces full. Therefore, determining whether the risk of two bets (calling and raising) is worth the possible reward of the pot depends: 1.Upon the chances that your opponent has only two aces rather than any of his other possible hands. 2.On whether that opponent is the type of player who would fold them if you raise. Let's say you decide there's only about a 25 percent chance that your opponent has two aces and a 75 percent chance he has aces up or better. Furthermore, if that player does have only aces, you think there's only about a 50 percent chance he will fold if you raise. Then the reward of the pot is probably not worth the risk of two bets, and you should fold. In general, when you have alternate plays dependent upon your opponent's hand, you choose the best play against his most likely hand or hands. Let's say you figure an opponent to have Hand A 40 percent of the time, Hand В 35 percent of the time, and Hand С 25 percent of the time. Usually you would pick the best play against Hand A, which is your opponent's most likely hand. However, if Hand A requires one play, while both Hand В and Hand С require quite another play, you would ordinarily make the second play since it

would be right 60 percent of the time — 35 percent of the time when your opponent has Hand В and 25 percent of the time when he has Hand C. When analyzing a poker situation, you go through four steps in deciding on your best play. 1 . Determine the possible hands your opponent may have. 2. Assess the chances of his having each of his possible hands. 248 Chapter Twenty-four 1.Determine your best play against each of his possible hands. 2.In most cases, pick the play that will most often be correct. Analysis in Practice To see how this sort of analysis works in practice, we'll look at a couple of examples. Draw Poker $5-$ 10 Limit Opponent You open for $5 in early position. Everyone folds except the player under the gun who originally checked to you and who now raises another $5. We'll assume you know this player will never make such a play without three-of-a-kind or better. We'll also assume that with the antes and your implied odds it would be incorrect to fold even if you knew your opponent had a pat hand. So the question is whether you should simply call the $5 raise or reraise another $5. Analysis at the Table 249 Your opponent's raise tells you he has either trips, which must necessarily be smaller than your three aces, or a pat hand. If he has trips, you have the best hand and are the favorite to win the pot; if he has a pat hand, you have the second-best hand and are an underdog to win the pot. According to draw poker distribution, your opponent will have three-of-a-kind about 65 percent of the time and a pat hand about 35 percent of the time. When he has a pat hand, you should obviously not reraise. However, it's nearly 2-to-l he has trips. Should you therefore reraise? The answer is no because when you only call and your opponent draws cards, you can draw one card, as though you had two pair, and check-raise after the draw. Assuming he calls your raise, which he will almost always do, and neglecting the slight chance of your opponent improving to a full house when you don't, you win $30 (plus the antes) by playing this way — $10 before the draw and $20 afterward when you check, your opponent bets $10, and you raise to $20. In contrast, by reraising $5 before the draw and coming out betting $ 10 afterward, you win a total of $25 — $15 before the draw and $10 afterward. Thus, the 65 percent of the time your opponent has three-of-a-kind, you win $5 more by calling instead of reraising. At the same time, the 35 percent of the time he has a pat hand (and you don't improve to a full house), you lose only $10 instead of $15, a savings of $5. Therefore, in this situation a call is the correct play since it is right all the time — whether your opponent has three-of-a-kind or a pat

hand. You 250 Chapter Twenty-four Here is a trickier situation from hold 'em: Hold 'em $10-$20 Limit (Small Pot) Board Your opponent, who is a good player, checked and called your bet on the flop. When the deuce falls, your opponent checks again. Should you check or bet your pair of kings? In hold 'em, any time an opponent bets, calls, or raises, good players ask, "What could my opponent have done that with?" Then they think of the various hands the opponent might have to do what he did. So when your opponent called your bet on the flop and then checked on fourth street, you try to determine what hands he might have that prompted him to play the way he did. Your opponent could be slowplaying a better hand than yours — say, K,9 or 6,6. You estimate there's a 25 percent chance he has such a hand. He might have a fairly good hand such as K, J or K,10. You figure those hands at 25 percent, too. Your opponent might have a mediocre hand like K,4 or A,9 or 10,10. The chances Analysis at the Table 251 of those hands you put at 35 percent. And you figure there's a 15 percent chance your opponent has 8,7 and is drawing to a straight. You know that if you bet on fourth street after his check, your opponent will probably call with his fair hands, with a straight draw and at least call with his big hands. However this player will probably fold his mediocre hands because the pot is not big enough to justify calling with them. Therefore, after your opponent checks on fourth street, it turns out the correct play may be to check it right back. 12 Your intentions are to bet on the end if your opponent checks and call if he bets. The rationale for this play is that, like many players, this opponent will fold his mediocre hands if you bet on fourth street to avoid having to call twice to see what you have. Your checking on fourth street makes it easier for him to call on the end, not only because you have made it cheaper but also because you have shown weakness. Obviously checking is also the better play that 25 percent of the time you have the worse hand. Finally, checking on fourth street induces a bluff on the end. The drawbacks to checking on fourth street are: 1.It gives your opponent a free card to outdraw you. 2.There's a 25 percent chance your opponent has a hand like K,J or K,10, with which he would probably call twice. It is important that the pot be small — say, under $60 in a $10-$20 game — to make checking right because you gain only one bet by checking and betting on the end into your opponent's mediocre hands, but you lose the whole pot if the free card gives your opponent the best hand. Changes in the structure of hold 'em since this was first written has made

this play debatable. However, the thinking process behind it remains valid. Opponent You 252 Chapter Twenty-four Notice that the percentages support checking as the correct play on fourth street. Opponent's Possible Hands Better than Yours Mediocre hand Fair hand (K,J or К,Ю) Straight Draw Because you expect your opponent to fold his mediocre hands if you bet on fourth street, and you want to win at least one more bet from those hands, the correct play 60 percent of the time is to check. It is correct to bet only 40 percent of the time. You usually pick the play that is likely to be right most of the time: Therefore, you check. Analyzing the Cost of a Mistake Unfortunately, the play that is likely to be right most of the time is not always the correct play. When you have a choice of plays, you also have to decide how bad it will be if you make a mistake. Here is an obvious example. If your opponent bets on the end and you think the chances are better than 50-50 that that opponent has the best hand, the correct play most of the time is to fold and save a bet. However, it costs you not just one bet but the whole pot when folding turns out to be a mistake — that is, when you fold the best hand. Therefore, you would call, even though the chances are that you are making a mistake. The reason you call is that this mistake costs you only one bet, while the opposite mistake — folding when you have the best hand — costs you the whole pot. (This is simply another way of stating that you should call when the pot odds you are getting in relation to your chances of having the best hand make calling a play with positive expectation.) Analysis at the Table 253 There are other situations, as well, where making the wrong play can cost you a considerable amount of money, so you should not necessarily choose that play though it is favored to be right over 50 percent of the time. Such situations come up particularly in no-limit poker. Suppose, for example, you have two queens in no-limit hold 'em, and you put in a small raise before the flop. Everyone folds except one player, who fires back with a gigantic reraise. You know that this player will make such a play not only with two aces and two kings but also with ace, king. Assuming you have nothing other than Bayes' Theorem available to put your opponent on one of these three hands, the odds work out to be 4- to-3 in favor of your opponent's having ace, king rather than a pair of aces or a pair of kings. Thus, 4/7 of the time your pair of queens is the favorite, and 3/7 of the time it is the underdog. However, when your opponent does have ace, king, your queens are only a 13-to-10 favorite since there are five cards to come, any one

of which could give your opponent either a pair of kings or a pair of aces. So while you will average winning 13 times, the other 10 out of 23 times you will lose the hand when you call the raise and your opponent has ace, king. On the other hand, those three times out of seven when your opponent has two aces or two kings, your two queens are a big 4 1 /2-to-l underdog, meaning in those instances you will lose 18 hands out of every 22 you play on average. Therefore, you cannot say, "My queens are 4-to-3 favorites to be the best hand. So I must call." It works out that the 3/7 of the time your opponent has two aces or two kings, you hurt yourself so much that you don't gain it back the 4/7 of the time when he has ace, king. The general principle operating here is the following: When one alternative will have slightly bad consequences if it's wrong and another second alternative will have terrible consequences if it's wrong, you may be right to choose the first alternative even when the second is slightly favored to be the correct play. Best Play Check Check Bet Bet Approximate Chances 25 percent 35 percent 25 percent 15 percent 254 Chapter Twenty-four Here is an example of the same principle in a limit game, where the consequences of making the wrong play are not nearly so severe as in the no-limit example: Seven-Card Razz $15-$30 Limit Analysis at the Table 255 when your opponent does have an 8,7 made and reraises, you still have a good chance of outdrawing him. However, when he has paired, he has only a slim chance of beating you since your 9 low is already the best hand and you have an excellent chance of improving to beat your opponent — even if he makes his 8,7. In the long run then, you do better by raising than by calling though raising will be right only 45 percent of the time. SUMMARY Accurately and quickly analyzing risk-reward decisions at the poker table in the heat of a hand comes only with experience. Some top players do it intuitively. In this chapter we have presented the theoretical basis for these decisions. Most of the time, when the choice of plays is problematic, your best play is the one likely to be correct more than 50 percent of the time. However, when the favored play has very bad consequences when it is wrong, and the less-favored play has only slightly bad consequences when it is wrong, it may be correct to choose the less favored play. OPPONENT Your opponent bets $30, and you know this opponent will bet anything in this spot except two pair. Should you call or raise? Probability tells us your opponent is a slight favorite — about 55 percent — to have his 8,7 low made when he bets, assuming he started with three small cards. When he does have an 8,7 low, you should not raise since

you are a slight underdog and will probably get reraised. However, when one of your opponent's upcards has paired one of his hole cards the remaining 45 percent of the time, a raise is very profitable since you are a big favorite. Thus, a call is correct 55 percent of the time, and a raise is the better play 45 percent of the time. Nevertheless, the best play is to raise because raising will be slightly wrong 55 percent of the time, but calling will be very wrong 45 percent of the time. In other words, even You Chapter Twenty-five Evaluating the Game Before sitting down, good poker players stop and evaluate the game, especially when they have many games to choose from as they do in Las Vegas, California, or New Jersey. However, a serious player should evaluate even a weekly private game before deciding whether to become a regular. There are two reasons for evaluating a game. One is to determine whether the game is worth playing. The second is to determine how to play in that particular game. When professional players consider whether a game is worth playing, they estimate their expected hourly rate and decide whether that rate is satisfactory. Social players in a home game are not generally so concerned with hourly rate. However, even they do not want to become regulars in a game where they have much the worst of it; nor do they want to get involved in a game whose stakes are either too high for their financial position or too low to be interesting. Additionally, social players should consider the game — or games, if it's dealer's choice — that are played and be sure they're comfortable with them. They should also consider the speed of the game. If they're really interested in playing cards, they probably do not want to become involved in a game in which there's a new deal only about every four or five minutes. To determine whether a game is worth playing and how to play in a particular game, the two most important considerations are the structure of the game and the players in the game. 257 258 Chapter Twenty-five Evaluating the Structure and Adjusting to It By the structure of the game, we mean principally the ante, the betting limits, and the rules of betting. The structure may deter an average or even an above-average player from sitting down, but it should rarely deter a good player. The good player should be able to adjust his play to suit any structure he happens to confront. There is however one instance where the structure might cause even a very good player to stay out of a game: When it has made fair players into good players by accident. Most players don't sufficiently alter their style of play according to the structure; they tend to play a fairly consistent game. However, sometimes the structure is exactly suited to the style of a group of players. Specifically the ante and/or the blind might by coincidence be an amount

that makes these players' style of play approximately correct. For instance, there are some very aggressive seven-card stud players in Las Vegas who play a little bit too loose in an ordinary game, but in a game with a very high ante, their style of play is almost perfect. The Ante and Other Forced Bets The key question to ask about the ante and other forced bets like the blinds in hold 'em is: How big are they in relation to the betting limits? As we saw in Chapter Four, when the ante is large, you must loosen up, try to steal more antes, and almost never slowplay. When the ante is small, you tighten up, steal fewer antes, and slowplay more. If you find you do better and are more comfortable in a tighter, small-ante game, that's what you should look for, and vice versa. For example, if you are especially good at disguising your hand, at slow laying, and at trapping opponents, then a small-ante game suits your style. If on the other hand you are an aggressive player with a keen sense of when to bluff and Evaluating the Game 259 hen not to, a large-ante game is likely to produce the best results. However, whatever your style of play, you should avoid a game where the ante is simply enormous in relation to the betting limits. In that case, the pot is so large to begin with that it's worth calling with almost anything, and the game may almost be reduced to dealing out the cards and seeing who has the best hand. An important aspect of the ante structure is the size of the initial bet and the size of the initial raise after the initial bet. Changes in these two bets can mean significant changes in strategy. To illustrate, we will use the standard $ 15-$30 razz game in Las Vegas and a $15-$30 razz game I've played in Reno. Usually, a $15-$30 Las Vegas razz game has a $1 ante, and the high card has a forced bet of $5. Anyone can then raise $10 to make it $15. With this structure, it is almost always correct when you have a good hand to raise with the next-to-last low card if everyone else has folded. If you just call the $5 forced bet with a decent hand, the last low card is correct in calling behind you, even with nothing at all, simply because that player is getting about 31 /2-to-1 odds on his $5 and figures to win if he catches a baby and you don't. However, by raising in this spot, you cut down the last low card's odds to about 2-to-l. Now if that player wants to take the chance of outdrawing you on the next round, he is taking the worst of it unless he has a good hand himself. In the Reno $15-$30 game, on the other hand, the high card brings it in for $10, and then anyone can raise and make it $25. That structure dictates a completely

different strategy in the situation just described. Under these circumstances it becomes almost always correct to simply call the initial $10 bet with the next-to-last low card when you have a hand. You are hoping for an overcall behind you since the player is no longer getting sufficient pot odds to gamble on outdrawing you. The difference in strategy is based on the Fundamental Theorem of Poker. By calling, you have not only induced your opponent to make a mistake with a weak hand, but you've given 2 6 0 C h a p t e r T w e n ty - fiv e t h e i m p r e s s i o n t h a t y o u r h a n d i s w e a k e r t h a n i t i s . I f y o u r o p p o n e n t c a l l s , y o u w e l c o m e i t . I f h e r a i s e s , th at's fi n e t o o . T h e i n t e rw o rk i n g o f d i ffe r e n t s tru c tur e s a n d s t r a t e g i e s c an a l s o b e s e e n b y c o m p a r i n g t h e o l d $ 1 0 - $ 2 0 h o l d 'e m g a m e i n R e n o an d th e $ 1 0 - $ 2 0 h o l d 'e m g am e i n L a s V e g a s . I n V e g a s th e fi r s t b e t i s $ 5 , an d a r a i s e r c an m ak e i t $ 1 0 . I n R e n o th e fi r s t b e t i s $ 4 , a n d t h e r a i s e r c a n m a k e i t $ 1 4 . T h e fi r s t e ffe c t o f t h e s e d i ffe r e n c e s i s t o m ak e y o u p l ay s o m e wh at t i ght e r i n V e g a s s i n c e y o ur i n i t i a l i n v e s t m e n t i s a d o l l ar m o r e . H o w e v e

r , i n R e n o y o u mu s t h av e a s o m e wh at b e tt e r h an d t o ra i s e s i n c e y o u ar e i nv e s t i n g a t o tal o f $ 1 4 — $ 4 m ore th an a rai s e r in V e g a s inv e s t s — an d th e i n i t i a l p o t th a t y o u ar e r a i s i n g i s s m a l l e r . T h at i s , th e r at i o o f th e r a i s e r's m o n e y t o th e fi r s t b e tt o r's m o n e y i s $ 1 4 - t o - $ 4 a s o p p o s e d t o $ 1 0 - t o - $ 5 i n L a s V e g a s . T hu s , i n L a s V e g a s i t i s fr e q u e n t l y c o rr e c t t o th r o w i n a $ 5 r a i s e t o d e c e i v e y o ur o p p o n e n t s an d g e t the m to che ck to you on the flop; but in Reno i t i s usua l ly too e xp e n s i v e t o r a i s e s i mp l y fo r d e c e p t i o n . A d d i t i o n a l l y , wh e n y o u c a l l th e i n i t i a l $ 5 b e t i n V e g a s , y o u ar e a l m o s t a l w ay s c o mm i tt e d t o c o m e i n fo r a s e c o n d $ 5 . H o w e v e r , i n R e n o y o u m ay v e ry w e l l h a v e a h a n d t h a t i s w o rt h a $ 4 c a l l b u t s h o u l d b e t h r o w n aw a y b e fo r e c a l l

i n g $ 1 0 m o r e . T h e B e tt i n g L i m i t s T h e fi r s t th i n g t o c o n s i d e r ab o ut th e b e tt i n g l i m i t s i s wh e th e r y o u c an a ffo r d th e m . E v e n i f y o u th i nk y o u h av e mu c h th e b e s t o f i t , y o u s h o u l d n o t p l ay i n a g am e w h o s e l i m i t s ar e s o h i g h i n r e l ati o n t o y o ur b ankro l l th at y o u c ann o t p l ay y o ur h an d s c o rre c tly b e c au s e y o u d o n't w an t t o r i s k g o i n g b r o k e . A t th e s am e t i m e , w h e n y o u th i n k y o u h av e th e b e s t o f i t , y o u s h o u l d p l ay a t th e h i g h e s t l i m i t s y o u c an a ffo r d w h e n e v e r p o s s i b l e . T h e e x c e l l e nt n o hp r o fe s s i o n a l p l ay e r J ay H e i m o w i t z , fr o m M o nt i c e l l o , N e w Y o rk , t e l l s th e s t o ry o f h o w h e s tart e d p l ay i n g i n a 2 5 - 5 0 - c e n t p o k e r g am e i n th e e ar l y 1 9 6 0 s . " I n o t i c e d I w a s w innin g ab o ut $ 2 0 a w e e k , an d th at $ 2 0 a w e e k w a s th e di ffere n c e b e t w e e n my w i fe C ar o

l an d I g o i n g o u t t o d i n n e r , " H e i m o w i t z E v a l u a ti n g t h e G a m e 2 6 1 " T h e n I g o t t h e b r a i n s t o rm th a t i f I p l a y e d i n a $ 1 l i m i t g am e m ayb e I'd w i n $ 4 0 a w e e k , an d w e c o u l d g o o ut t o d i nn e r t w i c e'" T o d a y H e i m o w i t z , a s u c c e s s fu l B u d w e i s e r b e e r d i s t r i b u t o r , p l ay s n o - l i m i t h o l d 'e m fo r t e n s o f t h o u s a n d s o f d o l l ar s a g a i n s t th e v e ry b e s t h o l d 'e m p l ay e r s i n th e w o rl d , b ut th e p o i nt o f h i s s t o ry i s th a t , e v e ryth i n g e l s e b e i n g e qu a l , w h e n y o u h av e th e b e s t o f i t , th e h i gh er y o u p l ay , th e m o re y o u w i l l av e ra g e winning . A s s u m i n g y o u ar e p l ay i n g a t a l i m i t th a t s u i t s y o u , th e i mp o rt ant qu e s t i o n i s th e r at i o o f b e t s i z e s fr o m e ar l y r o un d s t o l at e r o un d s . I f th e b e tt i n g l i m i t s i n c r e a s e dr a s t i c a l ly fr o m th e e arly r o un d s t o th e l at e r r

o un d s , y o u mu s t p l ay qu i t e a b i t d i ffe r e nt l y th an i f th e l i m i t s r e m a i n fa i rly s t e a dy . I n m ath e m at i c a l t e rm s , th e g r e at e r th e e s c a l at i o n o f th e l i m i t s , th e h i g h e r y o ur i mp l i e d o d d s o n e ar l y r o un d s . T hu s , y o u t e n d t o p l ay l o o s e r e ar l y i n g am e s w h e r e y o u m ay w i n b i g g e r b e t s l at e r . Wh e n w e s ay l o o s e r , w e m e an y o u t ak e c h an c e s w i th h an d s th at h av e s o m e c h an c e o f i mp ro v i n g t o b i g h an d s . Y o u d o n o t p l ay m e di o c r e h an d s th at c an o n l y i mp r o v e t o fa i r l y g o o d h an d s . I n o th e r w o r d s , i f y o u c ann o t b e r e a s o n ab l y s ur e th at a h an d w i l l b e th e b e s t h an d , e v e n i f i t i mp r o v e s , th at h an d i s n o t p l ay ab l e . H o w e v e r , a h an d l i k e a h i gh i n s i d e s t r a i g h t d r a w , w h i c h y o u w o u l d n o t p l a y i f t h e b e t s r e m a in e d fa i rly s t e a dy , m ay b e w o rth p l ay in g i f y o u fi gur

e t o w i n a b i g b e t l at e r o n wh e n y o u h i t . O f c o ur s e , th e g am e s w i th th e g r e a t e s t e s c a l a t i o n i n l i m i t s fr o m e ar l y t o l at e r o un d s ar e p o t - l i m i t an d n o - l i m i t . N o - l i m i t p o k e r d o e s n o t t e c hn i c a l l y h av e an e s c a l at i n g l i m i t s i n c e any o n e m ay b e t any am o unt r i g ht fr o m th e s t art , b ut u s u a l l y th e b e t s b e c o m e i n c r e a s i n g l y l ar g e r a s th e h an d p r o g r e s s e s . T hu s , a s w e s aw i n C h ap t e r S e v e n , i n p o t - l i m i t an d n o - l i m i t g am e s i mp l i e d o d d s — n o t th e o d d s a p l ay e r i s g e tt i n g fr o m th e p o t — o ft e n b e c o m e th e p r i m ary c o n s i d e r a t i o n i n b e tt i n g o r c a l l i n g a b e t . W h e n a g am e h a s fa i r l y s t e a dy b e tt i n g l i m i t s — m o s t c o mm o n l y l i m i t s l i k e $ 2 - $ 4 , $ 5 - $ 1 0 , $ 1 0 - $ 2 0 , w h i c h i n c r e a s e o n l y tw o fo l d fr o m th e fi r s t r o un d t o th e l a s t —

y o u mu s t s t art o ff w i th a g o o d h an d an d th r o w aw ay h an d s th a t r e qu i r e y o u t o g e t 2 6 2 C h a p t e r T w e n t y - fi v e l u c ky . Y o u h av e t o p ay t o o h i g h a p r i c e t o s t ay i n , i n p r o p o rt i o n t o w h a t y o u m i g h t w i n th e fe w t i m e s y o u h i t . I t i s e s p e c i a l l y i mp o rt ant t o g e t ri d o f s u c h h an d s i n g am e s wh e r e th e r e i s a gr e at d e a l o f r a i s i n g o n th e fi r s t r o un d . F r e qu e n t l y y o u fi n d p e o p l e p utt i n g i n tw o an d th r e e r a i s e s b e fo r e th e fl o p i n l i m i t h o l d 'e m g am e s . I n g am e s l i k e th e s e , i t i s i mp o rt ant t o p l ay h i g h p a i r s an d h i g h c ar d s an d t o s t ay aw ay fr o m h an d s l i k e F o r th o s e s t art i n g h an d s t o b e p l ay e d p r o fi t ab l y y o u n e e d a g am e w i th l o w e ar l y b e tt i n g an d h i g h l at e r b e tt i n g . T h at i s , y o u n e e d a g am e w h e r e i t d o e s n't c o s t y ou mu ch to dr aw to a b ig h and th a t c an m ak e y o u a l o t o f

m o n e y i n th e l a t e r b e tt i n g r o un d s . T h e B e tt i n g Ru l e s S o m e o f th e qu e s t i o n s y o u s h o u l d a s k b e fo r e s i tt i n g d o wn t o p l ay ar e : I s c h e c k - r a i s i n g a l l o w e d ? I s a fl a t b e t i mp o s e d , o r i s th er e v ari ab l e b e tt i n g ? In s e v e n - c ar d s tu d , do e s th e l o w c ard b ri n g i t i n o r th e h i g h c ar d ? H o w m any r a i s e s ar e a l l o w e d ? D o e s th e p l ay e r w h o o p e n s th e p o t h av e t o b e t fi r s t n e x t r o un d ? W h at e v e r th e ru l e s , y o u s h o u l d b e th o r o u g h l y fam i l i ar w i th th e m b e fo re y o u s i t do wn t o p l ay . D o n't m ak e th e mi s t ak e a fri e n d o f m in e m ad e th e fir s t ti m e h e e v er p l ay e d draw p o ker in G ard en a . H e i s th e o n l y m an I kn o w w h o m a d e a r o y a l fl u s h b u t l o s t th e h an d . I n G ar d e n a y o u n e e d j a c k s o r b e tt e r t o o p e n , an d a j o k e r i s u s e d a s a b u g . T h a t i s , th e j o k e r m a y b e u s e d w i t h s tr a i g h t s , fl

u s h e s , an d a c e s ; i t c ann o t b e u s e d t o m ak e a p a i r e x c e p t w i th a c e s . My fri en d N . S . b o ught into a $ 2 - $ 4 draw p o ker g am e fo r $ 4 0 , an d th e fi r s t h an d h e p i c k e d up w a s an a c e - h i g h s tr a i g ht : E v a l u a t i n g t h e G a m e 2 6 3 He was in third position behind the dealer. The man under the gun checked, the second man checked, and N.S. gleefully bet $2. Everyone behind him folded, but then bang! The man in first position raised, and the man in second position reraised. Stupefied, N.S. called the double raise, and the first raiser called the reraise. When it came time to draw cards, the first man stood pat. The second man stood pat. N.S. was smart enough to realize his straight was beat, if not by the man in first position, certainly by the man in second position. So he cleverly discarded the ace of clubs to draw to a straight flush in hearts — or any kind of flush, since with the joker he'd have an A,Q high. Drawing to N.S. actually had four cards that would make the straight flush — the and When he looked at the card he'd drawn, there it was — the king of hearts! He'd made a royal flush, the pure nuts of pure nuts. The man in second position bet. N.S. raised. The man in first position called. The man in second position reraised. N.S. reraised. The man in first position eventually folded his jack-high flush, but the reraising continued until the entire $40 with which N.S. bought into the game was in the pot. The second player turned over a full house — kings full of 9s. With a broad smile N.S. revealed his royal flush. He was about to gather in the pot when his opponent asked, "Where are your openers?" "Openers?" N.S. said. "I had a straight." "But you drew one card," said his opponent. "You don't have openers." Remember that in Gardena card rooms you need jacks or better to open. The joker can be used only with aces,straights, and 264 Chapter Twenty-five flushes. Since N.S. had thrown away his ace of clubs and had indeed drawn one card to make the royal, he had no proof whatsoever that he had opened with a legal opening hand. Of course, there's a posted rule in Gardena card rooms to cover such situations: "When splitting openers, player must declare same and protect split card by turning it face up under a chip." N.S.

had not informed himself of this rule, his royal flush was declared dead, and the full house won the pot. Beyond knowing the rules, it's important to use them to your advantage — as the man in Gardena with the full house certainly did. However, here we're not talking about exploiting technicalities but rather adjusting your play to suit the rules of the game. Suppose, for example, the game does not allow checkraising. Well, that rule takes away a very effective tool, which presumably you can use better than other players in the game. But it changes your playing strategy in that it gives more power to the player in last position. Therefore, when you are in last position, you must bet quite a lot more since you are no longer putting yourself in jeopardy of a check-raise. You would semi-bluff more on earlier rounds because the worst that could happen would be that you'd get called—not raised. Even in first position you must bet more often than you ordinarily would since you can't checkraise. (However, against tough players it may be still better to check and call, rather than bet out with a very good hand in first position, because you may induce them to bet with a hand they would have folded if you had bet.) Adjusting Properly to the Structure The important thing is to adjust your play to the betting rules, the betting limits, and the ante structure with which you are confronted. This ability to adjust is one of your greatest edges against the good but nontheoretical player. It takes quite a while for the nontheoretical player to find instinctively the correct method of play in an unfamiliar structure. In the meantime, that player makes costly mistakes. Evaluating the Game 265 For example, the $15-$30 hold 'em game that used to be played at the Golden Nugget in downtown Las Vegas attracted some of the toughest hold 'em players in the country. However, as good and as solid as they were, most of them didn't realize that the structure of this game, compared to that of the more common $10-$20 hold 'em games they knew, necessitated a change in strategy. In the $10-$20 games there is ordinarily a 50-cent ante and a $5 blind. It costs $5 to come in and another $5 to raise. However, in the $ 15-$30 Golden Nugget game, there was no ante, but there were two blinds — $5 and $10. It cost $10 to come in, and to raise it cost another $15 for a total of $25. Thus, in this game it cost considerably more to come in, relative to the betting limits, than it did in the $10-$20 game — especially when there was a raise. When you call the $5 blind in the $10-$20 game, you are investing half of the $10 bet on the flop; but when you called the $10 blind in the Golden Nugget $15-$30 game, you were investing two-thirds of the $15 flop bet. When you raise (or call a raise) in the $10-$20,

you are investing as much as the bet on the flop — namely, $10; but when you raised or called a raise in $15-$30, you were investing almost twice as much as the bet on the flop — $25. Additionally, when you call the $5 blind in early position in $10-$20, you risk being raised only the amount of the initial bet; but when you called the $10 blind in $15-$30 in early position, you risked being raised another $15 — one-and-a-half times the initial bet. The effect of these structural changes in the $15-$30 game, which made it more expensive to come in, was that you had to play very tightly and play only hands that didn't depend on high implied odds. Handslike ace, king and big pairs went up in value, while handslike 6,7 suited and baby pairs, which are playable in $ 10-$20, went down in value. These differences were so significant that anyone who understood them and adjusted to them properly had an edge in the $15-$30 hold 'em over players who may have been great in $10-$20 but who insisted on playing the same way in the $15-$30 game. 266 Chapter Twenty-five Evaluating the Players and Adjusting to Them When you are deciding whether to play and how to play, the other players in a given game are much more significant than the structure. Rarely will the structure deter good players from sitting down, but if they look around the table and see nothing but top players, relative to their own abilities, they should probably find another game. There is an old and true adage in poker: If you look around and don't see a sucker in the game, you're it. At the same time, everybody in the game does not have to be worse than you. For a game to be potentially profitable, all you need are one or two bad players or five or six mediocre players. However, if everyone in the game is as good as you or nearly as good, you may not be taking the worst of it, but you cannot expect your hourly rate to be very high. Players Who Play Too Loose Once you have decided that the caliber of your opponents allows you to sit down and play profitably, your next step is to evaluate their mistakes and see how you can best take advantage of those mistakes. The most common mistake players make is playing too many hands. In Las Vegas I frequently find this tendency to be the only weakness in some opponents. Everything else about their play is top-notch. Consequently, there is little I can actively do to take advantage of these players' mistakes other than not play as loosely as they do. Yet just playing better starting hands than they do on average is a decent edge. Sometimes I play a very unimaginative game against them, simply to make them think I'm not much of a player. I thereby encourage them to play even more hands. When the night is over, I usually have the

money, and they are shaking their heads, wondering how I beat them. Well, I didn't outplay them, just as they suspect, nor did I get lucky. I simply played better openers than they did, and so Evaluating the Game 267 hen I was in a pot against them, more often than not I ended up with a better hand than theirs. Often players who play too many hands will make many other mistakes as well. A typical loose player will call too much, not just on the first round but on all rounds. These players are the kind you encounter most often in home games. They play poker only once a week, and they want action. Against such opponents, conservatism and patience pay big dividends. You play your solid cards, and you don't bluff nearly as much as game theory indicates to be correct. There is clearly no value in bluffing when you know you'll be called — except perhaps once or twice early in a session for advertising purposes, to make doubly sure you'll get called later with your legitimate hands. Players Who Play Too Tight Occasionally you'll run into the opposite type of player — the player who plays too tight. These players may play too tight on the first round or on every round, but the tighter they play, the more they are giving away. You take advantage of the player who's too tight on the first round by stealing antes with more frequency than game theory would indicate to be correct. In fact, you should test such a player by raising the forced bet just about every time you and he are the only players left in the pot. You shouldn't raise every single time the situation comes up, because eventually that tight player will realize you're robbing him and he'll loosen up, which you don't want him to do. However, you should try making a play on that player at least two times out of three when he isthe only person left behind you on the first round. Many players who play too tight on the opening round tend to play too loose later on. Since they're playing only good starting cards, they hate to throw them away. Consequently, if you get called by such a player when you try to steal the antes on the opening round, it is very important to give up your bluff because this type will not fold on later rounds, having called your raise. However, if you have a legitimate hand which you figure to be the 268 Chapter Twenty-five best hand, bet it out since this player will probably give you crying calls all the way. Much rarer are the tight players who throw away too many hands on all rounds. Against them, you should semi-bluff just about any time you're able to represent a good hand, and you should bluff more than game theory would indicate to be correct. Other Mistakes to Look For As we saw in the first section of this chapter, some otherwise excellent players are

incapable of adjusting to different structures. Therefore, you may sometimes decide to sit down in a game with them specifically because you know they are playing on unfamiliar turf. You take advantage of their weakness by playing more correctly, according to the structure, than they do. One of my favorite types of player is the one who never bluffs. You have a tremendous advantage over these players because you just about always know where you're at. Against most players you have to call with a marginal hand since you usually have two ways of winning — either by improving to the best hand or by having them beat when they're bluffing. However, you can assume that players who never bluff have hands when they bet, and you only call when your hand has a fair chance of beating theirs or when you're getting good enough pot odds to chase. You never need to consider calling on the chance that they may be bluffing. Even players who bluff much less frequently than they should offer you a big advantage, especially when you make plays to stop the few bluffs they might be tempted to try against you. Over a period of time, you can save a tremendous number of bets by not having to call such players. At the same time, you are likely to make money from them since you only play against them with a legitimate hand that has a reasonable chance of beating theirs. Ironically, though, against such players you face the psychologically upsetting fact that you only profit from their mistakes when you fold and lose the pot to them. Your profit Evaluating the Game 269 comes from having lost less to them than you would have lost to players whose legitimate hands you might have paid off. This is an example of the poker principle that any bet saved means more money earned at the end of the session and at the end of the year. Sometimes the only weakness I can discern in opponents is that they will never check-raise bluff. Even this relatively small flaw gives me an edge. Knowing that these opponents always have good hands allows me to fold hands I might otherwise have called with when I do get check-raised. Anytime I can do this I save money, and these savings add up in the long run. Other players will never make any kind of bluff raise; against them I can save even more money since I always know they have good hands when they raise. Occasionally you encounter players who never check-raise. You take advantage of this major mistake by betting more hands after they check than you would against other players who have checked. Since these players don't check-raise, you know they are checking because they have only fair hands at best. You are actually in a better position than you would be when a hand is checked to you in a non-check-raising game, because in these games a player will occasionally check a good hand to induce you to bet

a weaker hand. The players who never check-raise will hardly be so cute: When they check, it's because their hands are not worth betting. Players who bluff much more than they should give you a tremendous opportunity for a profitable session. You should do everything you can to induce them to bluff even more and then call them. There is one player whom I run into now and then in Las Vegas who bluffs much too much. I never bet into that player because he will usually fold. Instead I check, and he will almost automatically bet; then, depending upon my hand, I either call or raise. It's true that by playing against him this way, I give him many chances for a free card, but that risk is more than compensated for by the times he just keeps on bluffing at the pot. (Though players who bluff too much can produce a profitable session for you, they are also much more dangerous than players 2 7 0 C h a p t e r T w e n ty - fiv e w h o n e v e r b l u ff, e s p e c i a l l y i f y o u ar e o n a n y k i n d o f l i m i t e d b ankr o l l. To t ak e a dv ant a g e of th e s e p l ay e r s' m i s t ak e s, y ou mu s t i n du c e b lu ffs an d n e arly a l w ay s c a l l th e m , e v e n wh e n y o u h av e a m e d i o c r e h an d . O b v i o u s l y p l ay e r s w h o b l u ff t o o mu c h g e t th e i r s h ar e o f g o o d h an d s l i k e th e r e s t o f u s . Wh e n th e y g e t m o r e th an th e i r s h ar e , y o u w i l l t e n d t o p ay th e m o ff wh e n y o u w o u l dn't p ay o ff o th e r s . T h e r e fo r e , up t o a p o i nt , w e r e I o n a l i m i t e d b ankr o l l , I w o u l d p r e fe r m y o p p o n e n t s t o

b e t i g h t , n o nb l u ffi n g p l a y e r s r a th e r th an w i l d , b l u ffi n g p l ay e r s . ) T h e r e ar e e n d l e s s k i n d s o f m i s t ak e s y o u c an d e t e c t i n y o ur o pp o n e nt s' p l ay , an d wh en y o u d e te c t th e m , th er e i s alw ay s a w ay t o t ake a dv ant a g e o f th e m . F o l l o w i n g i s a l i s t o f th e m o s t c o mm o n m i s t ak e s p o k e r p l ay e r s m ak e , a c c o mp an i e d b y th e b e s t s tr at e g i e s t o u s e t o t ak e a dv ant a g e o f th e m i s t ak e s . T yp e o f M i s t a k e 1 . B lu ffs t o o mu c h . 2 . B l u ffs t o o l i tt l e . 2 . S t o p a b l u ff, th e n fo l d i f y o u c an n o t b e a t a h an d ( un l e s s th e r e ar e m o r e c ar d s t o c o m e an d y o u ar e g e tt i n g g o o d e n o u gh o d d s t o c h a s e ) . fa i r 3 . N e v e r b l u ff, b u t b e s u r e t o c o m e o ut b e tt i n g w i th a d e c e nt h an d . 4 . D o n't s l o w p l a y . B e t y o ur d e c e n t h an d s fo r v a lu e . T yp e o f M i s t ak e 5. Folds too oft en on the end . 6 . P l a y s v e ry t i g h t o n t h

e fi r s t r o u n d , b u t t h e n w o n't t h r o w a h a n d away 7 . N e v e r c h e c k - r a i s e s . 8 . N e v e r b l u ff r a i s e s . B e s t S tr a t e g y 1 . I n du c e a b lu ff, th en c a l l . N e v e r fo l d s any h an d o n th e e n d . 34 R ar e l y fo l d s a fa i r h an d o n any r o un d . Evaluating the Game 271 Best Strategy 1.Bluff more than you normally would, but don't bet your fair hands for value. 2.If this player has not yet called and no one else is left, try to steal the antes no matter what you have. If the player calls your raise, give up on a bluff. However, you can play a fair hand for one card. If the next card improves you, the player still won't fold. 3.Bet many more hands behind this player than you would behind someone who does check-raise. 4.Fold fair-to-good hands when this player raises. Bet weaker hands than normal into him since his response will give you more information than you usually get. 272 Chapter Twenty-five Appendix A Best Strategy 9. If you are first and have little, check to see what this player does. If he also checks, you can be pretty sure a bluff will work the next round. 1.Play solid poker, and cut down on your bluffs. 2.Play solid cards, but play them meekly. Make this player think he can run over you. 12. Semi-bluffs too much. 12. Semi-bluff raise. 13. Play as many hands as possible against this type of player, just as you would if you were using marked cards. Rules of Play Five-Card Draw After the ante each player is dealt five cards face down. Starting with the player to the dealer's left, each player checks, bets, or raises. To open, a player must usually hold a pair of jacks or better. In many games a joker is used, usually as a bug but sometimes as a wild card. Once the first round of betting is complete, each active player, starting to the dealer's left, has the option of discarding from one to five cards and receiving replacements from the dealer. Sometimes the rules of a game restrict to three the number of cards any player may replace. After the draw, there is a final round of betting, usually starting with the player who opened the pot. In the showdown the best high hand wins. Seven-Card Stud Three cards are dealt to each player, two face down and one face up. Depending on the betting rules, either the

low card or the high card on board starts the action. When there are two low (or high) cards of the same rank, either the card of the lowest ranking suit (clubs, then diamonds, then hearts) or the card closest to the dealer's left starts the action, once again depending on the betting rules in effect. After the first round of betting, a fourth card is dealt face up, and now the high hand on board starts a second round of betting. (If there are two identical high hands, the one closest to the dealer's left begins.) 273 10. Plays too loose. Type of Mistake 9. Never slowplays. 11. Plays too loose on early rounds and too aggressively later on. 13. Plays weakly and in a way that gives away his hand. 274 Appendix A A fifth and then a sixth card are dealt face up with a round of betting after each. A seventh card is dealt face down, followed by a final round of betting. In each case the high hand on board starts the action. In the showdown the best high hand wins. Hold 'em Hold 'em is most easily described as a variation of seven-card stud. Two cards are dealt face down to each player, and then a total of five community cards are dealt face up in the center of the table. Each player uses the five community cards in combination with his hole cards to form the best five-card hand. After the first two cards are dealt to each player, there is a round of betting, beginning with a forced, blind bet by one, two, and sometimes three players to the immediate left of the dealer or the button if there is a house dealer. In limit hold 'em there is usually only one forced blind. After that first round of betting, the dealer turns over three cards, called the flop, in the center of the table. These are the first three community cards. Thus, if the flop is a player holding in the hole has two pair; a player holding in the hole has a four-flush and an open-ended straight; and a player holding in the hole has three 8s. Following the flop, there is a round of betting, followed by a fourth community card, then another round of betting, then a fifth and final community card and a final round of betting. Each round of betting begins with the first active player to the left of the dealer or button. In the showdown the best high hand wins. Five-Card Stud Two cards are dealt to each player, one face down and the other face up. There is a round of betting, starting either with the lowest card or the highest card on board, depending on the betting rules. A third card is dealt face up, and there is a round of betting, Rules of Play 275 tarring with the best high hand on board. A fourth and fifth card dealt face up with a round of betting after each. After the final round of

betting, the best high hand in the showdown wins the pot. Draw Lowball In standard lowball (also called California lowball) the best low hand is A,2,3,4,5, followed by A,2,3,4,6; then A,2,3,5,6; etc. Frequently the joker is used as a wild card. In deuce-to-seven lowball the best low hand is 2,3,4,5,7. Each player receives five cards face down. There is a round of betting, starting with the player to the dealer's left. Ordinarily the rules require that the player to the dealer's left bet blind. After that betting round, players may draw up to five cards. Following the draw, there is a final round of betting. Usually the rules of play require a 7 low or better to bet in order to win any money put into the pot after the draw. The lowest ranking hand in the showdown wins the pot. In standard lowball, straights and flushes are ignored. However, in deuce-to-seven lowball they count and therefore are not considered a low hand. In standard lowball the ace is a low card; in deuce-to-seven it is a high card. Another lowball variation makes A,2,3,4,6 the best low hand and counts straights and flushes as high hands. When I discuss lowball in this book, I am always referring to standard or California lowball. Razz Razz is seven-card stud lowball with A,2,3,4,5 the best hand. Straights and flushes are ignored. Two cards are dealt face down and one face up to each Player. Usually the high card on board (excluding the ace, which counts aslow)startsthe action. A fourth card is dealt face up, and 276 Appendix A there is a round of betting, beginning with the best two-card low on board. A fifth and sixth card are dealt face up with a round of betting after each, starting with the best low hand on board. A seventh and final card is dealt face down, followed by a final round of betting. In the showdown the best low hand wins. High-Low Split This name covers several popular forms of poker. The game may be five-card draw, five-card stud, or seven-card stud, and in the showdown the best low hand and the best high hand split the pot. Sometimes, however, the rules may require that players have to declare — either simultaneously or consecutively — whether they are going for high, for low, or for both. In five-card high-low split games the best low hand is always A,2,3,4,5, as in draw lowball. In seven stud games the best low hand is sometimes A,2,3,4,6, with straights and flushes counted as high. Aces always count both as low cards and high cards. (Hence, two aces may be a low pair as well as a high pair.) In stud high-low split games, the high hand on board usually starts each betting round. A variation of high-low split requires a player to have an 8 low or better to qualify for low. If no one has an 8 low or better, the best high hand wins the whole pot. A ppendix В Glossary of Poker Terms Action: The betting in

a particular hand or game. A game with a lot of action is a game with a lot of betting. The player who starts the action is the player who makes the first bet. Active player: A player still in the pot. All-in: Having all one's money in the pot. Ante: A bet required from all players before the start of a hand. Baby: A small card, specifically an ace, 2, 3, 4, or 5. The term is used especially in razz and high-low split. Back door: In seven-card stud and hold 'em, three cards to a flush or a straight after five cards have been dealt. In general, the term is used for a hand made on the end, which a player was not originally trying to make. Bad beat: Having a hand that is a big favorite defeated as the result of a lucky draw, especially when the person drawing was playing incorrectly by being in the pot in the first place. Bad game: A game in which your opponents are too good for you to expect to win; a game in which you're an underdog. Bankroll: The amount of money you have available to wager. Belly buster: A draw to an inside-straight. Also called a gutshot. 277 278 Appendix В Best of it: A situation in which a wager can be expected to be profitable in the long run. Bet: To put money in the pot before anyone else on any given round. Bettor: The person who first puts money in the pot on any given round. Bet for value: To bet in order to be called by a lesser hand. You are betting to make money, not to make your opponentsfold. Bicycle: Ace, 2,3,4, 5 — the best possible hand in lowball. Also called a wheel and a baby straight. The term is used in all games. Blank: A card that is not of any value to a player's hand. Blind: In hold 'em, draw lowball, and some other games, a forced bet that one or more players must make to start the action on the first round of betting. The blind rotates around the table with each new deal. The person whose turn it is to bet is said to be in the blind. Bluff: A bet or raise with a hand you do not think isthe best hand. Board: The cards that are face up in a player's hand. In hold 'em, the community cards. Bring it in: To start the betting on the first round. Bug: A joker that can be used to make straights and flushes and can also be used to make a pair with aces, but not with any other cards. Glossary of Poker Terms 279 Busted hand: A hand that does not develop into anything of value. Button: When there is a house dealer, as in the card rooms of Las Vegas, the button is a round disc that rotates around the table to represent the dealer for the purposes of indicating which player is to be first to act. A

button is necessary in hold 'em, draw lowball, and five card draw. Buy in: The minimum amount of money required to sit down in a particular game. Call: To put in the pot an amount of money equal to an opponent's bet or raise. Call a raise cold: To call a double bet — that is, a bet and a raise. Caller: A person who calls a bet or raise. Chase: To continue in a hand trying to outdraw an opponent's hand you are quite sure is better than yours. Card room: The area in a casino where poker (and sometimes panguingue) are played. Check: To decline to bet when it is your turn. Check-raise: To check and then raise after an opponent bets. Chip: A round token in various denominations representing money. Among many professional gamblers it is also called a check. Cinch: The best possible hand, given the cards on board, when all the cards are out. 280 Appendix В Closed hand: A hand in which all the cards are concealed from one's opponents. Come hand: A hand that has not yet been made, with more cards still to be dealt. Thus, a four-card flush would be a come hand. Crying call: A call with a hand you think has a small chance of winning. Cut the pot: To take a percentage from each pot as the profits for the person or the casino running the game. Dead hand: A hand a player may not continue to play because of an irregularity. Dead money: Money put in the pot by players who have already folded their hands. Dealer's choice: Poker in which the player whose turn it is to deal may choose the game for that particular hand. Draw: 1. To take one or more cards. 2. A form of poker in which each player receives five cards and then has the option of discarding one or more of them and receiving new cards in their place. Drawing dead: Drawing to try to make a hand that cannot possibly win because an opponent already holds a bigger hand. A player drawing to make a flush when an opponent already has a full house is drawing dead. Draw lowball: A form of poker in which the best low hand wins. See Appendix A. Glossary of Poker Terms 281 Draw out: To improve your hand so that it beats an opponent who had a better hand than yours prior to your draw. Door card: In stud games, the first exposed card in a player's hand. Double belly buster: See Open-ended straight. Early position: A position on a round of betting in which you must act before most of the other players. Edge: An advantage over an opponent. Effective odds: The ratio of the total amount of money you expect to win if you make your hand to the total amount of bets you will have to call to continue from the present round of betting to the end of the hand. Equity: The value of a particular hand or combination of cards.

Even money: A wager in which you hope to win the same amount as you bet. The term is also used to describe situations in which the chances that one result will occur are the same as the chances the opposite result will occur. Hence, whether an honest coin comes up heads or tails is an evenmoney proposition. Expectation: The average profit (or loss) of any bet over the long run. Favorite: In poker, before all the cards are out, a hand that has the best chance of winning. Fifth street: In stud poker, the fifth card to be dealt to each Player. In hold 'em the fifth and final community card on board. 282 Appendix В Fill: To draw a card that makes a hand. For example, to fill a flush is to draw a fifth card of that suit. Fill up: To make a full house. Five-card draw: A form of poker in which players start with five cards and then may draw to replace them. See Appendix A. Five-card stud: A form of poker in which each player gets one concealed card and four exposed cards. See Appendix A. Flat call: To call a bet without raising. Flat limit: A betting limit in a poker game that does not escalate from one round to the next. Flop: In hold 'em the first three exposed community cards, which are dealt simultaneously. The word is also used as a verb. For example, to flop a set is to make three-of-a-kind on the flop. Flush: Five cards of the same suit. Fold: To drop out of a pot rather than call a bet or raise. Forced bet: A required bet to start the action on the first round of a poker hand. In seven-card stud, for example, usually the low card on board must make a forced bet. Four-flush: Four cards to a flush. Four-of-a-kind: Four cards of the same rank. Four jacks is four-of-a-kind. Fourth street: In stud games, the fourth card dealt to each player. In hold 'em, the fourth community card on board. Glossary of Poker Terms 283 Free card: A card that a player gets without having to call a bet. Freeze out: A game in which the players involved continue play until only one player has all the money. Full house: Three cards of one rank and two of another. Three aces and two 10s is a full house. Gardena: A city in the Los Angeles greater metropolitan area with public card rooms in which draw poker and panguingue are played. Giving a hand away: Playing your hand in such a way that your opponents should know what you have. Good game: A game in which there are enough players worse than you for you to be a substantial favorite. Gutshot: A draw to an inside straight. Also called a belly buster. Heads-up: Playing against a single opponent. High-low split: A form of poker in which the best high hand and the best low hand in the showdown normally split the pot. See Appendix A. Hold 'em:

Also called Texas hold 'em. An increasingly popular form of poker in which players use five community cards in combination with their two hole cards to form the best five-card hand. See Appendix A. Hole: In seven-stud games, the first two concealed cards. In five-card stud games, the first and only concealed card. Hourly rate: The amount of money a player expects to win per hour on average. 284 Appendix В Implied odds: The ratio of the total amount of money you expect to win if you make your hand to the bet you must now call to continue in the hand. Inside straight: A straight which can be made only with a card of one rank, usually somewhere in the middle of the straight. When you hold 6,7,9,10, only an 8 will give you a straight. Thus, you are drawing to an inside straight, or you have an inside-straight draw. Jacks or better to open: Draw poker in which a player needs at least a pair of jacks to start the betting. Joker: A fifty-third card in the deck, which may be used either as a wild card or as a bug. Kicker: A side card, usually a high one. Someone holding 9,9,A has a pair of 9s with an ace kicker. Late position: A position on a round of betting in which you act after most of the other players have acted. Lay the odds: To wager more money on a proposition than you hope to win. Legitimate hand: A hand with value; a hand that is not a bluffing hand. Limit: The amount a player may bet or raise on any round of betting. Limit poker: A poker game where the minimum and maximum amounts a player may bet or raise on any given round of betting are fixed. Glossary of Poker Terms 285 Live card: In stud games a card that has not yet been seen and is therefore presumed likely to be still in play. Live one: A loose, weak player with a lot of money to lose. A rich sucker. There is a story, perhaps apocryphal, about a poker game in Gardena in which one player had a heart attack and died. The player to his left shouted to the floorman, "Hey, Louie, bring us a live one." Lock: A cinch hand. A hand that cannot lose. Long odds: The odds for an event that has a relatively small chance of occurring. Long shot: An event that has little chance of occurring. Hence, in poker a hand that has little chance of being made. Loose: Playing more hands than the norm. Lowball: A variety of poker games in which the best low hand wins in the showdown. See Draw Lowball and Razz in Appendix A. Mathematical expectation: The mathematical calculation of what a bet can be expected to win or lose on average. Middle position: A position on a round of betting somewhere in the middle. In an eight-handed game, the fourth, fifth, and sixth players to act would be said to be in middle position.

Move all-in: To bet all the money one has on the table. Multi-way pot: A pot in which more than two players are involved. 286 Appendix В Negative expectation: The amount a wager may be expected to lose on average. A play with negative expectation is a play that will lose money over the long run. No-limit poker: Poker in which players may wager any amount up to what they have in front of them on any given round. Nuts: The best possible hand at any given point in a pot. Odds: The chances, expressed mathematically, that an event will occur. Also, in the term pot odds, the ratio of the size of the pot to the amount of the bet you must call to continue. Off-suit: Not of the same suit. On the come: Playing a hand that has not yet been made. For instance, if you bet with four cards to a flush, you are betting on the come. On tilt: Playing much worse than usual because, for one reason or another, you have become emotionally upset. Open: To make the first bet in a poker hand. The term is used especially in draw poker. Open-ended straight: Four cards to a straight, which can be made with cards of two different ranks. Thus, 6,7,8,9 is an open-ended straight, which can be made with either a 5 or a 10. Theoretically, 5,7,8,9,J is also open-ended in that either a 6 or a 10 will make the hand. The latter hand is also called a double belly buster. Open-handed: A poker game like seven-card stud or razz in which some cards in each player's hand are exposed. Open pair: An exposed pair. Glossary of Poker Terms 287 Out: Cards which will improve your hand. Also, ways of improving your hand. The term is used particularly in reference to a hand that needs to improve to become the best hand. Outdraw: See Draw Out. Overcall: A call of a bet after another player has already called. Overcard: In stud games, a card higher than any card your opponent has showing. Pair: Two cards of the same rank. Two 8s is a pair. Pass: To check. Also, to fold. Pat hand: In draw poker games, a complete hand before the draw. A pat flush would be a five-card flush before the draw. Pay off: To call a bet or raise when you don't think you have the best hand. Pay station: A player who calls bets and raises much more than is correct. He's also referred to as a calling station. This type is great when you have a legitimate hand, but he's just about impossible to bluff out of a pot. Pocket: Another term for hole. Thus, two aces in the pocket means two aces in the hole. Position: The spot in the sequence of betting in which a player is located. A player in first position would be the first person to act; a player in last position would be the last person to act. 288 Appendix В Positive expectation: The amount

a wager may be expected to win on average. A play with positive expectation is a play that will win money over the long run. Pot: The total amount of money wagered at any point in a hand. A hand itself is also referred to as a pot. Thus, three people in the pot means there are three active players still playing the hand. Pot-limit poker: Poker in which players may bet or raise any amount up to the current size of the pot. Pot odds: The ratio of the amount of money in the pot to the bet you must call to continue in the hand. Pure nuts: The best possible hand. In lowball, A,2,3,4,5 is the pure nuts. If in hold' em the board is a player holding a 5,6 has the pure nuts. Put someone on a hand: To determine as best you can the hand (or hands) an opponent is most likely to have. Rag: See Blank. Raise: To bet an additional amount after someone else has bet. Raiser: A player who raises. Rake: An amount retained by a casino from each pot, usually no more than $2 or $3. Razz: Seven-card stud lowball. The original name of the game was razzle dazzle. See Appendix A. Glossary of Poker Terms 289 Represent: To make your opponents believe you have a bigger hand than you are showing on board. Thus, if in seven-card stud you raise with an ace showing, you are representing a pair of aces. You may or may not in fact have a pair of aces. Reraise: To raise after an opponent has raised. Reverse implied odds: The ratio of the amount of money now in the pot to the amount of money you will have to call to continue from the present round to the end of the hand. River: The seventh and last card, dealt face down, in seven-card stud and razz. Rolled up: In seven-card stud, three-of-a-kind on the first three cards. Round of betting: A sequence of betting after one or more cards have been dealt. A round of betting continues until each active player has either folded or called. Rough: A lowball hand that is not perfect. Thus, an 8,4,3,2,A is a perfect eight. An 8,7,4,2,A is a rough eight. Royal flush: An ace-high straight flush. is a royal flush. Sandbag: To play weakly with a strong hand. To check-raise or slowplay with the probable best hand. Score: A big win. Seat charge: In public card rooms, primarily those of California, an hourly fee for playing poker. 290 Appendix В Semi-bluff: To bet with a hand which you do not think is the best hand but which has a reasonable chance of improving to the best hand. Set: Three-of-a-kind. The term is used particularly in hold 'em. Short odds: The odds for an event that has a good chance of occurring. Short-stacked: Playing in a game with a relatively small number of chips remaining. Showdown: The turning up of all active players' cards at the end of the final round of

betting to see who has the best hand. Side pot: A second pot for the other active players when one player is all-in. Seventh street: In seven-stud games, the seventh card dealt to each player. Sixth street: In seven-stud games, the sixth card dealt to each player. Slowplay: To check or just call an opponent's bet with a big hand in order to win more money on later rounds of betting. Starting requirement: The minimum initial hand a player considers he needs to continue in a pot. Start the action: To make the first bet in a particular hand. Steal: To cause your opponents to fold when you probably do not have the best hand. The term is used especially in reference to stealing the antes — that is, raising on the first round of betting so that everyone remaining in the pot folds. Glossary of Poker Terms 291 Steal the antes: See above. Steam: To play badly because you are emotionally upset — especially to play considerably more pots than you normally would when your hands do not justify it. Straight: Five cards of mixed suitsin sequence. is a straight. Straight flush: Five cards of the same suit in sequence. is a straight flush. Structure: The limits set upon the ante, forced bets, and subsequent bets and raises in any given game. Stuck: Losing money, especially a substantial amount of money, in a given session or over a period of time. We might say, "Sammy is stuck $1,500 in the game." That is, Sammy has lost $1,500. Stud: Poker games in which some of each player's cards are exposed. Sucker: A player who can be expected to lose money, especially one who is not as good as he thinks. Suited: Two or more cards of the same suit. Take the odds: To wager less money on a proposition than you hope to win. Texas hold 'em: Another name for hold 'em. Three-of-a-kind: Three cards of the same rank. is threeof-a-kind. 292 Appendix В Third street: In stud games, the third card dealt to each player. Three-flush: Three cards of the same suit. Tight: Playing fewer hands than the norm. Trips: Three-of-a-kind. Turn: The flop in hold 'em. Also the fourth card in seven-card stud, and sometimes the fourth community card in hold 'em. Two-flush: Two cards of the same suit. Underdog: In poker, before all the cards are out, a hand that does not have the best chance of winning. Under the gun: The first person to act on the first round of betting is under the gun. On later betting rounds, the player to the immediate left of the bettor issaid to be under the gun. Up: Expressions like aces up, kings up, and 6s up mean two pair with two aces, two kings, or two 6s as the highest of the two pair. Unless an opponent has a top pair of the same rank, the rank of the second pair is of no importance. Up-card: A card that is dealt face up. Value: What a hand is worth in

terms of its chances of being the best hand. Wager: A bet. Wheel: See Bicycle. Glossary of Poker Terms 293 Wild card: A joker or any other card mutually agreed upon by the players in the game which can be used to represent any card needed. Wired pair: A pair in the hole. World Series of Poker: An annual series of some fifteen poker tournaments with buy-ins ranging up to $10,000, which is held each spring at the Horseshoe Casino in Las Vegas. The competition is generally recognized as the premier competition among the best poker players in the world. Worst of it: A situation in which a wager will be unprofitable in the long run.