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When does ICM become significant in MTTs? The Independent Chip Model (ICM) was invented in 1987 by M. Malmuth and is one of the most important formulas for understanding tournament poker strategy! But it took us almost 35 years to fully utilize the concept… ICM is great at evaluating tournament stacks, but until recently, it was nearly impossible to calculate for large-field MTTs with many players remaining. So instead, everyone has been evaluating tournaments with Chip EV models when many players remain. Recent advances in poker science now allow us to calculate ICM when hundreds or even thousands of players remain. This begs one important question though – at what point does ICM become significant in tournaments? When is it worth switching to ICM solutions? We ran a series of experiments in partnership with Helmuth, founder of Holdem Resources Calculator , to find out 🧪💥🔍 Table of contents Quick Recap – What is ICM? ICM vs Chip EV Methodology Experiment #1 – 200 Player Freezeout Experiment #2 – 1000 Player Freezeout Experiment #3 – More Strategies Experiment #4 – Varying stack depths Experiment #5 – Addressing a Misconception How this impacts your strategy Alternatives to ICM Conclusions Quick Recap – What is ICM? The Independent Chip Model is a mathematical formula that converts your tournament stack from chips to dollars . ICM uses stack sizes alone to determine how often a player will finish in each position (1st, 2nd, etc.), then assigns tournament equity based on the payouts of those positions. Tournament equity is just your expected share of the prize pool, given the payout structure, your position in the event, and stack sizes. Read this article if you want to learn more about how ICM is calculated. Watch this video if you want to understand ICM using a more visual and intuitive approach. ICM vs Chip EV Chip EV = A strategy that maximizes chips ICM = A strategy that maximizes dollars These two are not the same. The fundamental tradeoff of ICM is that it sacrifices chips sometimes to win more money. This is because of a concept called “Risk Premium”. In MTTs, it can sometimes be worth avoiding marginal spots to survive longer. Losses hurt more than equivalent chip gains help. Conversely, a chip leader may get to play more aggressively as they expect the other stacks to play more cautiously. This risk-averse dynamic doesn’t exist within a chip EV strategy. A chip EV strategy simply maximizes chips without fear. So is this tradeoff valid? Should you sacrifice chips for dollars? 🤔💬 Read more to find out. Methodology The goal of these experiments is to find out at what point ICM becomes a significant factor in MTTs . At what point should you switch from a Chip EV model to an ICM model? We’ve run a series of experiments to find out. We’ve simulated a number of tournaments with different strategy profiles competing against each other. The contestants ICM 100% (Pure ICM) cEV 25% -> ICM 75% cEV 50% -> ICM 50% cEV 62.5% -> ICM 37.5% cEV 75%

you do not fear a reraise and your raise will encourage your opponents to check to you on the next round - you should raise more than half the time. However, you want players with this type of flop. Consequently, if there is a bet and several players remain to act behind you, it is often better to just call. (You still should consider raising if the pot is large, especially if you have overcards.) 70 Part Two: Strategic Concepts Incidentally, even if you can't get a free card with your flush draw, since the odds against making your hand are approximately 2-to- 1, your raise is also correct if you are sure that at least three players will call. But not if a pair flopped. In this case, you can make your flush and still lose the pot, so you usually should just call. (See "Part Three: Miscellanious Topics" - "Staying With a Draw" on page 1 17.) Keep in mind that any time you are in a late position on the flop and have a hand that is worth a call, you should seriously consider raising. In fact, sometimes it is worth raising when you are absolutely sure that the bettor has you beat. Here's an example. Suppose that five players have put in three bets each before the flop. You are in last position with and are sure that no one has aces or kings since you put in the last raise. The flop is: If the player to your right bets after everyone else has checked, you should raise, even if you are sure that he has two tens. Since the pot has become very large, it is important that you maximize your chance of winning it, even if you often cost yourself a few more bets. In the example given, your raise on the flop probably has increased your chance from about 15 percent (had you just called) to about 25 percent. By knocking people out, you have made it The Free Card 71 more likely that you will win if a queen or a jack comes. Though this play may cost you more money, it is well worth it. Additionally, it may save you money if your raise has scared the bettor into just calling and then checking on fourth street. As far as your back-door flush and straight chances are concerned, you probably would win with these hands, even if you let everybody in. However, the extra back-door chances are what made it wrong to fold originally, and as we've just shown, if you don't fold, it is better to raise. Here is another example of how back-door potential can improve your hand and make a raise correct. Suppose you have and the flop is Notice that the flop includes an ace and one of your suit. If someone else bets, you should raise. Now bet on the turn with the intention of just showing down on the river if you do not improve. If you get check-raised on fourth street, you usually should fold,

the flush draw. If there is also a flush draw on the flop, you might make your straight with the same card that fills your opponent’s flush. For example, you hold 9-10 and your opponent holds A-3 of hearts. The flop comes A? 7? 8?. In this case, you’d have eight cards to fill your straight, but notice that if you fill it with the 6? or the J?, you’d lose anyway, leaving you with only six pure outs. Even if you hit your nut straight on the turn, your hand is still vulnerable to any of nine remaining hearts on the river. There are some hidden advantages to open-ended straight draws. When a third flush card hits on the board, it sets off alarm bells in your opponents’ heads, knowing that any two hearts make a flush. If they hold top pair, two pair, or even a set, a third flush card might cause them to put on the breaks. Straight draws aren’t quite as obvious. When you hit one, you will likely gets lots of action from anyone holding an overpair, two pair, or a set. If you flop 10-9-6 to a hand like 7-8, an opponent holding a hand like 10-10 will go to war with you. You would need to have precisely 7-8 to have him beat, which wouldn’t be the case with a flush board. If the board is 10-7-2 of hearts, that same player with a set of tens may be a little more cautious, realizing that any hand with two hearts has him beat. 139 Semi-Bluffing with Straight Draws Again, if you bet when two hearts flop, your opponent might decide to put you on a flush draw. However, when you bet a straight draw on the flop, it’s not quite as obvious. This actually gives you more semi-bluffing opportunities than you would have when betting flush draws. Let’s look at an example of a situation where you may decide to run a semibluff with a straight draw. You find 6-7 in the big blind. An early position player raises, and you call. The game is six-handed, and you know that your opponent would raise with any two cards 10 or higher, most ace-high hands, and any pair. (Later, in the shorthanded section, you’ll learn why this is not a bad strategy.) The flop comes 4-5-9 rainbow, giving you an open-ended straight draw. This flop gives you an excellent opportunity to win this pot, whether you make a hand or not. You can play it several ways: bet out, check-raise, or check-call. Let’s look at each option: Betting Out. This play is acceptable but not exceptional. By leading out, you should be able to gather some information about your opponent’s hand. If he folds, great! If he decides to call, it’s unlikely—but not impossible—that he has a pair of nines or better. More often than not, he’ll be trying to make a pair on the turn with a hand like K-J. If he calls, you should usually bet the turn no matter what card hits.

Most of Hero's equity is true equity. He will essentially never be folding before the river and turn cards like an 8 and a 9 give him 4 more outs when behind in most cases. This is clearly not a fold, but it's also not a raise! Why not? Recall from Chapter 5 on value betting that in order to bet for value Hero must be ahead of Villain's continuing range to his bet. Well, there's little difference in applying this rule here, just change the word 'bet' to 'raise'. I have one student in particular who used to automatically raise in spots like this. When prompted for his reason he'd say: "Well, because I'm way ahead!" While this is true, it doesn't legitimise a value raise. Just because we're ahead of Villain's c-betting range does not mean we're ahead when called after we build a huge pot by raising the flop and shoveling lots of money into the middle. Some very old school 2003 poker logic used to run as follows: "Hero is ahead here so he should take the pot down now." This reasoning, or lack thereof I should say, is very bad. The benefit it alludes to securing is that of protection, which as we know can be important when Hero has the best hand a very large amount of the time and where Villain is folding a good amount of worse hands that have significant equity. The problem with this logic in the hand above is that Hero doesn't have the best hand an enormous amount of the time as Villain has better Jx, two pair, sets and overpairs in his range. We are ahead quite often here, but we're also behind a significant chunk of the time too. Moreover, as we noted, Villain doesn't really have so many hands with good equity vs. us when we're ahead. The aforementioned hands with 6 or 8 outs at best are not a big part of his range. Protection is not such a good idea here and comes with a great cost. The cost of raising is that every time Hero is behind he bloats the pot considerably while also making Villain fold many of the hands he is ahead of. He gets much better value here with this frequently best bluff catcher by letting Villain bet worse hands on later streets, not by narrowing his opponent's range to the point where he's only happy if Villain folds. To raise is to say: 'Okay Villain, I'll build the pot more, but only when you have the best hand.' Raising is an abysmal play. Let's keep the 2003 logic in 2003. Decent players no longer raise here precisely because poker understanding has evolved a lot since then. That said there exist many bad players who still play this way today, just as there exist many remote tribes that still believe that the sun revolves around the earth. It's the existence of these players that keeps poker lucrative and allows people to make a comfortable living playing online poker. Hero calls 4BB.

Harrington on Hold ’em: Expert Strategy for No-Limit Tournaments Volume I: Strategic Play 1 Dedication For my mother, Alice Harrington Ladyfingers: You raised tens on lousy three-flush? The Man: That’s what it’s all about, isn’t it? Making the wrong move at the right time. From The Cincinnati Kid (1965) 2 About Dan Harrington Dan Harrington began playing poker professionally in 1982. On the circuit he is known as "Action Dan," an ironic reference to his solid, but effective style. He has won several major nolimit hold 'em tournaments, including the European Poker Championships (1995), the $2,500 No-Limit Hold'em event at the 1995 World Series of Poker, and the Four Queens No-Limit Hold 'em Championship (1996). Dan began his serious games-playing with chess, where he quickly became a master and one of the strongest players in the New England area. In 1972 he won the Massachusetts Chess Championship, ahead of most of the top players in the area. In 1976 he started playing backgammon, a game which he also quickly mastered. He was soon one of the top money players in the Boston area, and in 1981 he won the World Cup of Backgammon in Washington D.C., ahead of a field that included most of the world's top players. He first played in the $10,000 No-Limit Hold 'em Championship Event of the World Series of Poker in 1987. He has played in the championship a total of thirteen times and reached the final table in four of those tournaments, an amazing record. Besides winning the World Championship in 1995, he finished sixth in 1987, third in 2003, and fourth in 2004. He is widely recognized as one of the greatest and most respected no-limit hold 'em players, as well as a feared opponent in limit hold 'em side games. He lives in Santa Monica where he is a partner in Anchor Loans, a real estate business. About Bill Robertie Bill Robertie has spent his life playing and writing about chess, backgammon, and now poker. He began playing chess as a boy, inspired by Bobby Fischer's feats on the international chess scene. While attending Harvard as an undergraduate, he became a chess master and helped the Harvard chess team win a number of intercollegiate titles. After graduation he won a number of chess tournaments, including the United States Championship at speed chess in 1970. He also established a reputation at blindfold chess, giving exhibitions on as many as eight boards simultaneously. In 1976 he switched from chess to backgammon, becoming one of the top players in the world. His major titles include the World Championship in Monte Carlo in 1983 and 1987, the Black & White Championship in Boston in 1979, the Las Vegas tournaments in 1980 and 2001, the Bahamas Pro-Am in 1993, and the Istanbul World Open in 1994. He has written several well-regarded backgammon books, the most noted of which are Advanced Backgammon (1991), a two-volume collection of 400 problems, and Modern Backgammon (2002), a new look at the underlying theory of the game. He has also written a set of

a big one like if i could remove one error from all my friends and my students who are getting into micro stakes low stakes because low stakes casino tournaments things of that nature it's when loose passive players finally get active that's usually because they had a pretty big hand just because he had top pair on the flop doesn't mean you need to continue this would be the one i would tell them the most like it's okay to not pay off nut peddlers it's just fine you'll go home your bed's still going to be there your bagel's going to taste the same in the morning your coffee is still going to be there for you nothing bad is going to happen and once again i hope you noticed we needed 30 equity on that turn to call if you were saying we got a call there but you didn't know what equity you needed what you likely had or even just a guesstimate or anything like that if we didn't even realize like holy smokes even when we call here he still gets to see the river if we weren't thinking through all of that we were we were just getting out a lot we were just purely saying i thought my hand was good on the flop and damn it it should still be good on the fl on the turn and that's not how poker works things change all the time so here you have ace king villain 11 opens on you full color red that is time go ahead and raise it up this person calls and the board comes ace queen seven so here would you like to check our bet time is up we check here and villain 11 checks back turn is the three of diamonds would you like to check her bet time is up go ahead and fire 6.5 k and this person folds so a couple of notes here i'm trying to trying to give you some work you you were kind enough to show up here today you were ready to train so i'm here to let's get the work in i i want the work to be good you know your time is valuable so let's get as much as possible out of it so here i went for a play i went through a micro sex play i love i do this a lot in casino tournaments here so you check here and a lot of guys who are just getting into the game they think a check is like oh cool he missed and they just they fire a lot of hands they should check back here like if you got eights here with the eight of diamonds you probably shouldn't be firing that's a pretty bad board but a lot of the times you you'll be playing like a 50 100 casino tournament or just the three dollar tournament online you check to someone they go yippee skippy and they fire and you just

if you enter too many pots. Rather, you should adopt a very selective starting hand strategy. But, when you do decide to play a hand, you should proceed aggressively. This way, you win the maximum with your high quality starting hand. Also, aggressive play has the added bonus of occasionally causing an opponent to fold a hand that is either the best at that point, or would have improved to win the pot. Passive players don’t win at poker. Tip # 47 of 52 Paying attention while playing helps you learn to read hands better. To apply this tip, it doesn’t matter whether you are involved in the pot or not. You can really jump-start your game by closely following the play of hands when you are out of the pot. Not only will you develop a better handle on your opponents, but you will learn what sorts of hands tend to win in different situations. What is the number one skill that allows the top poker players to be so successful? Is it their ability to sit patiently waiting for premium cards? Or is it their great success with timely bluffs? In reality, the top players are highly skilled in many areas, but what really sets them apart is their ability to read hands*. In most cases, this skill was probably not a God-given gift. Rather, it is the product of much hard work as they progressed up to the top of the poker food chain. These top players have an ability to focus whether in or out of a hand on how the pot is played out. After enough trials, they develop a sense of what sort of hand each player is likely to have. Simply by actively paying attention in the game, you can learn to read the hands of your opponents. Here is a checklist of what you should be observing about your opponents while out of a hand: • Level of aggression: What sorts of hands do your opponents bet, raise, or reraise with? For example, some players have no problem raising with just a flush draw, whereas others only call even after they have completed the flush. Also, do your opponents bet after the flop with just ace high, or do they need a pair to fire in a wager? How often do they bluff? Do they play much more aggressively when they are in late position? Do they raise preflop with two suited cards, or do they need a pair or big ace to raise? • How position affects their starting requirements: Some players play only top-notch hands from early position. Others disregard the importance of position altogether. Learn how the play of each of your opponents is influenced by their position by observing how often they enter pots from various positions, as well as seeing what sorts of hands they turn over. • Who bluffs, and who doesn’t? Learning this can help you save some bets on the river when a known non-bluffer bets. It also prevent you from making an ill-advised laydown against

By analyzing a player’s Average ROI, we can get a better understanding of whether they are actually beating poker in the long term. The previous example is, of course, extreme as even the worst players will cash some of their tournaments, get deep and make final tables with some frequency, but it illustrated the point. However, having a high Average ROI doesn’t guarantee a player will make money after playing a number of games and, also as we saw, having a negative Average ROI doesn’t guarantee a player will lose money after playing a number of games. This is due to the high variance inherent to MTTs. Decreasing Variance and Increasing Profitability in MTTs The two main ways of decreasing variance while increasing your profitability in MTTs are to increase your Average ROI and to increase your volume. First, you should focus on increasing your Average ROI because it’s pointless to put in a lot of volume if you can’t even beat the games, so you should only increase your volume once you are certain you can beat the games you want to play. Another way to increase profitability is to play higher stakes, although this will also increase your variance because, in general, the higher the stakes, the tougher the games. So, you can expect your ROI to be reduced as you move up in stakes. Also, there aren’t nearly as many high stakes online tournaments as there are low-mid stakes tournaments, so the volume a high stakes

it may be best to instead raise because he is often on a draw and you need to eliminate the field. If your pair is JJ, TT, or smaller, it is extremely important to bet into most flops, since there are many overcards that can beat you. However, if an overcard is present on the flop and you are check-raised, you usually should give it up. Occasionally, you might look at the turn card. (This would be one of those loose calls we talked about earlier in the text.) But unless you make a set, you generally should fold on fourth street if your opponent bets. 126 Part Three: Miscellaneous Topics If an overcard is not present (thus giving you an overpair) and you are raised, you have the option to either reraise or just call (and perhaps raise on a later street). However, after you bet, if there are one or more callers between you and the raiser, then it is very important to make it three bets. By reraising, you are hoping to make the pot a two-person confrontation. In heads-up situations, you do not automatically discard your hand when an overcard flops. Suppose you have and your oppc the flop comes ent bets. If h is equally likely to bet a ten as a king, then you should of course continue to play. In fact, you might even want to raise, especially if you think there is some chance that your opponent may be betting a draw. However, keep in mind that this is a dangerous play, and to make it, you must know your opponent well. In addition, you sometimes can semi-bluff with a pair in the hole. Notice that you are not exactly semi-bluffing, since your hand has only a small chance of improvement. You are betting into overcards in the hope of folding out medium pairs. Playing Pairs in the Hole 127 For example, suppose the flop comes and you hold Your bet might cause an opponent with 99, TT, JJ, or QQ to fold - especially if he plays "weak tight." (Even if you don't succeed in getting anyone to fold, it is critical to bet your hand so that players holding overcards to your pair don't get a free card.) Again, if someone else bets or you are check-raised, you usually should fold unless the pot is heads-up and you are against an aggressive player who may be trying to run you off your pair. Remember that automatically going to the end is a big losing play when you hold pocket pairs in these situations. However, many of your poor-playing opponents automatically will make these calls, and their bad plays will prove profitable for you. Playing Trash Hands Suppose you have a hand like k+ + 1 If* i in the big blind and get a free play against three or four opponents. The flop comes: How should this "trash" hand be played? Is it correct to bet in order to stop free cards from beating you? Or is this a check-and-fold situation? The

Cutoff (CO) The player to the immediate right of the Button and left of the Hijack. The Cutoff is the second last position to act postflop.

Raise blind To raise without looking at your cards.

Diagram 19: Skill Edge (p=0.52) As Hero’s stack size increases, the slope at the point of the curve decreases. For example, the curve is steeper at 2 than at 18. The line’s slope is the marginal value of each chip Hero adds to their stack. With identical skill edge, the marginal value of each chip added is 0.05, but in the case of skill edge or skill deficit, the value function isn’t a straight line and thus the marginal value of chips added will vary depending on the total chips Hero already has. The last chip added to Hero’s stack when they have the skill edge is the least valuable (0.021). The last chip added to Hero’s stack when they have the skill deficit is the most valuable one (0.096).

range of hands, there will still be times when he folds and Hero is left out of position vs. the BU opener with no weaker player in the pot to compensate for this disadvantage. Hero must therefore be a bit stricter with his calling hand requirements in this situation. It should also be noted that vs. Aggro Fish, Hero should flat a tighter range as he's more likely to get squeezed by this player type, though close attention should be paid to how the Fish in question plays this type of pre-flop spot. Looking back to Figure 33, Hero will also have the luxury of expanding his SB calling range vs. an early position open if there's a Fish in the BB, but he'll need to be a bit more aware of reverse implied odds. In Figure 32, Flatting KQo SB vs CO to try to get into a pot with the Fish is only viable because this hand is also in fine shape against the stealer's opening range. When Hero faces an UTG open he'll need something with better implied odds that is less dominated in order to make a Fish- hunting call.

advantage that we're going to be betting most of the time right so as we see here we have 61% bet most of the time what about out of position okay now under the gun plus one raises and the button calls remember how I said from out of position you're rarely going to have a huge Advantage because the Rangers are going to be on top of each other this is one of the rare exceptions where you actually do still have a decently big Advantage but even then you can't bet every time because your opponent have a whole lot of ASX in their range as well the button calling range should be quite decent and for that reason we don't get to bet every time we are betting very often I want to make it clear 28% from out a position is not a lot of checking usually you're checking a whole lot more than this but as you see we're betting the majority of the time with all sorts of stuff it's interesting to see hands like eight seven sixes fours and two threes betting a ton you may be surpris that these essentially count as draws SL Bluffs in the spot because if you do bet one of these hands and you spike the two outer you stand to win a whole lot of chips and you don't actually have a ton of logical Bluffs I mean we already are betting most of our King queens and King tens and queen tens right so like find other logical draws there really are not a whole lot of them so we're really getting after it here and I wanted to show this example because we do have a big range Advantage you're going to find that we check a whole lot more from out of position as the Flop gets a little bit worse all right Queen 10 five all Spades interesting spot you're going to find that on this board where the current nuts is likely to be the by the river a flush right if a flush is likely to be the nuts by the river this is a spot we're going be betting small remember as the board is more Dynamic more draw heavy such that the current nuts is kind of unlikely to be the nuts by the river you usually bet bigger like in the previous spot here we're going to be betting smaller so notice here we are betting small across the board and this is a spot where I'm sure if we ran this with a one big blind bet size we're going betting a lot of one big blind bets in the spot um under the gun plus one versus the big blind notice we have a lot of flushes we have a lot of AI flush draw right this is a great spot for the initial razor and the big blind cers have a lot of off suit junk and a lot of off suit un a suited junk

determined is silly but instead of playing your normal game you decide to move up to two five whenever you get stacked three times at one two and if you get stacked at two five a few times you get really mad and move them to 510. the next thing you know you're broke don't do that make sure you keep good bankroll management you have to practice good bankroll management I have a bankroll Bible at pokercoaching.com bankroll check that out please next get off of detrimental substances is that how you spell that word get off of stuff that messes up your brain especially when you're going to go play poker uh look I'm all all for partaking and having a little party but but when it comes time to focus and play poker you really want to make sure you have a clear mind so this means not going out and partying all day before a big poker tournament or a cash game session it means even before you go to play a tournament series maybe you make a point to have a reasonably clear mind but things like caffeine actually which you know it's probably not really what you're thinking about in terms of detrimental substances uh I make a point to get off caffeine like a week before I go to play a poker tournament so that if I do need it when I'm playing a poker tournament it actually works because if you're on a lot of caffeine at home all the time and you kind of need it when you're playing poker but it doesn't do anything because you're addicted it's not gonna work right so I would generally recommend you get your brain and mind as clean as you possibly can when it is time to do anything that requires a decent amount of thought and focus and recall like poker does I'd also recommend you get in good physical shape I don't think you need to be super duper buff but you also don't want to be very much out of shape I I would recommend it against being super duper buff which I know a lot of people don't have trouble with but I see a lot of the poker players who are super duper buff and they are hungry all the time and they're eating a lot of food all the time because they have giant muscles they have to maintain right so I would recommend just being in reasonably good shape it's not even that hard to do if you just start eating kind of healthily you know get off of fatty carbs get off sugar and then you get in the gym sometimes and you know you go in there you work out decently hard you make nice sweat going you're going to be in at least okay shape and that's going to help you in life next I'd recommend you get good sleep I highly recommend you get good sleep I value sleep over basically anything else I

case. The problem isn’t that you believe you’re better than your opponents. It’s that you believe this entitles you to the pot, leading to overconfidence, arrogance, riskier plays, and ultimately tilt. If you find yourself experiencing entitlement tilt, remember: Being more skilled does not entitle you to the pot. Having a stronger range does not entitle you to the pot. You may not recognize your opponent’s skill or strategy (maybe they’re deviating to exploit you) Address the lies you tell yourself to protect your ego. illustration Revenge tilt Revenge tilt tends to be aimed at specific players. Maybe you feel targeted by some opponent, or feel that they’re trying to disrespect or single you out with their play. So you go out of your way to attack them. This causes you to change your strategy and react sporadically. 👊 REVENGE! 👊 Remember: When you seek out revenge you surrender control! You’re no longer playing your A-game. You’re playing a strategy designed to attack someone. There’s a difference between calm logical exploitative tactics, and angry vengeful tactics. Check your ego. Stay in control. Weaponize patience. Identify specific situations or players who cause you to surrender control of your normal strategy. Resolve the flawed reasons and improve the technical mistakes that led you there in the first place. Desperation tilt Desperation is hard to recognize in the moment. This type of tilt is what causes you to chase losses, overplay your bankroll, and take on way more risk than you should. Desperation tilt is arguably the most dangerous type of tilt as it can destroy your bankroll rather than your session. This is driven by the typical gambler’s fallacy of gambling to break even by taking higher risk lines or gambling outside your roll to get unstuck. It’s exacerbated by an inherent human bias to focus on the negative that assuages our ego. “I’m good but unlucky” causes less damage to our ego than “I’m not good enough”. Desperation tilt is incredibly dangerous . If you regularly experience symptoms of desperation tilt you need to take immediate and non-negotiable steps to mitigate it: Have a sense of urgency – recognize desperation tilt before it becomes full blown. Set a strict stop loss – combine with other prevention methods for maximum effectiveness. Develop an emergency response – Shut down your session before it snowballs. Other types of tilt Below we cover other common types of tilt not addressed in the first Mental game book: Scared Money This is a conscious decision to play defensively out of fear of losing money. Fix this by using proper bankroll management. Winner’s Tilt More common than people realize. When you run extremely well you’re more likely to take on tremendous risk and overplay your hands. Learn to recognize when you’re running hot and check your overconfidence. Dissociation Tilt A very common zombie-like autopilot state that leads to random button clicking and a lack of caution. Distraction Tilt Not giving your full attention to the game. Caused by multitasking (e.g. watching videos or on social media while playing). This prevents

is not really a problem because you will simply fold and lose a pot you were going to lose anyway. Lighter check-raises are how the BB punishes you for continuation betting too often . If your opponent rarely makes such raises—a trait especially common to many live recreational players especially—then you can and should exploit them by betting more aggressively yourself. The first and most important exploit is simply to bet much more often . Getting the solver-approved sizing right is a very secondary concern. Betting small with your entire range is a good first approximation that will capture most of the value of this exploit for you, so don’t worry if you aren’t confident about when to bet larger. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny

easy for you to hit your hand but still lose because you have made a second best hand. You should also discard any of these if one of the limpers, particularly the first player in, is known to limp with very good hands. However, against bad players who will come with many hands they are definitely playable. If you are dead last - that is, if you are on the button - and there are already callers, you can play hands in Groups 1-7. If you have a small pair and are against four or more callers, the correct play is to sometimes raise. This is another example of making the pot larger so that if you hit your hand, your opponents may be more inclined to call you with just overcards on the flop. In addition, they all may check to you, thus giving you a free card and another (small) chance to make your set. Also, this play is sometimes correct with small suited connectors. Again, don't get carried away with these plays. But making them occasionally can be very effective. 38 Part One: The First Two Cards If you are on the button, a lot of players are already in, and the pot is not raised, you can call with many additional hands. This includes those hands in Group 8 and even hands as weak as: The reason for this is the tremendous implied odds that you will be getting if the flop comes just as you would like it to come. However, don't take this idea too far. It is unlikely that it would ever be correct to call with a hand like: As already mentioned, if no one has called, you can raise the blinds from the last position (button) with any hand in Groups 1-8. With a hand like an ace with an unsuited weak kicker, you still should raise the blinds if they are either very tight or very weak players. When we say weak, we are referring to a player who will let your ace win in a showdown. For example, suppose you raise with something like The First Two Cards: Late Position 39 and are called by the blind. If this person is willing to check on the river with nothing, even ifyou show weakness by not betting on the turn, then he is the type of player you would be happy to play a lone ace against. The same caveat applies to a hand like Kx, but even more so. That is, against typical opposition, usually pass with Kx. However, if you do play a hand like Kx on the button, make sure that you always raise. Never just call the blind if you are the first one in. (There is an exception to always raising with Ax or Kx if you play them first in on the button. See "Part Five: Playing Short-Handed" - "When the Blinds are Very Loose" on page 197) The First Two Cards: Live Blinds Playing your first two cards out of the blinds is very different

10.2 Linear 3-Betting The figure below is an example of a linear range. Note the difference in shape and lack of segmentation into subranges.

Passive A style of play known for very little betting and raising, and a high frequency of passive actions like checking, folding, and calling.

Cinch: The best possible hand, given the cards on board, when all the cards are out. 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. Community cards: The cards dealt face up in the center of the table that are shared by all active players. 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. 316 Appendix B: Glossary 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 out: To improve your hand so that it beats an opponent who had a better hand than yours prior to your draw. Double belly buster: See Open-ended straight. Early position: A position on a round ofbetting 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. 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. Family pot: A pot in which most of the players at the table are involved. Fifth street: The fifth and final community card on board. Fill: To draw a card that makes a hand. For example, to fill a flush is to draw a fifth card of that suit. Appendix B: Glossary 317 Fill up: To make a full house. Flat call: To call a bet without raising. Flop: 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. 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: The fourth community card on board. Free card: A card that a player gets without having to call a bet. Free roll: A situation where two players have the same hand but one of them has a chance to make a better hand. Full house: Three cards of one rank and two of another. A4AVA+949V is a full house.

not be certain your hand is good to make raising correct. You want to make it difficult for players behind you to remain in the pot. Raising serves to protect your hand; that is, it becomes very expensive for opponents to stay in the hand with you, and they will likely fold. This generally increases your chances of winning the pot, and that is a good thing. Don’t Give Them Odds to Call Suppose you have K-Q and the flop comes K-9-5. You flopped top pair. If the player to your right bets and you are next (with a few players yet to act), you must raise here. Yes, it is possible you are behind. The bettor could have A-K or 9-9, for instance. However, most likely you have him beat at this point. The problem with just calling is the players behind you. If you call, they will probably call as well with hands like Q-J or A-9. Raising here relates to the concept of pot odds. You don’t want to call and give your opponents a favorable price to overcall in an attempt to draw out on you. Rather, raise and take away the value of their hands. They may choose to call anyway, but you have done your part. They are throwing money away if they call — throwing it away to you. Don’t give your opponents the proper pot odds to draw out on you. Build a Pot Another reason to raise a bet to your right when you feel you have the best hand is to build a bigger pot. There is nothing wrong with getting more chips to the center when you have the lead. Aggressive play will enable you to win the maximum with your good hands. Don’t Slow-Play Some players choose just to call on the flop when they have a big hand such as a set or a straight. They want to wait for the “expensive” rounds to bet their hand. Slow-playing* can cause problems, however. First, doing this will occasionally cost you the pot. By just calling, you may allow an opponent to see a cheap turn card that produces a miracle** straight, or helps him develop a good draw. Then, when you do later decide to put some chips into the pot, you may find to your dismay that you are the one who has been trapped. A second reason not to slow-play is that players in lower-limit hold’em games typically call anyway. Why play deceptively when you don’t have to? Slow-playing is generally done in an attempt to gain later action on a hand you feel you won’t be able to get any action on if you play it aggressively right away. However, you rarely run into this problem in the games we’re talking about, so go ahead and raise if someone bets. Tip # 19 of 52 When a player in front of you has bet, it's fine to call with a good draw or a medium-strength hand. Although taking a raise-or-fold approach is typically the best way to

my hours and i know what i spend my time on and that is a deliberate choice you can get one of a hundred apps that will help you track time and you should do that back in the day i used to do it with pen and paper but you can get these really cool apps where you you just click a button and say i'm doing this right now i'm working or i'm doing this right now i'm about to go to bed i'm sleeping you click the button and it'll track the time the funniest thing is people who say i work 60 70 80 hours a week they start doing this and they find oh it's like if you get them like really like when you're at work like turn off the work timer when you're at a coffee break or out to lunch with friends or you know a big group of us are going to get coffee even though we just got in at 9 30. there's people that find out they're working 28 hours a week and they're saying i'm out of control i'm so busy it's like we could curb this a little bit here what should you do we're going to check and it gets checked again the river is the ace of hearts it gets checked to you would you like to check or bet poker players should get those apps because a lot i hear this ass all the time i don't have time to study they everybody has time to play nobody has time to study you ever find that interesting i i make them track their hours and we end up finding out they they watch tv 20 25 hours a week which is by the way it's your life do whatever you want but take that tv watching time and may instead of it being 20 hours make it 16 and then just put four hours in this study we're going to check here and they check back why what should you be thinking of here there's always something going on in a hand what should you be thinking of here if you bet out of position you have to ask yourself am i willing to fire three streets if you're not willing to fire three streets that means at some point you are going to check and you are going to cap your ranch and you have to ask yourself if you're prepared for that now if you're ever playing on america's card room i wouldn't recommend or anytime you're playing with more aggressive players i wouldn't recommend capping your range if you can avoid it so we can't really go for three streets here because you have to ask yourself what one of the kids call it now value targets what are your value targets tens nines are they calling three streets probably not now here if you said i'm gonna bet and then i'm gonna bet again what's your issue i'm not saying that's bad

It costs you $80 to call a pot of $355. Your pot odds are about 4.5-to-l. 2. To improve your hand on the very next turn, you have to catch one of the six remaining aces or kings. You've seen five cards so far, so there are 47 cards you haven't seen. Six of those are good for you, 41 are bad. Your odds against improving on fourth street alone are about 7-to-l against, much worse than your pot odds. 3. If you don't improve on fourth street, you'll usually face a bet that you won't be able to call. So it's mainly the odds of improving on the next card that you care about, not the odds that you might improve on fourth street and fifth street combined. (Those odds are about 3-to-l against.) 4. Your opponent might be bluffing. 5. Your opponent might have flopped a set, so you can't win even if you hit. He might also have a holding like ace-jack or king-jack, which beats you now and negates some of your out cards. Early in a tournament, and lacking any information on your opponent's style, you should probably assume that the chance he's bluffing roughly cancels out the chances that he has a hand you can't beat, and treat this directly as a pot odds problem. You're not getting the pot odds you need to call, so you're done with the hand. Action: You fold. Hand 4-4 Situation: A few hours into a major tournament. The players are a mixed bag, but tend to be conservative. The small blind is a tight player who suffered a couple of bad beats about an hour ago. Your hand: 5♥5♠ Action to you: Players A and B fold. Player C calls. Players D and E fold. Question: What's your play with this hand? Answer: A call here in good position is reasonable with a low pair. Your goal is to see a cheap flop and hit a set, after which you'll just need to figure out how to extract the most money from whoever is left. In addition, you may end up with position on your opponent, which might let you win the pot if you don't hit a set. If you don't hit your set and anyone shows strength, you'll need to beat a quick retreat. Action: You call for $100. The two players behind you fold, but the small blind goes all-in for 69 his last $500. The big blind and Player C now fold. The pot is $850, and it costs you $450 to call. Question: What's your action? Answer: The pot is now offering you slightly less than 2-to-1 odds on your money. Before you just shove your chips automatically into the pot, let's see if we can't do some simple calculations that might tell us if your call is clearly correct or not. First question: What hands might your opponent have gone all-in with? We noted that the small blind was a tight player. We also noted that he lost most of his chips an

all in on us very easily villain eight could move all in on us very easily villain 10 could move on all in on us very easily even villain 11 could possibly do it we're not going to see the flop that often and again i'm just going to keep saying it when you try to isolate these situations when it it sounds really you know like big high floating words like database analysis or whatever all it is is collecting [Music] you could do the same damn thing with a pen and paper just writing down the results of every time you do something and then averaging out the totals and see what it is and essentially all the software does is do that for you with hand issues and yeah it's just something i see all the time which is guys call here all the time and you you'll see them be negative 50 big lines negative 100 big blinds for every time they run that because if they fold it they'd just be negatively annie that's fine but what ends up happening the reason they lose so damn much is because somebody moves all in on them so often and then if you hit you're six or seven even if everybody folds behind you which would be great and now you hit your six or seven the big stack did open under the gun it's not unlikely he'd have a big card he connected with too so you don't even know if you want to connect with that so just taking that back to fundamentals folks so let's go ahead uh villain three in this situation uh villain three has been a little active and you have king jack off suit on the button what would you like to do here now that villain 3 has opened okay time is up if this one more time guys is going to be full so many times people are playing micro six tournaments it and it's very fun to get there get involved and to go after it and things of that nature and they'll say like oh i've seen this guy open a few times before you know we've only played like 11 hands and they've raised like four of them this guy's clearly a psychopath it's a little bit more likely the guy just picked up a few hands you know it's a it's really fun to say oh he's active okay i'm on the button oh i got to do something it's not necessarily the guy's still opening under the gun now if you if i had told you like i just saw this guy open six three suited from middle position or something like that in that case what do you do at that point you could three bet you could attack a little bit you you want to re-raise isolate when you have the best hand so typically when you have the best hand in your imposition you want the person to play a big pot

blind to your hand. This, by the way, makes your hand completely blindto your opponents as well, because your bet sizing isn’t connected to your hand in any way beyond the hand being playable or not. Now, while I know you’ll never again make the mistake of pinning your raise to your card strength, your opponents routinely will, so it’s worthseeing what happens when they err in the name of “mixing it up.” Your opponents fall into two groups, loosely defined as “amateurs” and “pros.” Let’s look at each one in turn. There Are Amateurs Amateurs raise big with hands they’re afraid of, hands they really don’t want to take to a flop. Two 8s is a great example of that. This hand hates overcards and rightly so, since the majority of the time, at least one overcard will flop and then pocket 8s can get hard to play, especially against several opponents. The problem for most players is that while they’re scared of a hand like 88, they also know they’re supposed to play the handand they’ve probably read somewhere they should raise with it. But their fear of the hand causes them to raise too much; they desperately want all their opponents to go away. They raise big, realizing somewhere in their reptilian brains that they might face hard decisions after the flop if one or more people play with them. Their way of making aneasier decision is to try to chase people out of the pot by raising big with their weaker, more vulnerable, 88 or AJo or KQ. Ah, but on the flip side, when they’re really strong, when they have a hand like aces, then they raise small. They don’t, you recall, want to scare off the customers. They’re greedy and they know that if everyone folds to their raise with aces, they’ll want to cry and cry and cry. Let’s see how wrong-headed that thinking is. Say that in the name of “not revealing the strength of your hand” or “mixing it up,” you limp with aces in early position. Obviously, you’re hoping to limp and then re-raise, but all that does is turn your cards completely face up and let a hand like AQ make a good fold. If AQ raises your earlyposition limp and now gets re-raised by you, that hand surely knows to fold, because your hand screams strength. So all you got is the one raise out of your play, six chips in a one-chip/two-chip game. However, if you open for a raise like you do with any other hand, with a raise that’s blind to the strength of your hand, AQ doesn’t know where you’re at. He’ll certainly call, so the pot’s guaranteed to be as big as it would be if you limped withaces. But maybe he’ll re-raise, giving you a shot at his whole stack if he looks like he’s pot-committed. Certainly, the open raise is more profitable against real hands than limping and re-raising. But you’d still be sad if you raised and he folded, right? Don’t be.

aces, and you may win a huge pot. You can still reraise with kings, however. Sometimes one of your two opponents will be holding a pair of aces, and you'll be a happy. But many times the two players are holding queens and aceking, or something even weaker. Raising with the kings will all show a profit in the long run. QQ: A pair of queens is usually worth a call here. If you don't improve on the flop, or you end up facing an all-in bet, you'll have to make a tough judgment call. But enough oddball situations can occur to make the call a reasonable play. Long ago I saw a hand with a pair of queens all-in before the flop against three other players. The other three players all turned over ace-king! The queens held up. All other hands: Fold. No matter what else you have, you don't belong in this pot. 89 Case 5: You are on the button. Three limpers in front of you. This situation occurs all the time on online play, but not so much in live poker. It presents some interesting opportunities that the other situations do not. AA through TT: Raise strongly with these hands, perhaps four to five times the big blind. This is a great situation for you. Your raise will often be mistaken as an attempt to steal the pot from some hands that haven't shown real strength, and you'll sometimes find yourself reraised by the small or big blind. 99 through 22: With these hands you should just call. If you flop trips you can look forward to winning a big pot. If not, you can let the hand go without having invested too much. AK, AQ: With ace-king you can raise whether the hand is suited or unsuited. With ace-queen I would usually raise only with a suited hand. I'd usually just call with ace-queen unsuited. Ax: With ace-jack and ace-ten I would call whether the hand was suited or unsuited. With a kicker smaller than a ten I would call if the cards were suited but fold them if they were unsuited. There's too much danger that one of the limpers holds an ace-small combination as well. Suited connectors: Suited connectors are a great holding in this situation, and I would call with all the connectors down to five-four suited. You have a chance to see a cheap flop with a big pot, which is giving you the right odds and position for your suited connectors. Before playing your suited connectors, make sure that the limpers aren't on short stacks. It's the big implied odds when you hit your straight or flush that makes this an attractive call, but if your opponents are short-stacked, you won't be able to win enough chips to make the play worthwhile. Unsuited connectors: In this situation I would also call with the unsuited connectors down to five-four. I'm hoping to hit a straight or a straight draw, and I'm not paying much to do it. The big implied odds when I

happens after you call and win? The bubble is over, everybody loosens up, and your chip lead is not as impactful. There is a strong case for folding the Pocket Aces here and prolonging the bubble. The micro-stacked Small Blind isn’t going to post their big blind for almost an orbit, and there is a very good chance you can win a lot of uncontested pots before the bubble eventually bursts. In the early days of SNGs Sit and go A poker tournament with a specified number or maximum number of players that starts when a certain number of players have registered. Unlike regular tournaments, which started at a specified time. this was a legitimate strategy enjoyed by good players on the bubble. They would give the micro stack a walk Walk When all players fold preflop, the hand is over and the big blind wins the small blind. The big blind is said to have received a walk. because the bubble was where they made the most EV Expected Value (EV) The anticipated value one expects from any hand, position, or play. EV is calculated as a weighted average of all possible outcomes weighed by the probability of each of those outcomes. , so the longer it went on, the more profitable it was for them. The importance of covering people This brings us to Progressive Knockout tournaments. PKOs are already so complex they will never be completely solved, especially when you factor in this skill of table management. Covering people in PKOs is so crucial that it is often correct to take significant risks to get the chip lead at the table, and sometimes correct to pass on good spots to maintain the chip lead. This is never more true than the very first hand of a PKO , where the Bubble Factor of every player is 0.82. If you have read our article on Bubble Factor you will know that this means it is correct for two players to get all-in against each other with as little as 45% equity without any extra dead money in the pot. This is unheard of in regular MTTs and is even wider than identical ChipEV spots. The result is a “negative risk premium”, as shown below. The reason for this is that there is so much more upside to winning the hand than in regular MTTs. You essentially win four types of equity: The ICM equity from the regular ‘payout’ portion of the prize pool. The immediately realized equity for winning the bounty. The potential future equity of winning more bounties because you cover everyone else at the table. The potential future equity of winning your own bounty when you win the whole tournament. Covering players at your table in a PKO makes every hand more profitable. How much more profitable is it to cover your opponents in a PKO? Let’s look at two similar spots from the GTO Wizard database to highlight this. In both these examples, we are looking at a PKO spot with 70% of the field remaining, the

adjusting it for any equity and other bonuses he'll realise when we flat his 3-bet. Our goal is to make the addition of 3-bet bluffs to Villain's range a 0EV one. This means that Villain needs to be hitting his adjusted RFE on the 3-bet bluff exactly. When we call the 3-bet and go to the flop, even Villain's weak 3-bet bluffs like 64s will sometimes flop equity, win at showdown, be able to make +EV c- bets, and so on. Villain's RFE will need significant adjustment for these advantages. We'll estimate that Villain needs 10-15% less fold equity than the risk and reward calculation first indicates. Of course, not all of Hero's continuing range will be hands that he calls with. He will be 4-bet bluffing sometimes too and claiming the entire pot right away against the weaker parts of Villain's 3- bet range when he does so. So in our model hand, Villain risks 8.5BB (9 - 0.5 SB) for a potential gain of 4BB (dead open + SB + BB) RFE = 8.5 / (8.5 + 4) = 68%. Let's reduce this by 10-15% compensating for the aforementioned bonuses those times we flat and make the rough estimate that Villain ceases to profit from adding extra bluffs to his range when Hero folds 55% of his range or less. The minimum defence frequency then is 100% minus the amount Hero should fold and so MDF = 45%. We'll keep this rough benchmark value in mind and try to emulate a strategy that folds roughly this much, but where all of its non-folds are +EV in a vacuum. Hero's CO opening range contained 338 combos. He must look to defend 45% of that range in some way in order to get close to a balanced strategy. 45% of 338 is 152 and so this is how many combos we need to defend. These 152 combos will need to be split between +EV 4-bets and +EV flats. We'll also need to take care to ensure our 4-bet bluffing range doesn't start to dwarf our 4-bet value range or else we become exploitable to light 5- betting and do away with balance - the very thing we're aiming at. Let's separate the CO opening range into subranges that meet all of these requirements and then talk about why we've chosen each hand for each job. Building A Strategy Our opening range will now be split into the following four parts, from strongest to weakest: 4-bet/call Call 4-bet/fold Fold

Diagram 46 Table 111: IP Metrics by Flop Structure Diagram 47

the pot and they call with Queen nine of Spades what have we accomplished there so it's not that we incentivize the big blind to stay in the pot pot because we'd rather bet small ace Jack just bets small here doesn't want to bet big why the bigger we bet the more they fold and therefore the more we narrow their range to Stronger hands this board is connected and has a flush drop so the bigger we bet the more likely the opponent just has Queen nine of Spades King three of Spades Queen three of Spades baits uh seven six of Hearts 63 suited how is Ace Jack doing against those hands is it dominating them or is it flipping against them it's flipping so you don't get any value so we need a bet small to allow wider hands to come in to in order to get value with Ace Jack so one of the biggest mistakes I see with bet sizing and I want you to pause this if you're watching the recording and relisten to this like three times CU this might be the probably the most important thing in this webinar the more connected and flush draw the board so if there's a flush draw on the board and it's connected as in there's a lot of open-ended straight draws possible you don't want to bet big because you're narrowing their range too much to combo draws and strong draws that if you have like even if you have like kings here you're just going to narrow the range to too many combo draws that are doing um really well well against your Ace Jack King Jack pocket queens now if I made this to like a four of Hearts different story because there's no flush draws now or if I made the four of Spades the deu of Spades different story because there's less straight draws now so if you were here last week it was the same mistake I made when I had Queen nine of diamonds on versus a small blind and I bet big on Jack five on Jack 54 two diamonds and I wasn't supposed to bet big because I just narrowed the small blinds range way too much to ace high and King High flush draws and open-ended straight draws so we can look here at 853 twoone it's kind of different it's not as so we have a lot of straight draws a lot of FL a flush draw but the issue is here which we have um overpays right so this has kind of got two things going on where it's a flush drop board we're probably not going to like so you okay here we go you see there's kind of two strategies going on here now on 853 when we added the flush draw here we still want to bet big with these hands that need like pocket 9ines pocket 10s Jacks Queens like we need a lot of value and protection however there's a

Figure 12 - When the BU's a Nit For this dynamic adjustment we are going to revert to exactly the same sizing strategy we'll be using on the BU itself. As explained in the next section, we'll be opening for 2x where the blinds are Regs or Nits and for 3x when there's a Fish in the SB or BB. Where there is a mixture of these conditions in place, or if the degree of Fishiness is less, we'll settle on a 2.5x open. See this section for a full explanation. With 3-Bettors Ahead Just as in the HJ, we're forced to tighten up here and reduce the amount of steals in our range when faced with this threat. The situation is more severe when the light 3-bettor is on the BU as defending out of position is generally pretty difficult to do with any kind of wide range in a +EV manner - even with a reasonable skill edge post-flop.

as superintendent of schools or at least a principal. It didn’t work out that way. In fact, the top job offered to me was that of a basketball coach at Dalhart (Texas) High School at a salary of $4,800 a year. It didn’t make sense; I was making more than that just playing poker. I used to travel around to the different colleges in Texas setting up games and making a fair living by my wits. At that time, however, the idea of becoming a professional gambler had not occurred to me even though it was apparent I played better than most. After graduation, I went to work as a business machines salesman, a profession that ultimately could have made me some twenty-five or thirty thousand a year—or so I thought. But it wasn’t in the cards. My first day on the job, I called on a few prospective accounts. I didn’t get much further than the front door, and I wound up in a poker game before the day was out. It was a seven-stud game where I cleared a month’s salary in less than three hours. 16 “My God,” I thought, “what am I doing trying to sell machines nobody wants to buy from me when I can sit down at a poker table and make ten times the money in one-sixth the time?” It didn’t take me very long to figure out what to do. I quit the company and began my career as a full-time professional poker player. I’ve never regretted that decision. Turning Pro The first games I played that amounted to anything were down on Exchange Street in Fort Worth, Texas. I’d be surprised if you could find a tougher street in the whole world. There were shootings, muggings, robberies, and just about every kind of violence imaginable. The stuff we see on TV today is tame compared to what Exchange Street was like almost any hour of the day. But at the card table, amidst all that violence, everything was as gentlemanly as could be. They were two different worlds. My buddy Dwayne Hamilton and I frequented a card room run by a gangster named Tincy whose main claim to fame was having killed half a dozen people. He ran an honest game, though, and Dwayne and I did fairly well. No-limit hold’em was our main game. After we accumulated a good-sized stake we moved uptown to the three hundred and five hundred buy-in games where we played with doctors, lawyers, and other professional people. For the next five or six years we made the Texas circuit, playing bigger and bigger games throughout the state. Occasionally we’d drop into the big games in Oklahoma and Louisiana. During this period, I met Amarillo Slim and Sailor Roberts, a couple of the finest poker hustlers I’ve ever met. We hit it off from the start and after Dwayne moved back to Fort Worth, Sailor, Slim, and I decided to go into business together. We must have hit every town in Texas, relieving the locals of their money.

give up. I’m done with the hand.” When this guy checks, now you have to decide not only whether your hand is worth betting, but also whether he’schecking because he’s done with the hand or he has evil ideas about what he’ll do if you bet. This is often where people make a certain mistake, interpreting that river check as weak and betting too liberally with a hand that either loses a showdown or faces a big raise. Word of warning. On theriver, “Check” doesn’t equal weak, especially when your opponent is feisty. In Position, Aggressive Player Checks to You, Strong Hand Keeping in mind that check doesn’t equal weak against aggressive opponents, what do you do when your hand is strong, you suspect your aggressive opponent is also strong, and he checks into you? You might think that after I’ve put all these thoughts of monsters in your head, I’ll say, “Check behind,” but instead, you bet and generally bet big. You think you have the better hand, right? And you know he’s strong, so you know he’ll pay you off. But wait! He’s aggressive. Maybe he’s checking to induce a bluff. A small bet here might tell the story of a stab at the pot and get a raise out of him. However, it might also look like one of those famous desperate-not-to-miss value bets, and therefore be read as strong. That will get you a call for sure, but probably not a raise. A bigger bet, though, can be interpreted as a please-don’t-call bet (aggressive players love to make this judgment) and induce the raise you’re after from your strong opponent. And even if that bet gets flat-called, you still get more out of him than youwould with a small suspicious bet. Remember, you’re looking for the biggest bet your opponent will at least call here. Since you read him for strong, he’ll probably call any bet. So why not make it bigger? The small bet, the “sure-value” bet, really only gets good value if it induces a raise. If you know your opponent loves tocheck-raise the river, by all means go for the smaller check-raise-inducing bet. If you only get called, though, you definitely lost value. With the big bet, you might get the raise, but you’ll definitely get the call, and for a larger amount than the “sure-value” bet would earn. Now, let’s give you the same strong hand, but you think Mr. Aggressive is weak to medium-strength. Here, you bet the biggest amount that will get him to make a heroish call. That might be quite small, where he just figures he’s getting a good price. Or it might be quite big, if he’s the typewho interprets big bets as weak. You have to decide, knowing your opponent, how big you can go. To hit your target of the maximum amount you think he can call, don’t look so much at the size of the pot, but rather at the size of his stack. Very often, particularly in tournament situations, players’ willingness to call is less

your hand is equivalent to the high end of the raiser’s range, go ahead and re-raise. You’re happy to pick up the pot right there and not have to play the hand out of position and you can actually narrow the field with the re-raise by knocking out the big blind. For these tworeasons: WHEN YOU HOLD A REAL HAND IN THE SMALL BLIND, RAISING IS IMPERATIVE Honestly, even if you’re giving away the strength of your hand, you really don’t mind. Your best outcome is when everyone folds, not when youextract value from a big hand in bad position. That’s an ugly situation, and even pocket aces don’t make it significantly less ugly. So let them knowyou’re strong. Encourage them to fold, or at least to know that they’d better hit their hand, because you’re definitely betting something real. The only exception is in playing middle pairs against an early-position raiser. With those hands, it’s almost always correct to flat-call from the small blind. You know the early-position raiser has a very good hand, so a re-raise there would be imprudent. You can call, look to hit the set, and fold if you miss. Play the hand cheap for a big payoff instead of risking a re-raise against someone likely to be strong. Against a late-positionraiser, with his much wider range, you can try to win the pot right there. With your pair, you’re probably raising with the best hand anyway. Another good example of how the raiser’s position affects your small-blind action is with a hand like AJ. Against a solid early-position raiser, folding that hand in the small blind makes a ton of sense. You don’t want to call and play out of position when your hand is likely behind or even dominated. And re-raising would be unwise against a player showing strength. So you fold. The situation changes if the raise comes from late position where the raiser could have anything, and a hand like AJ would likely be at the top of his range. I’ll fold that AJ to an early-position raiser with a tight range, but likely re-raise against a button raiser to try to win the pot right there. He could have anything or nothing at all and when Ire-raise there, I expect to do so with the better hand. Notice that calling isn’t an option. Now, the big blind plays differently from the small blind. When it’s raised by someone in the field and folded around to you, you’re already headsup against the raiser, so re-raising can’t narrow the field short of ending the hand, which is unlikely, since re-raises from the big blind carry less clout than re-raises from the small blind. Why? Because whenever players act with even one player left to act behind them, that player’s raises areperceived as stronger; the assumption is that the player must have something to raise when someone is still left to act. In a sense, the small blind’sre-raise leverages the presence of the big blind to gain more respect. The big blind’s re-raise doesn’t get

player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout)

Hand Range 174: BB vs UTG 4-bet (40bb) • Call 50.1% / • Fold 49.9% Defending the BB Versus IP (60bb)

Poker subsets and abstractions No Limit Hold’Em is an extraordinarily complex game: a truly accurate representation of the game consists of more nodes than there are atoms in the universe As a result, players worldwide have sought to create simpler game models to minimize the computational requirements of solving poker. These gamespace simplifications are “abstractions”. What is an abstraction? An “abstraction” is a way to simplify the game of poker. This game is so complex that we must reduce the gamespace to solve it. There are a variety of methods used to do this: Using subsets of flops to represent the full set of flops (preflop solvers) Bucketing similar hand classes together (preflop solvers) Limiting the available bet sizes (pre and postflop solvers) Applying betting caps (pre and postflop solvers) What is a subset? There are 22100 possible flops in Holdem, out of which 1755 are strategically different. This is a huge number, so programmers and poker pros have worked to reduce this number to make poker easier to solve. A “subset” is a collection of strategically chosen flops representing the full set of all possible flops. Preflop cannot be solved independently; it is inseparable from postflop poker. Preflop strategies are generated as a result of trying to optimize postflop EVs. Preflop ranges are constructed to create the most +EV scenarios with each individual hand on later streets. With 1755 strategically different flops, the preflop game tree becomes exponentially larger than postflop game trees. Flop subsets were created to simplify the solving of preflop. These subsets are designed to accurately calculate postflop EVs by representing a wide variety of different flops. Each flop is assigned a weight. You can take the weighted average EV of each combo across every flop in the set to approximate preflop EVs. Preflop cannot be solved independently; it is inseparable from postflop poker. Preflop strategies are generated as a result of trying to optimize postflop EVs. Preflop ranges are constructed to create the most +EV scenarios with each individual hand on later streets. With 1755 strategically different flops, the preflop game tree becomes exponentially larger than postflop game trees. Flop subsets were created to simplify the solving of preflop. These subsets are designed to accurately calculate postflop EVs by representing a wide variety of different flops. Each flop is assigned a weight. You can take the weighted average EV of each combo across every flop in the set to approximate preflop EVs. In other words, if you know the EV of each combo on every flop within a good subset, then you’ll be able to work out good preflop strategies. The first attempt was by Will Tipton , who used human logic and math based on frequency restraints. The next major attempt was done by Piosolver . They actually solved all 1755 flops, comparing subsets to the full solve. We credit Piosolver for the subsets used in GTO Wizard . Click on this link to see all flops represented in those subsets. How can I use subsets in GTO Wizard? GTO Wizard has solutions for all 1755

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Hopefully, you recognized this example as another where fold equity pre-flop is not our primary concern. It's true that our success rate here is estimated at a meager 50%, but there are two important reasons why this is a mandatory open. The Fish in the BB folds to a large number of c-bets meaning that Hero doesn't need much in the way of hand strength or pre-flop fold equity. BB is also likely to be a weaker player meaning that if Hero does connect well, Villain will often make mistakes with marginal hands, increasing Hero's value betting prospects those times when Villain has flopped a second best hand. The Nit in the SB is rarely getting in Hero's way. He gets to play in position vs the Fish, or else win the blinds, a huge majority of the time. Again, sizing needs to shoot up to take advantage of the Fish folding a lot post-flop. The bigger the pot you build, the bigger the pot you win, but of course you still want the Villain in the BB to call pre- flop if he's going to play so meekly post-flop. Hero opens to 3BB.

percent or better, you are getting the correct price from the pot to make the call. The more certain you are that you have the best hand, the more likely you should raise, particularly if there are some logical hands that your opponent might have with which to call. The water gets murkier when you hold a longshot hand. Here, you need to know the size of the pot, so you can accurately assess the price you are getting. For example, if there is $72 in the pot and it costs you $8 to call, the pot is laying you a price of 9-to-1. Your hand needs to win only one time in 10 for calling to be correct. So, not only should you know how much is in the center, you should also be able to make a good estimation of your chances of winning the pot. With practice, you can develop this skill. The lesson of longshot hands is that you can call fairly often on the river if you feel you have a decent chance of winning the pot. You need not be correct every time, or even most of the time, for calling to be the proper play. At the same time, make sure you are realistic. Don’t throw money away in situations in which your opponent is 95 percent certain to have you beat. Experience and focus in the game help you become skilled at accurately determining your chances of winning the pot. Tip # 40 of 52 Bet the river with the best hand. This might seem like an obvious statement, but it is amazing how often hold’em players check the winning hand on the end. They may think, “the pot is big enough,” “I’d better check just in case someone caught that third four,” or “I doubt anyone will call me, so I may as well check.” The problem with this is that the pot is not big enough, that four on the river is probably a safe card, and someone will call. It is very important that you do not leave money on the table*. You must bet the river when you have the best hand, and collect those extra calls that your curious opponents will bestow upon you. This is one of the few times in poker in which you can bet and get a call from a player who has no chance to beat you. So, take advantage of the opportunity to bet the river for value. When you are first to act, you should bet if you feel you hold the winner, because you are apt to get called by slightly worse hands. However, if you check, these hands might then check right behind you. The exception to their checking is those times that they outdraw you, in which case they would bet and you would probably call. So, those times you hold the winner, you cost yourself a bet or two by checking to your opponents. However, you still lose a bet those times you are beaten. Tip # 41

Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. They’ll tell you that you’re playing range-vs-range, and that you need to think about your overall range rather than only looking at your hand. While this is undoubtedly good advice, it leads to a widespread misconception about the nature of poker. So, at the end of this article, you may look at poker strategy in a new light. Fixed vs Dynamic Strategies Firstly, we need to understand the difference between fixed and dynamic strategies. A dynamic strategy adjusts to its opponent. Therefore, a dynamic strategy can change over time. Exploitative strategies are dynamic. A fixed strategy will not adjust to its opponent. It simply plays the same strategy no matter what. GTO is a fixed strategy, always playing its range the same way given the same spot. This distinction is important because it tells us about the nature of indifference, GTO, and exploitative poker. Mixing mistakes vs pure mistakes There are fundamentally two different kinds of mistakes in poker: Mixing mistake – Only loses EV if the opponent adjusts. Incorrect frequencies. Exploitable by an adaptive opponent. NOT punished by fixed strategies. Pure mistake – Lose EV even if the opponent doesn’t adjust. Taking an action that strictly loses EV against the opponent’s strategy. Loses even if the opponent doesn’t change their strategy. GTO strategies gain when your opponents make pure mistakes. However, GTO, a fixed strategy, does not adapt to gain from its opponent’s mixing/frequency errors. When a hand mixes between actions, e.g. raise or call, those actions should theoretically always have the same expected value (against the GTO strategy). This is the definition of indifference. Therefore, changing the frequency of mixed decisions shouldn’t effect your return – so long as your opponent’s strategy stays the same. The calling station experiment Two GTO bots play a HU match (no rake). Bot 1 – Always plays a precise fixed GTO strategy. Bot 2 – Also plays GTO, except they always CALL any hand that’s indifferent between calling and some other action. Which bot has the edge? Click here to see the answer The answer is neither! The calling station bot is calling indifferent, it’s not making any “pure mistakes”. Bot 1 is playing a fixed strategy, and will not adjust to exploit it. Bot 2 is exploitable to value-heavy strategies but doesn’t lose EV because Bot 1 never adjusts. That’s the nature of equilibrium. You can replace the calling station bot with one that always raises any hand that’s indifferent between raising and any other action. We can call this the maniac bot. Maniac Bot, who’s only ever making “mixing mistakes” and never makes pure mistakes, will not lose or gain anything against the GTO strategy. The same goes for Nit Bot – a bot that plays GTO but always folds any hand that’s indifferent between folding and some other action. Nit Bot won’t lose anything against the fixed GTO strategy either, as GTO won’t adapt to punish the nit. Polar toy game experiment Let’s

today I'm going to give you 10 gigantic incredibly important mandatory tips that you must fully understand if you want to have success at Cash games let's get right to it tip number one is to stop open limping if you open limp on a regular basis in cash games especially if they take a rake out of each pot you will lose okay simple as that an open limp just to be clear is whenever you are the first person to voluntarily put money in the pot so if they Guild the cards small blinds in there big blinds in there you're under the gun you're first to act if you match the big blind you're going to lose a poker okay stop doing that understand that many of your opponents are going going to do exactly that and that is why they are stuck at the small or medium Stakes games you simply cannot allow all the other players to see the flop for only one big blind they're not making a mistake they should call one big B blind very often at that point and play in position against you with anything decent also you let the big blind see the flop for free say they have the Jack four off suit if you raise they have to fold if you limp sometimes they make three of a kind or Jack high and that's good enough and that's not what you want to have happen so you need to raise also whenever you L you induce people behind you to raise because they're going to think that you have a somewhat weak range and if they think you have a somewhat weak range because they presume you would have raised with your best stands well they're going to raise you now you have to play out of position in a slightly larger pod than you would like to be in with what's probably not a very good hand also like I said by limping assuming everyone limps behind the casino is going to take a rake out of the pot you do not want to pay rake to the casino rake is not your friend less rake is better not more so make sure you do not limp instead simply raise whenever you're first to act in a live cash game and you want to raise raise is something like three or four big blinds I do not care if the standard raise in your game is to something like seven big blinds don't play poorly do not model your strategy after bad poker players who cannot move up from the small Sak games okay you need to model your strategy after good strong winning poker players and no good strong winning poker players open raising to seven big blinds before the Flop so raise first in tip number two is to raise with reasonable ranges players play nowhere near reasonable ranges at all so let me show you what I have right here we have two different sets

decided to play it may be best to call. If the scare card does come, you can throw your hand away. But if a blank arrives, you raise to thin out the field. In addition, if you call on the flop and intend to also call on fourth street, keep in mind that the pot odds you are getting are not as good as they appear. The additional call that you plan to make lowers the effective odds that you are receiving from the pot. (For 82 Part Two: Strategic Concepts a more detailed discussion of these concepts, see The Theory of Poker by David Sklansky.) Sometimes, however, the opposite will be the case. That is, your odds actually are better than the odds that the pot is offering you. This occurs when you plan to continue playing only if you hit your hand. Otherwise, you will fold. What this means is that the pot does not have to offer you seemingly correct odds to play a particular hand. That is because it is offering you implied odds. An example is to call before the flop with a small pair, getting as low as 5-to-1 odds as long as there is little fear of a raise behind you. (The odds against flopping a set are approximately 7%-to-1 .) Against players who give a lot of action; you can make this call even if you are getting a bit less than 5-to-1 .) A second example is to try for an inside straight on the flop when you have odds of only about 8-to-1. (The odds against making your gut shot are approximately 1 1 -to- 1 .) Say, if you hold and the flop is you can call even if you are getting a little less than the required 11-to-1. However, if a two flush is on board, or for some other reason you are not sure that your hand will be good if you hit it, you probably would want odds of at least 11-to-1 to call. Odds and Implied Odds 83 Finally, even if the odds don't seem to justify it, you still should make a loose call every now and then, as you don't want to become known as a "folder." If you are regarded as a folder, other players will try to run over you, and otherwise predictable opponents may turn tricky and become difficult to play against. (Once again, for a more thorough analysis of pot odds and implied odds, see The Theory of Poker by David Sklansky.) Bluffing Bluffing is the act of betting on the last round when you are quite sure that you do not have the best hand, or on an earlier round when you have little chance of making the best hand. When you bluff, you are hoping that your opponent will fold. Typically, you should bluff when you think the size of the pot, compared to the estimated probability that your opponent will fold, is large enough to make this play profitable (in terms of long-run expectation). For example, if there

Microstakes The lowest stakes offered on internet poker rooms, described as "micro" due to the fact that the lowest possible big blind stake is often $.02 US.

Table 75: HJ Action Frequencies (15bb) Hand Range 246: HJ vs LJ (15bb) • All-in 10.4% / • Fold 89.6%

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as implied collusion. If, for practical purposes, your opponents are colluding against you, it is better to stay in the hand as cheaply as possible. Implied collusion occurs most often when the pot is large from the beginning (many people called pre-flop raises) and everyone has the correct pot odds to stay, no matter how great the odds against their draw. When you are on a draw, there are cases when it is correct to call bets when the pot is small, provided that the size of the pot you expect to win is large enough to justify calling the bet. In this case, you are basing your decision to play on implied pot odds-the ratio of the expected money in the pot against the cost to play. Estimating the implied odds requires you to judge your opponents' behavior and intentions. For example, in a small-pot game where you expect additional callers later on or in an additional round of betting, it is correct for you to call as well. TACTICS 63 These following scenarios illustrate the importance of playing pot odds to your advantage. Scenario 5-You hold A4 J4 and the flop is A+ J+ 34. You bet and everyone folds, except for one player who you suspect is on a flush draw. The turn card is 54, and she checks to you. Worried that the last card might be the diamond she needs, you check. The last card is indeed a diamond. Shebets; you call. A showdown confirms her to have a flush. You saved money on this hand by not betting your two pair at the turn, but you made a terrible play. Your opponent paid nothing to draw to her flush. She got a free card since she had nothing to lose by staying in the hand. Four out of five times (80%), she will not hit the flush and you win the hand. You must make her pay to beat you. Over the long run, you will win much more money than you lose. Scenario 6-You hold A4 94 in a late position and the flop is 54 84 K+. There is a bet and seven callers including you. At the turn, a Q4 appears. A bet is followed by a raise that six people call. The pot is now over $100, and you need to call a $12 bet to stay in. You hesitate, knowing that 80% of the time you will not make your flush. Because of the large pot, you must call this bet. In this situation, you may win only one out of five tries, but the one $100 win is greater than the $60 cost of making this play five times. Over the long run, you will come out ahead. Your opponents are correct in making you pay to beat them, but you are correct in calling. However, if the pot contained only $40, your best play is to fold because the amount you win doesn't justify the cost. Summary of Play After the Turn If you have the best hand, make

Equity is your share of the pot as determined by your current chance of winning or splitting at a point in the hand. It is how often you would win the pot on average if there were no further betting and all cards were played out. Equity can be easily obtained using an equity calculator. Here are two that you can access for free: pokerstrategy.com/poker-software-tools/equilab- holdem or propokertools.com/simulations. There are various different ways to consider equity as we will now see. Hand vs Hand Equity Poker hands cannot be ranked according to strength because each hand’s strength is relative to the opponent’s hand or range of hands. Let’s examine the following three hands using equity and try to decide which one of them is the strongest: AKo, JTs, or 22 (Table 4). Table 4: Hand vs Hand Equity Calculations As we can see, AKo has more equity than JTs, and 22 has more equity than AKo. You would think that, through logical deduction, 22 must also have more equity than JTs. However, it turns out that JTs actually has more equity than 22. Therefore there is no way to independently rank these three hands. Even if hand vs hand equity can’t be used to rank poker hands in a vacuum, it can help us develop an understanding of the way poker hands match up against each other (Table 5).

your hand. If you bet and get flat-called by the field, good luck. You haven’t been moved off your hand, but you’re still not feeling too frisky, because they didn’t all call with nothing. If the turn is a blank and it’s checked to you, you could try betting again on a bluff, but if the board does hit, you need to bevery leery of action in front of you, and who likes to have to be leery in position? Again, your best strategy is simply not to get into this mess in thefirst place. If it does happen, maybe because your pre-flop raise didn’t get the desired result—just set damage control as your goal. Let’s say it’s not checked to you, but you face a bet from one of the three players in the pot. How you’ll proceed depends on which positionmakes the bet and whether callers are in between you and the bettor. Again, we’ll designate your opponents as A, B, and C, with C immediately to your right. If it’s checked to C and he bets, consider a raise here as a semi-bluff; out of all the possible leaders into this pot, the player to your right is most likely to be taking a shot at the pot. You’re certainly allowed to call shenanigans on him. But be sure you understand that you’re not raising for value here, thinking your hand is in any way great. You’re raising because you think the bettor is telling tales. If you get called by anyone after you raise, your callers will hold either better hands or better draws thanyou. You’re raising to fold the field. If you don’t think you can achieve that goal, you could always flat-call and try to hit your flush. But before you get excited about that possibility, let’s look at the math of it. Your opponent will probably bet between half- and full-pot. If he bets half-pot, you’re getting 3-to-1 on your call—almost theright price to hit a flush with one card to come. If he bets any bigger than that, you’re not getting the right price and you have a mathematical fold. Remember, you’re calling to see one card, not two. You can’t count on getting to the river for free, so you can’t get the right price to call. Most players massively overvalue the implied odds here, the chance to get paid off big. But the texture is too obvious to overvalue that. So your call is iffyat best. Another thing you can’t count on is not getting check-raised by players A or B when you call player C. Nor can you count on your 8-high flush being the best flush draw out there. And don’t forget that if you hit on the turn, 20% of the time a fourth suited card will come on the river, exposing you to redraws. You can’t bluff if you miss and you might not get paid off if you hit. So there go your fold equity and your implied odds. Best course: Call with caution and hope things

and try to reduce the field to a single opponent. Action: You raise, putting in $10,000. Players F and G and the blinds all fold. Player A folds. Player C calls. The pot is now $24,350. Flop: 9♦7♠2♣ Action: Player C bets $12,000. What do you do? Answer: That was an excellent flop: three low cards in three different suits, with very remote straight possibilities. Your opponent is known to be aggressive. Here he appears to be making a standard continuation bet of half the pot. We'll discuss continuation bets more in Part Six; for now, just note that it's a post-flop bet designed to win the pot for the early leader who may not have improved. While you almost certainly have the best hand right now, you shouldn't automatically raise. That would be a good play against a tight player, but here you have position on an aggressive player with an excellent hand, and a better strategy is to bring out the feared Rope-a-Dope and just let him try to take the pot from you. A simple call is the right idea. You might want to spend a little time thinking about the call, just for some extra dramatic effect. Action: You call. The pot is now $48,350. Fourth Street: 3♠ Action: Player C bets $15,000. The pot is now $63,350. You have $48,000 left. Player C (after his bet) has $15,000 left. What do you do? Answer: The fourth street card certainly didn't scare you, although it's possible that your opponent now has some straight or flush draws. You should now put your opponent all-in. Some players get greedy here and just call, with the idea that they will bet on the river and collect all the rest of the chips when their opponent thinks they're pulling a desperation steal. I don't like that approach for two reasons: 1. Player C probably has something, and you'd be giving him a free chance to beat you. 2. If Player C is on a draw, he still has hope now. If he misses the draw on the river, all hope is gone, and he will fold. Action: You actually just call. The pot is now $78,350. Fifth Street: 5♥ Action: Player C checks. What do you do? Answer: If Player C was going for a flush, his chance just evaporated. There's a remote chance that you're beaten by a low straight or a fluke set, but you don't have enough time in tournaments to worry about these things. You must accumulate chips and knock players out, and this looks like a good chance to do both. Put him all-in. If he's been nursing a small pair, he may call because the pot odds are very good and his stack is too weak if he folds. Action: You actually check, and Player C shows a pair of eights. You take the pot. Player C cost himself a lot of money when he made an elementary blunder before the flop. His original call of Player A's raise was fine; A was aggressive and might

it means a lot to me you'd spend your time learning about poker from me I really appreciate that guys thank you for tuning in good luck to all of you alright guys I'll answer your questions now in just a second I will be right there I'm just taking the recording I just did and says thank you for your amazing content you are welcome and Robert says in the third hand could have smallish that beacon seen seen as a blocking middle so yeah that's a good way to put it Lawrence says thank you very instructional mm-hmm so Douglas has a want to player checks and you bet that same player re raises your bet what does that mean to you just call Douglas people tend to be really poor at raising post-flop as a bluff especially at low to medium stakes because if you think about it have you ever seen a guy get caught bluffing at the table what's the general consensus it's always like oh look at you trying so people they feel shamed and they don't do it again you know so it tends to be the hand that's not that's not 100% but it does come up so and someone said could you show the five tips again yeah I'll show that in just a second guys so one second everybody I just want to make sure I save this footage so we can get a nice little replay here and Chad says are you playing any WSOP events I will definitely be playing the main event I never missed the main event I have not missed the main event in ten years I try to play some others but it's hard making these takes a lot of time let's see ray says any meetups planned in Vegas I definitely will try to do that Ryan says I joined late and missed most of the webinar but thanks I will be getting mastered flop seems like a great value I appreciate God Chad says I'll be wearing the patch is nice teryn says do you like coaching more than playing that's a really good question I actually find playing to be more fun but I find coaching to be more rewarding coaching is rewarding because it's a very it's very intense right like when you're giving somebody in a strategy that they're literally gonna put money on you really have to be right in that intensity I wouldn't say it's fun but it is really rewarding when you get it right ken says are you playing the WPT this week at parks I promised a buddy of mine I would go to his MMA fight so I can't go ah the code I just go to poker coaching comm slash assassin and it'll be right at the bottom Renee says Alex I've noticed that when I play thirty orbit levels let me hold on guys let me just in case they want me to record this well the master the flop package ever be

prepared for larger bankroll swings. By loosening up you can catch some good cards that nobody would have expected you to have, like flopping a 7 2 Full House and letting other loose aggressive players drive the betting. Recognizing when the odds are correct and even creating the conditions to have the odds in your favor is an advanced poker skill that will increase your profit tenfold. Starting Hand Chart I have tried to put together a simple starting hand chart for quick reference with the template being the hands strength based on winning percentage. I separated the games into three categories, loose, typical and tight. A loose game is one with six to ten players regularly seeing the flop with sparse or no pre-flop raising. A typical game is two to five people seeing the flop with one out of every four hands having a pre-flop raise. A tight game is where there are two to three people seeing the flop and there is a pre-flop raise three out of every four hands. In the notes section unless it is specified then all is assumed. For example, if it says “all positions” then you can play this in any position in any type of game. “All positions (25% early 50% mid tight)” means that in loose and typical games you can play this in all positions. In tight games, it specifies when to play in early position and in middle position. Another example is “Early (loose) Middle (typ) button/blinds (tight)” which means that in loose games you can play this in any position, in typical games from middle to blind position and in tight games you can play this on the button or from the blinds. Early position is the under the gun seat (UTG) and one past that seat, middle position is the next three seats, late position is the next two seats until the cutoff and then the last seat before the blinds is called the button. This is a No Limit Hold’em starting hand chart. Starting hand Occurs Hands Won % Hands Split % Notes/position play in different games AA 0.45% 31.00 0.49 All positions any game - raise and re-raise. KK 0.45% 26.02 0.61 All positions any game - raise and re-raise. QQ 0.45% 22.03 0.76 All positions any game - raise and re-raise. AKs 0.30% 20.19 1.88 All positions any game - raise and re-raise. JJ 0.45% 19.09 0.92 All positions any game - raise and re-raise. AQs 0.30% 18.66 2.17 All positions any game raise in late position. KQS 0.30% 18.08 2.09 Early (loose) Middle-late position /blinds (typical/tight) raise from button AJs 0.30% 17.47 2.46 Early (loose) Middle-late position /blinds (typical/tight) raise from button. KJs 0.30% 17.05 2.36 Early (loose) Middle-late /blinds (typical/tight) TT 0.45% 16.83 1.12 All positions any game raise depending on situation and table type. AK 0.91% 16.67 1.97 All positions (75% early tight) raise from late position. ATs 0.30% 16.63 2.74 Early (loose) Middle (75%% typical) late/blinds Late (tight 50%) QJs 0.30% 16.58 2.39 Early (loose) Middle (50% typical) late/blinds Late

usually better than the ranges live because online players typically play better than Live players right also usually have fewer reads online compared to live so anyway right here I think we just want to raise it's definitely annoying when you raise the opponent folds but this type of loose aggressive splashy battling player is the type of player who will not fold all that often definitely do not Jam all in by the way some people saying rip it all in I hate ripping it all in because then your opponent can never Bluff you want to keep the opponent in the pot with Bluffs it's vitally important everybody here worried about getting full value and protecting your range or thinking about the wrong things the main value the main point here is you got to keep your opponent in with all their garbage that is what we are trying to accomplish you know we go for 27k things is fine and reasonable again you don't want to go too big because if you go too big your opponent cannot float with all sorts of garbage and they cannot re-raise with all sorts of garbage then the opponent makes it 63 with 90 behind how do you feel about this this is a weird one at this point I do not expect to get re-raised very often at all because I mean but when I raise I'm either saying I have some total garbage or I have a super nut hand right or I have some high Equity draw I'm probably not raising the high Equity draws because I don't want to get re-raised right uh so I think it's a spot where shoving's the The Logical play just because if he folds out any hand with Equity I don't care and if he does have a hand like A7 I don't care if he folds right that's that if I know he has A7 I want to keep men the thing is it's like this might be the type of player who just takes a hand like Jack ten of Hearts decides to blast it um yeah I don't know I don't know definitely a rough spot I mean it's a rough spot in that I don't know if I'm supposed to presume the opponent's range it's so garbage that I'm supposed to call or if I'm supposed to just presume the guy has an over pair top pair or a draw or something and he wants to get it in and again people saying that this board does not connect with his range you must have missed it five seconds ago where I said the guy raises Queen four suited and calls three best with it and whatnot so this is the type of player who could definitely have random one pair of hand here anyway I don't know if it's a call or a shove I could be convinced either way I kind of presume that once the opponent puts in 63k with only 90 behind he just

are elegantly aligned. Now when it comes to K♥Q♥, say, you don’t have the nuts, but you do have the near nuts, which means you can be a lot less worried about getting drawn out on when a fourth heart hits. Yes, you’re fading the ace of hearts, but that’s only one card, not all of the eight hearts in the deck, as you’d be with that ugly 7♥6♥. Plus, because K♥Q♥ is connected, you have a lot of straight hands you can make, all nut straights. Obviously, if you hit the pair side of things, you’ll be on good-pair good-kicker, which presents some of the same decision-making challenges as AQ off-suit in a multi-way pot, so you’ll need to proceed with caution. But in this case the pairs aren’t the only thing you have going for you, which iswhy you’re playing KQs, but not K3s: so you’re never looking at good-pair bad-kicker or bad-pair good-kicker with no straight possibilities. Withtop-pair second-kicker, you can now play some of your one-hit flops. You should play carefully, but you can play. A number of hands fall into this category of “good to great in multi-way pots,” including KJs or even KTs or QJs in late position. Except when you’re very close to the button, don’t go down as low as K9s, with which you have to flop too perfect. On the button, you could go as low as T9s, because you get to see the disaster of a bigger flush in front of you before you commit to the hand. In early position, your KQs and KJs are okay; again, the math makes your draws work and the clarity of the situation makes your decision-making easy. To recap: In early and middle position in wide open games, play only the best unsuited aces, most pairs, pretty much all suited aces, and a smattering of suited connected paint. Around back, you can loosen up, adding in KT suited, closely connected suited queens, even that JT suited that everyone loves so much. But that’s only in back and only in a loose timid game where you can see cheap flops with lots of traffic, remainingalert to the possibility that the tenor of the game might change, when you’ll shift back to your normal, position-dependent, selective stance. And by the way, if it seems like you’ve loosened up a lot, you haven’t. You’re still folding most of your hands, but the ones you play have the potential to make the nuts and pay off big. So we come to this: IN LOOSE GAMES, PLAY HANDS THAT EASILY MAKE THE NUTS If the hand you’re looking at can’t easily make the nuts or near nuts, stop looking at it and throw it in the muck. Behind a Raise in a Normal Game In a perfect world, no one raises at the table but you and you always control the action. Well, the last time I looked, this wasn’t a perfect world. For the sake of having a complete pre-flop toolkit, then, we have to give some thought to

Hand Range 101: SB vs BB 25bb (Limp vs 3.3x Raise) • All-in 11% / • Call 43.7% / • Fold 45.4%

profound transformation due to artificial intelligence. Solves that previously demanded hours of computation can now be calculated in seconds with high accuracy. With GTO Wizard AI, we are bringing the next generation of poker studying tools to the market and enabling poker professionals to gain a competitive edge over their opponents. Check out these articles to learn more about GTO Wizard AI: GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players,… C-Betting As the OOP Preflop Raiser Position is an extremely valuable advantage in poker. Most players would describe the comfort zone… Overchoice: Making Sense of Multiple Sizings Solver solutions with multiple bet sizes often involve a lot of mixing between those sizes,… River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing

Table 40: Equities Versus a 100% Range Calling off with AKo is clearly very profitable in terms of chips, so now let’s calculate the $EV of the BB’s call with AKo in the same spot: Using HRC ICM calculator, the current value of BB’s stack after a fold is $18.02. Instead, after a call and a win, the value of this stack with the new stack distributions would be $27.12, so the $ value added to BB’s stack is: Then: So, calling off with AKo is unprofitable in terms of monetary value. Using the EV equations, we can calculate the minimum equity required to make this call profitable:

pot, this is probably true. But in other spots, having the bigger kicker is crucial. If an ace flops, a queen should win where a ten may not. You are also much more likely to flop top pair with a queen than with a ten. In addition, if you do flop top pair with a queen rather than a ten, you don't have to worry as much about overcards hitting on a later round. This adds up to a lot of extra pots and extra money. The ideas in this chapter are all very important. But even though playing your first two cards correctly is absolutely crucial to winning play, it will not automatically make you a winner. Perfect play on the first two cards will enable you to only break even at best if you are not adept at the later rounds. So read on. Hold’em Poker For Advanced Players By David Skalinsky and Mason Malmuth Check our site www.pokerpiraten.com to find more books on poker. Please support pokerpiraten to bring you more books by clicking on our sponsors: www.partypoker.com www.pacificpoker.com www.interpoker.com Strategic Concepts Introduction Most of the profit in hold 'em comes from knowing how to play after the first round. Unfortunately, the game quickly becomes so complex that it is impossible to discuss every situation, which is why it's important to develop general strategic concepts to guide you toward winning play. That is the purpose of this section. When you finish reading it, you should have a good idea of how to approach most situations at the hold 'em table. Although you still won't be an expert, as this additionally requires a great deal of experience, you should be well on your way toward achieving this goal. Also, at this juncture, we would like to recommend a more general book on poker concepts, namely The Theoiy of Poker by David Sklansky. While not specifically about hold 'em, this book is must reading for all serious players. Semi-Bluffing In The Theory of Poker, David Sklansky defines a semi-bluff as "a bet with a hand which, if called, does not figure to be the best hand at the moment, but has a reasonable chance of outdrawing those hands that initially called it." Notice that when you are semibluffing, there are two ways that you might win the pot. First, no one may call and you will win the pot immediately. Second, if you do get customers, you still may improve to the best hand. It is the combination of these two possibilities that makes this class ofplays profitable, and as we shall see, semi-bluffing plays a crucial role in any winning hold 'em strategy. Also notice that the semi-bluff necessarily means that more cards are to come. Obvious examples of semi-bluff situations in hold 'em are when you have flopped an inside straight draw, or second or third pair with an overcard kicker. In these examples, you would prefer that all of your opponents fold. However, ifyou are called, you still have a chance to win if the right card comes

steal the pot. 7. What else might happen if you check a lot of hands on the flop? The free card that you give occasionally may cost you the pot. 8. Can you check-raise semi-bluff? Yes. 266 Part Eight: Questions and Answers 9. Example? You have T+9+, and the flop is 8+442+. You bet and are raised, and you (correctly) call. The next card is the J+. You should check-raise. 10. Another example? You have Q4J4, and the flop comes Q+8+44. If any spade hits on fourth street, you should check-raise. 1 1. What is another very important reason to check-raise? In games of today's structure, the bet on the flop is often not large enough, when compared to the' size of the pot, to make it incorrect for drawing hands (and this includes hands like middle pair) to call. This means that you should check-raise a fair amount in an attempt to cut down the odds for opponents to draw out on you when the pot is large. 12. What is a good guideline to follow? Consider check-raising if it is unlikely that an overcard can hurt you. 13. Be specific: If you flop top pair and your top pair is aces, kings, or queens (and you have an overcard kicker with your queen), checkraising is frequently the correct play. 14. What if it is a large multiway pot, you have top pair, but you are afraid of an overcard? It still may be correct to check-raise, especially ifyou are in an early position. 15. Why? This is because the pot is now so large that if you bet, you can expect a lot of callers anyway. Consequently, in an effort to thin the field, it may be necessary to risk the dreaded free card. Odds and Implied Odds 1. If the bettor is to your right and there are other players who might raise behind you, what must you do? Adjust the pot odds considerably lower. 2. What does this mean? Fold more hands. 3. Example? You hold A484, and the flop is A4Q49+. If a solid player to your right bets, a number of players are behind you, and there has been no raise before the flop, you should fold. 4. What if you are against a loose bettor? You should raise rather than fold. 5. When else should you continue to play? Against a player who will only bet a draw. 6. Another example? In the same situation, fold K+J+ if the flop is J4T48V 7. What are other exceptions to folding these hands? If the pot has become very large and/or the game is very loose. 8. How does it affect the pot odds you are getting if you call on the flop and intend to also call on fourth street? They are not as good as they appear. 9. When is it correct to call before the flop with a small pair? When you are getting as low as 5-to- lodds and there is little fear of a raise behind you. Odds and Implied Odds 269

Unmatched pocket cards One matched pocket card Two Pair Inside Straight One matched pocket card Pocket Pair Three of kind Improve to Straight or Flush Straight or one pair Flush Straight Full House Pair one Two pair or Three of kind Full House Straight Two pair Three of kind Four of kind Outs 15 10 9 8 7 6 5 4 4 3 2 1 Two cards One card to come to come FACTS Minimum Pot Size A more useful way to think about drawing hands is to examine the minimum amount of winnings needed to justify the cost of continued play. The tables on the next page show for the number of available outs, the minimum pot size that must be won to justify the cost. If you cannot win the minimum amount shown in the table under the cost column, your bet is not getting the correct pot odds. There are two tables, one for two cards to come and the other when there is one card to come. For example, playing $3-6 Hold'em, you are on a flush draw (9 outs) with two cards to come. There is a $6 bet to call and you expect to spend $12 total to get to the river. In the table for two cards to come, the intersection of the $12 column and 9 out row shows $34. You must win at least $34 to justify spending $12, because in this situation, you will have about two failures for every success. For higher betting limits, multiply the dollar amounts by 10. Example: In a $5- 10 game, you are on an inside straight draw (4 outs) and must call a raise ($20) to see the last card. In the table for one card to come, think of the $2 column as the column for $20. The value in the row for 4 outs is multiplied by 10 to give $230. You must win at least $230 to justify a $20 bet on an inside straight draw. These tables are especially~useful for Internet competition, because pot sizes are precisely displayed on your screen and the table can be in front of you for reference. 52 THE INTELLIGENT GUIDE TO TEXAS HOLD'EM POKER Minimum Pot Size for Correct Pot Odds For your bets (costs for additional cards) to have correct pot odds, you must win at least the amount shown under the cost column, in the row with the number of outs available to make your hand. ONE CARD TO COME I Cost of Final Card I TWO CARDS TO COME I Cost of Final Two Cards FACTS Opponents' Playing Styles Playing styles have a big influence on how each player will choose to act in a hand. Playing styles generally fall into one of the following four categories: Loose-passive players are free with their money, but their actions tend to follow the other players. Loose-passive players enter most hands and call just about every bet, but they rarely bet or raise on their own. Generally, these players are the most profitable people to

When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) tournament is a type of tournament where a portion… How To Analyze Turn Textures In Poker Master the art of turn analysis in poker. Understand how the turn card changes the… Principles of Turn Strategy Learn the principles of turn strategy in poker and discover what makes the turn unique.… Poker Strategies: Tournaments vs. Cash Games Tournament poker is not as different from cash game poker as people sometimes assume. Most… How Solvers Work A Game Theory Optimal solver is an algorithm that calculates the best possible poker strategy.… The Most Powerful Play in Poker The central strategic implication of stack depth is the question of how much equity a… When does ICM become significant in MTTs? The Independent Chip Model (ICM) was invented in 1987 by M. Malmuth and is one… How to Study GTO Solutions Tools like GTO Wizard and other solvers should not be used to memorize specific strategies.… Principles of

passive calling station, bet big. Some passive players check and call, rather than check and get spooked. These playersare the best of both worlds. They won’t put a lot of pressure on you, but they do love to play sheriff. Give them as big a chance as they can stand. In Position, Passive Opponent Checks, Weak Hand In a situation where your hand is weak and you suspect your passive opponent is medium to strong and he checks to you, check behind unlessyou have some reason to believe that he’s ready to fold his hand, in which case you wouldn’t have read him for strong in the first place. The height of this player’s creativity is going for a check-raise on the river with a huge hand, especially against a player like you with a knowledgeableaggressive image, who can be counted on to bet. Well, that’s just an obvious trap. Don’t fall into it. However, when your hand is weak and you think Mr. Passive is likewise medium to weak, bet after he checks, whatever amount you think will make him fold. Here’s a situation where the only hand that can call you can beat you, but a lot of hands can beat you that won’t call you. I mean, if you’re on ace high, you’ll get this passive guy to lay down bottom pair all day long. He sees monsters under the bed. He sees monsters everywhere. Since you have a hand that can’t win at a showdown, try to avoid a showdown here. Remember, passive players are reliably passive. Without strong evidence that he’s got a calling hand, his check on the river indicates he’s already surrendered and moved on to the next deal. Unless this opponent has shown you that he really likes calling the river with almost anything just to see your hand, you have to be getting the right price to convince most of your passive opponents to fold here. The check signals true weakness, so take advantage of it. After all, if you bet half to three-quarters of the pot, you only have to trigger a fold 33%-43% of the time, which you’ll do against this type of guy (but probably won’t do against a calling station). Also, there’s no need to bet bigger. Bets within this range tend to look more or less the same to your opponent; they’re prepared to fold no matter what. So why bet huge? If you’re mistaken in your read (it happens), you’ll pay less to be wrong. Thus, tend to avoid full-pot betshere. One caveat to these river bluffs: You want to avoid betting against someone who’s pot-committed. In a tournament, the math may be such that he has to call you, because he has so few chips left and there’s so much in the pot. In cash games, and you hear this all the time, the guy says, “I might as well go home” as he donks off the last of his chips. Yet his ridiculous bottom pair is actually good and you just gave him extra chips,

I don't really want to check raise you because I don't have eights nines 10 Jacks Queens Kings Aces I'm just opening myself for you to just kind of Blast away with these over Pairs and like Blast away with 109 offit because yes I can have 74 suited every once in a while or pocket fours every once in a while or pocket Deuces but really I just have a pair of sevens and you can really just put me in the cage so I'm not going to really check raise much because I don't have the over pairs to protect myself yeah like you know if I bet small here yeah I can check raise A7 I can check raise King 7 you know check raise pocket sevens or pocket fours 74 or whatever but like they raise like you just it's we're not getting enough money into the pot by betting small with when we have Jacks you guys one of the biggest things is everyone's nuking money by not betting big in these spots with Jacks this is an overb you're betting 120% of the pot okay if this was 100 big blinds you probably bet like 200% of the pot here you had really really big the bigger the bigger the the S stacked pot ratio almost here the bigger you bet okay so let's not spent as much time but let's look at look at Jack 54 Jack 54 here it's actually using a lot of small betting here and I would have bet maybe a little bit more medium size here but why are we betting small here and not betting really big and there's two things going on here yeah the straight and flush draws so there's two things one it's Jack high so really we only really have an advantage around ace Jack and then Aces kings and queens okay so that's number one is the blank can have King Jack right and you notice here the big blind can have Ace Jack so we really don't want to start blasting away with King Jack when the big blank can just have Ace jacked so it's really just Queens Kings and aces are the only hands that really want to bet big here so that's number one the high card that's why we bet larger on lower high cardboards almost always and we don't really bet large on AI flops because the big blind has more coverage of top pair with decent kickers it's the over pair pairs that are really allowing you to bet large because the big blind can't have them the other thing is if we start betting really large on this board the big blind just has so many combo draws like if we bet 100 here we just really start to narrow the range to like8 six of Spades or 7 six or you know all these like nut flush draws King High flush draws like let's say we have Ace Jack okay and we bet 100% of

The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) tournament is a type of tournament where a portion of the buy-in goes toward a bounty on each player’s head. In PKO tournaments, when a player eliminates another player, they typically receive a cash prize for half of the eliminated player’s bounty . The remaining half of the bounty is added to their own head for other players to try to claim. When two or more players win in a split pot the bounty is divided equally across all winners. Note, some sites such as Pokerstars run PKO tournaments where ⅔ or even the full prize pool are dedicated to bounty prizes. For the purposes of this article, we will only be looking at the standard 50% bounty prize pool. The effects of bounties create an added layer of strategy! PKO tournaments tend to have more action as players are incentivized to knock out their opponents to earn bounties rather than just trying to survive and advance in the tournament. This format also encourages players with a chip advantage to play aggressively against shorter stacks as they can earn additional EV outside of the chips in play. GTO Wizard PKO Solutions GTO Wizard’s PKO solutions are based on the following structure: 200 Player Field (1000 player fields coming soon!) $200 Buy-in: $100 to the prize pool, $100 to the bounty pool 8 players per table 0.125BB ante per player Let’s examine a table when the tournament has just begun. Each player begins the tournament with 100 big blinds (BB) in their stack. Each player starts with a $100 total bounty: $50 is immediately capturable by the player who eliminates them $50 is added to the bounty of the player who eliminated them The bounties displayed underneath each player show how much bounty is immediately capturable. GTO Wizard has solutions for many tournament phases, including mixed and symmetric stack depths. But this is just the beginning! We intend to add many more PKO solutions to cover later tournament stages, final table spots, and a wider variety of bounty distributions! We acknowledge that it’s impossible to model every possible scenario in PKO tournaments. However, these solutions allow you to study how strategies should change throughout the tournament and how bounties and covering players impact optimal play. Understanding these general ideas is more important than memorizing solutions for specific situations , as it allows players to adapt to changing conditions and make better decisions in the tournament! ICM vs. Chip EV Generally Speaking, Chip EV is a poor indicator of stack value in PKO tournaments. Traditional Chip EV calculations rely on the proportion of chips you control in the tournament. We can model the value of a stack as follows: Stack Chip EV = Chip Portion ( Remaining Bounty Pool + Remaining Prize Pool ) Where “Chip portion” is the percentage of chips you control in the tournament. This simplistic calculation just assumes that if you control 10% of the chips, you should win 10% of the remaining prizes in the tournament. But

Hand Range 300: CO 25bb (2x vs SB 3x 3-bet) • All-in 19.7% / • Call 39.5% / • Fold 40.8%

Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) tournament is a type of

worse hand folds, because you’ve avoided the main problem of facing a difficult decision on theriver. Always be willing to give up a little potential earn from a worse hand if it prevents a sick card from coming on the river, which will happen, by the way, about one time in five, if you don’t include the worse ace’s kicker. Including that kicker, you’re up over 25%, and since you didn’t bet the turn, you just open yourself up to all sorts of texture-driven bluffs on the river. Remember that when you check behind on a fully dry board, you’re about a 9-to-1 favorite to face an okay river card. Here, you’re only a 3-to-1 favorite, against either an opponent who’s drawing to the texture or who’s willing to bluff at the texture. Once again, we see that the math lines up nicely behind the decision-making issue, because if you bet about half the pot on the turn and get called, you’re, in essence, offering yourself a 3-to-1 price on the river card. If it blanks, you can check behind, lose the minimum to AK (who won’t bet into you, because you bet the turn) or a made flush that forgot to bet, or win the pot against anyone else. And if you get check-raised on the turn? Well, what can you do? The texture hit, your opponent check-raised, and you’re probably folding. But that’s okay. Remember, if you were the one with the flush, you wouldn’t be checking here, you’d be betting, and possibly getting paid. In the long run, it’s a wash. Sure, you hate to fold to the check-raise, but your bet on the textured turn actually slows down a lot of bluffers—how do they know youdidn’t hit?—and as mentioned, people tend not to bluff out of position with check-raises on the turn. This all skews toward the judgment that thecheck-raise here is coming from a hand that hit. If your opponent calls your turn bet instead of raising or folding and the river hits another diamond for four diamonds on the board, you’ll have tofold if he bets out. If he checks, you should almost always try to bluff at it to win, as any hand without a diamond will almost always fold and even setsor a low diamond will go away as well. That makes the bluff well worth it and it doesn’t really need to cost you more than about half the pot to try. If the board comes a blank on the river instead and he checks, you should strongly lean toward checking it down, unless you decide that the onlyway for you to win is to bluff. In that case, you can bet with the knowledge that you’re not value betting, because you won’t get paid by a worse hand. If your opponent bets into you when the blank hits, you’ll have to take a read. The more you read it for a defensive bet, the more you should call or even raise to win the pot. Now what if you have the A♥Q♣

Table 56: BB vs SB Push Action Frequencies The simplest situation the BB can face is when the SB open jams. In that case, the BB’s calling range depends on the pot odds laid by the SB’s stack size. The fewer chips the SB is going all-in for, the more hands in BB’s range that will have the correct equity to call, and the more chips SB is going all-in for, the fewer hands BB has to defend to remain unexploitable. For some who are experienced with push/fold apps, the unexploitable calling ranges may seem tighter than usual. This is due to a combination of factors such as the bunching effect and the fact that the SB has other strategic options (limping or raising to non-all-in sizes) which has a drastic effect on both calling and pushing ranges. At 12bb when facing an all-in, the BB calls all pocket pairs, Ax, broadways, Kxs, K5o+, Q7s+, J8s+ and T8s+. This tightens up a little at 15bb (Hand Range 140). At 25bb, the BB cannot profitably call as many hands, so the calling range shrinks to pocket pairs 33+, A7o+, A6s+, suited broadways, KQo and QJo (QJo has more equity vs SB equilibrium push range than KJo) (Hand Range 141). At equilibrium with fewer than 30bb, the BB’s only 3-bet size is all-in. The solver likes trapping with the bigger pairs 88+ and the rejamming range is made of high equity hands that have poor post-flop playability, such as small pairs 77-22 and offsuit Ax (Hand Range 142).

Hand Range 105: SB vs BB 40bb (3.5x Open vs 2.75x 3-bet) • All-in 13.1% / • Call 40.4% / • Fold 46.5% Small Blind Strategy at 60bb The common trend seen as stacks get deeper is the increase in the limping frequency and a reduction in the raising frequency. There aren’t any hands that play a pure raising strategy, but there are many that play a pure limping strategy.

Defending vs BB Check-Raise on Paired Flops illustration This is a companion piece to Attacking Paired Flops from the BB ; you will get more out of it if you read that article first. In that article, we found that BB’s optimal response to a small continuation bet on paired flops involves a lot of check-raising , even more so than on the average flop. In this article, we will examine how the original raiser should respond to those raises. The BB’s check-raise presents difficult decisions not only about whether to fold but also about whether to raise. A well-constructed check-raising range will balance bluffs and value raises at a frequency that forces the bettor to continue not only with “obvious” hands such as pairs and draws but also with many hands that lack such coordination with the flop. In many cases, a balanced raising range also entails a polarized mix of nutty hands and weak bluffs , against which the bettor would prefer to call, and a linear mix of higher equity semi-bluffs and thin value bets , against which the bettor would prefer to three-bet. Thus, the BB’s check-raise presents difficult decisions not only about whether to fold but also about whether to raise. A Note on Continuation Betting One way to deal with tough decisions is to avoid them. If you don’t bet the flop, the BB can’t check-raise you . This is appealing logic, but it’s important to keep in mind that even though BB should check-raise paired flops aggressively, raising is still their least likely response in most situations. Fear of a raise should not deter you from realizing the many benefits of continuation betting against a BB caller. It is generally better to bet and then deal with the raise if it comes. This article will give you the tools to do just that. illustration One way to deal with tough decisions is to avoid them. If you don’t bet the flop, the BB can’t check-raise you . This is appealing logic, but it’s important to keep in mind that even though BB should check-raise paired flops aggressively, raising is still their least likely response in most situations. Fear of a raise should not deter you from realizing the many benefits of continuation betting against a BB caller. It is generally better to bet and then deal with the raise if it comes. This article will give you the tools to do just that. Fear of a raise should not deter you from realizing the many benefits of continuation betting against a BB caller. That said, checking is an important part of the preflop raiser’s strategy on many paired flops, especially those where the BB is significantly more likely than them to flop trips. The hands that benefit most from checking are usually unpaired overcards , the ones that would face the toughest decisions when raised. You can learn more about continuation betting–and not continuation betting–against the BB in this article . Deep Stacks The following chart shows the preflop raiser’s response to a 55% pot

there goes all your—shall we call it?—induced-bluff equity. Out of Position, Aggressive Opponent, Medium-Strength Hand Now your hand is medium-strength and you’re again against an aggressive opponent. Here it doesn’t so much matter what your opponent has interms of whether you bet or check. You know your hand can win by virtue of its medium-strength. But you’re also unsure of it by the same virtue of its medium-strength. Most people go for a blocking bet here, betting about half the pot, rather than checking and facing a pot-size bet that they have to call (against anaggressive opponent). But against a truly aggressive opponent, this is a bad idea for two reasons. First, a really good aggressive opponent cansmell a blocking bet from a mile away and raise it into oblivion, even when he has nothing. Remember, your mid-range hand is just the kind that can’t stand to be raised, so by betting, you risk folding a pot that belongs to you when you let your aggressive opponent read your bet for thedefense it was. Second, the aggressive opponent will bet a wider range of hands than he’ll call with. Remember, your hand isn’t that strong. You aren’t bluffing, but you aren’t beating the world either. If you bet, not a lot of hands worse than yours will pay you. But if you check, a lot of hands that you beat will bet. So check. Check to avoid getting raised off the best hand. Check with the intention to call, unless of course you have a strong read that you’rebeat when he bets. Then you can always fold. Otherwise, call to pick off the bluffs and win against all the thin value bets. And don’t get any fancy ideas that you should check-raise here. Remember, you aren’t bluffing. Your hand can totally win at showdown. But a raise won’t ever get paid off by a hand that doesn’t beat you. So if you raise, you turn a non-bluffing hand into a bluff. Oops. Out of Position, Aggressive Opponent, Weak Hand Next iteration. Your hand is weak and you suspect your aggressive opponent is medium-strength to strong. Check-fold. The great thing about this play, apart from it saving you money, is that it emboldens your opponent to further aggression. And if he’s using aggression like a blunt instrument, without paying much attention to situations or relative hand strength, later on he’ll bet thin (you’ve encouraged his aggression) and your hand will beat him. Were you thinking about lead bluffing here? Please don’t. I mean, your opponent is strong, right? Are you suicidal? How much will you bet? Halfpot gets a call or raise from real hands, and even a raise from some bluffs. Full-pot looks bluffy and gets a call from medium hands and a raise fromstrong hands. You’re not shoving, just barfing your chips into the pot. So, hello, that’s why it’s hard to bluff out of position. Very few bets make much sense here. When your hand is weak and you suspect your aggressive opponent is weak, you can either lead out

what 3rd would have got, but $24,283 less than what he would have won for finishing second. ‘reno8’ won $19,016 more than he would have for his third place finish. If this were an equal skill matchup then amazingly €urop€an only had $277,205 in equity despite a 10-to-1 chip lead. Assuming equal skill this is what ICM says would be their likely finish position chances: Then you have the matter of edge which is not insignificant here . It actually doesn’t look like a terrible deal on the surface. XingsMaster and reno8 essentially are playing a pseudo heads-up match for $57,184 (the difference between 2nd and 3rd place prizes) and have paid €urop€an $5,268 for the privilege of splitting $51,916 amongst themselves. €urop€an only winning 82.1% of the time might surprise some people and would lead them to argue that it is worth the other two players not dealing. The problem for the other two players is that both of them don’t win 90% of the time. Deal-making mindset issues Beyond the numbers, there are several mindset issues that can lead a player to reject a good deal or accept a terrible deal. First of all, there is the anchoring effect of the money itself. Some players might have looked at what 3rd place prize money would do for them personally (a new car, moving up stakes, a holiday, etc.) and are unwilling to look beyond that. Others will look at their position in the tournament and be unwilling to give up what their potential prize would be if they maintained their position. There is also a social pressure element to final table deals. It might be that you do not want to give the arrogant professional player $500 more than ICM because he has suggested he has an edge on you. On the flipside, it is easy to get bullied into a bad deal for fear of being ostracized by the other players. You will have a sense of where your own mindset issues will lie in this regard, but perhaps the best way to ensure you do not get pressured into a bad deal is by understanding ICM in the first place. If the social pressure is too much, an easy hack to push for a good deal or refuse a bad deal, without social stigma, is to just tell the other players you have a backer who has insisted on your terms. You can make this fictional backer the bad guy while still enjoying the final table camaraderie with the other players. Conclusion Even if you play on a site that doesn’t facilitate final table deals, it is a good use of your time to study them. Studying final table deals and understanding the value of your stack will help with strategic decisions, particularly where Bubble Factor is concerned. Understanding the ICM implications of final table deals puts you on a good footing for that once-in-a-lifetime final table you may find yourself on one day in your career . Key Takeaways There are lots of good reasons to deal,

It may be surprising that hands as strong as A9o always get folded whereas hands such as K2s get called. The main reason for this is that offsuit disconnected hands tend to struggle to realize equity, particularly when playing against tight ranges. When facing a LJ 4-bet, the BB 5-bets AA (61%), KK (57%), AKs, AKo (54%), QQ (16%) and A5s (38%) and can call all other pairs, ATs+, JTs (75%), T9s-65s, and 54s (64%) (Hand Range 77). Hand Range 76: BB vs LJ Open • 3-bet 5.8% / • Call 22.8% / • Fold 71.2%

Don’t Justify Their Optimistic Calls In the last section, we learned to avoid habitually offering your opponents too high implied odds. But there’s another related rule: Don’t justify your opponents’ optimistic calls either. What is “justifying your opponents’ optimistic calls?” Well, say you bet one- fifteenth of your stack with a good hand. Your opponent calls with a gutshot, because she figures that she’ll hit it one-eleventh of the time, and that she’ll stack you if she does and make fourteen times her investment. If she’s right, and she does stack you when she hits her straight, then, in addition to offering her high implied odds, you have made the error of “justifying her optimistic call.” If, on the other hand, you thwart her by folding before she gets your whole stack in, then you have done well. Many no limit players’ eyes are bigger than their heads. They often call decently-sized flop bets with longshot draws because they assume that if they get there, they’ll stack you a large percentage of the time. If they are wrong, though, and they get your stack only a small percentage of the time, then they will lose money in the long run on these calls. You can use this loose-calling tendency against your opponents if you refuse either to offer too high implied odds or to justify optimistic calls. That is, before you bet with good hands, you should mentally decide whether you are willing to pay offa big bet with the hand or not. (Obviously, sometimes you will decide one way, but change your mind later in the hand. Nevertheless, you should always be asking yourself, “Am I willing to lose a lot?”) Whenever you bet or raise, always have an an- swer in your head to the question: “Am I plan- ning to pay offa big bet on this hand, or will I fold if it comes to that?” If you are willing to risk losing a lot, then you should usually avoid offering too high implied odds to players with the most likely draws. Bet enough so that if they call, they will lose money over the long term even if they do get you to pay offa big bet when they get there. 29

to know and if you have if you're crossing over time zones and you have trouble sleeping melatonin okay rock steady do you adjust your preflop BET sizing in six max cash game online based on stack size um no no I mean generally in the games I play people are playing 100 bigs I just based on position the one time all adjust greatly is if there is a really loose player who's like playing like 80 90 percent of hands and I think that they'll call a bigger raise size I'll make it bigger so when I'm playing in position I can play a bigger pot but we'll go deep into that in the aggression webinar on April 30th can I read this yes if you had a start-over would you play to your bankroll or to your skill level bankroll I think it's too stressful to play outside of your bankroll even though even if your skill is there and stress really eats away at the human and I don't like that feeling so I find that when I'm playing outside my bankroll I just feel very uncomfortable and that's not a good place to be making decisions from so I I would play to my bankroll that's how I built my bankroll over my career I never went broke I'm never going to go broke I have safety I have security I have comfort I have confidence and that's a thing about respecting my bankroll I think playing at the skill level it's fine but it kind of shows a little bit of impatience and impatience in that can carry over to impatience in other places so I think it can kind of be setting up for disaster and well like it can build you up faster can break you down more so the higher you fly the harder you fall kind of thing and if you're someone who is comfortable with that and enjoys those kind of swings and likes the rush of that by all means go for it it's just personally not for me and like I have an extremely addictive personality I'm someone who would go for that kind of stuff but I know how easy I'd get carried away from it so in the interest of just protecting myself and doing what's best for me I don't I played in my bankroll I am very strict with bankroll management and money management and every time I've deviated from that I've seen the snowball effect the domino effect of doing so and it doesn't lead to good things so I played my bankroll for sure is a position significant different from cash games to tournaments it really just depends on stack sizes and yeah stock sizes ante how much dead money and then in tournaments also ICM comes into play which can make position even more valuable but in terms of like the strategies we discussed in today's presentation they apply directly to tournaments the same way they do in cash games the information

bb/100 A unit of measurement in poker equal to the average amount of big blinds won/lost per 100 hands.

turns up there but yeah you know the basketball shorts they've pissed all over and the graphic hoodie and it's pulled over and they haven't shaven in three days that guy probably wants you to know what an amazing Pro he is right so that guy is a little bit more likely to attack your see that's how if a guy just shows up in jeans and like an okay sweater or something like that that that doesn't really tell you much but if the guy's trying to show you how awful you can show up at the table that's one thing Oh Ralph wrote a very long one let's see if we can get to this Ralph Alex I have one question I'm running into one problem earlier tournament after I crush it 100 plus big blinds triple upend first three rounds how much do you tighten up or do you this problem lately I could email if you don't have time today thank you for the webinar thank you this has happened so much lately am I just running bad I think I need to become super tight is that wrong nope that is wrong uh let me tell you you ever watch a horse race number one a horse race will show you the very natural progression of a race which is the person whose album the lead at the beginning a lot of the time is not going to be there at the end I mean this happens in all sorts of races right happens a lot in distance where the guy who just burns out at the beginning everybody's just laughing at and then come like mile five on the marathon he starts finding out why that was such a bad idea but if you do get out to that lead the idea is until that everybody else catch up uh uh look guys I don't play as much live poker anymore I like internet poker I like live people kind of know who I am they going after me a little bit I also just don't have this much time traveling to travel as I used to a date out of this office does cost me a decent amount of money right and but when I do play live poker I just love it because I'm lucky enough to have run deep a lot of times in the last few years even though I only get to play like five live tournaments a year whereas before it was like 10 15 20 lucky enough to run really deep in some tournaments WPT Atlantic City I finished in the 20s or something out of the thousand runners or whatever it was in the main event I final table WPT Prague I finished in like the 20s or something and WPT Montreal got another final table in Montreal had a wcp main event run and it was all very fun but what people don't see is there's a lot of times like Ralph I get a big stack

the suited connectors. But if many pots are going to three bets or more, they are probably never worth playing, even if you can usually anticipate several opponents. One criteria to keep in mind when deciding to play a small pair or a medium to small suited connector is how passive/aggressive the game is, in addition to its being loose. Specifically, as just mentioned, small pairs play well in loose aggressive games providing that they are not too aggressive. This is because if you flop a set you can anticipate many bets going into the pot. If the game is too aggressive and you hold a small pair you will frequently be forced to play for several bets, and now your hand will not achieve the implied odds that it needs to be profitable. The First Two Cards: Early Position 25 If the game is passive, you prefer the suited connector to the small pair. This is because a "set" will have trouble collecting a lot of bets. On the other hand, if the suited connector flops something like a gut shot draw it won't necessarily be bet out of the pot. Here's an example of this last idea. Suppose you start with the 8474 mentioned above and the flop comes: If the game is passive you may still be around on fourth or fifth street to catch a six if it slides off. If the game is aggressive you may find yourself out of the hand. Sometimes the game will be moderately aggressive but will feature two or three players who will play virtually any ace. In games like this, (and they are very common even at limits as high as $20-$40), we recommend that you play A9s, A8s, 77, and 66 as long as the pot is not yet raised. Now if you hit your ace someone may have aces with you, but with a worse kicker, or if you flop your set someone may call a bet trying to catch that elusive ace. One hand that we have not yet addressed is a pair of jacks in the pocket. If no one has opened and you are in an early position, it is usually best to raise with JJ in a tight game and to just call with it in a loose game. With two jacks you would prefer either to have no more than one or two opponents in the hope that your hand holds up without improvement, or to have as many opponents as possible when the majority of your profits come from flopping three-of-a-kind. The worst scenario is when exactly three or four opponents see the flop with you. This most likely would occur if you called in a tight game or raised in a loose game. If you hold JJ and the pot has been raised and reraised before the action gets to you, you should fold. This is correct even when you are in a middle or late position. However, if you have already 26 Part One: The First Two Cards opened with JJ

example, joker ace equals two aces. Joker king would represent only one king and the beginning of a possible straight or flush. Joker 4 5 6 7 is a straight, and joker 7 J K A is a flush. c c c c The staying requirements are the same as in Five-Card Draw, Jacks or Better; that is, you open on kings or better. Two: Queens or Better with or without the Joker The joker counts the same as in Jacks or Better with the Joker, as above. Stay on kings or better. Three: Kings or Better with or without the Joker The joker counts the same as in Jacks or Better with the Joker. Stay on kings or better. Four: Aces or Better with or without the Joker The Joker counts the same as in Jacks or Better with the Joker. Stay on aces or better. Five: Anything Opens with or without the Joker also Any Pair Opens with or without the Joker The joker again counts the same as in Jacks or Better with the Joker. Since any five cards may open or any small pair, more players naturally stay in this game and draw cards to small pairs, two face cards, a three-card flush or straight; in fact, anything after the pot is opened. But just because the pot may be opened on anything or any small pair is no excuse for the careful player to open or stay on weak hands. You should open or stay on the same requirements as in Five-Card Draw - that is, kings or better. To play on small pairs, two face cards or three-card straights and flushes is simply throwing away your money. You should study Five-Card Draw, Jacks or Better, beginning on page 19 before playing this game. Six: Low Ball with the Joker The requirements to stay are the same as in Five-Card Draw' Low Ball, regardless of the joker. In this game the joker counts the same as an ace only. Seven: Spit-in-the-Ocean This game is a variant of deuces wild, five-card draw, except that only four cards are dealt to the players. A fifth card is dealt face up in the centre of the table and is wild, which gives everyone a wild card. The other three cards of the same denomination are also wild. The percentages in this game are about the same as in Five-Card Draw, Deuces Wild, page 70, except that Spit-in the-Ocean has only four wild cards and Deuces Wild has four wild deuces and the joker. More players will stay in this game than in Deuces Wild because everyone has a wild card in the centre of the table to start with. But my advice to you is: under no circumstances be influenced to stay because of this. Refer to Five-Card Draw, Deuces Wild, and the list of hands you should hold, page 70, before staying. Now and then you will run into a poker game not treated in this book, but if you have mastered the foregoing you will be able to

set of jacks is possible as well as any of the flopped sets.) You have $1,740 left, and there’s only $1,550 presently in the pot. To continue profitably, you have to win a significant

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THE CONCEPTS 172 Concept No. 18: Don’t get trapped with a fourth street top pair in multiway checked pots. Say you happen to be in a multiway limped pot, and you limped along with nothing great. You missed the flop, and it got checked around. The turn gives you top pair. Unless you have an ace kicker, you should often fold if someone bets more than half the pot. Specifically, you are playing $10–$20 with $2,000 stacks. You have Q♡J♡ in middle position. Two players limp, and you also limp. Two more players limp behind you, the small blind folds, and the big blind checks. The pot is $130, and there are six active players. The flop comes 7♠5♠4♣. Everyone checks. The turn is the Q♢, giving you top pair. It’s checked to the first limper who bets $100. You should often fold despite having caught top pair. There’s a decent chance you have the best hand, yet that isn’t reason enough to call. You are calling $100 to win $230, but reverse implied odds will haunt you. If you are ahead, then likely $230 is all you’ll win. But if you’re behind, you’ll probably have to face another bet and possibly a tough decision. There are three ways the hand could go wrong: 1. You could be behind already (to the bettor or someone else). 2. You could get outdrawn on the river. 3. You could get bluffed out either now or on the river. With so many opponents yet to speak, everything has to go right for you to win. It usually won’t happen often enough for you to show a profit. Concept No. 19: Don’t call in protected pots without a very good hand. A protected pot is one where anyone who bets should reasonably expect at least one player to call. If many players are still in the pot, it’s protected. If someone is all-in or close to it, the pot is protected. And if a player known to be very loose is still in the pot, it is protected. If one of your thinking opponents bets in a protected pot, that 4 bet carries a lot more weight that it would if the pot weren’t protected. Namely, the bet is far less likely to be a bluff. If someone expects to be called, yet bets anyway, you should give them credit for a strong hand. Don’t call such a bet without a very good hand yourself. Concept No. 20: Sometimes you should limp behind limpers with pocket aces. In limit hold ’em, you’d never want to limp behind other limpers holding pocket aces, but in no limit (with deep stacks) it can sometimes be a good play. You’d do this if you have opponents yet to act who like to raise a series of limpers with weak hands. “Deep limping” with aces balances your play and traps overzealous preflop stealers. You can reraise the raise (even better if someone calls the raise before you act), and you may even get more action than usual because no one

OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article , I asserted that “Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller from the blinds. You should not expect to enjoy the sort of range advantage you would against a caller from the blinds. Depending on your position and that of the caller, you may not have an equity advantage at all, and being out of position puts you at a significant disadvantage.” Thanks to new features that enable solving with custom preflop ranges , we can now consider this scenario with greater nuance. In particular, we will look at cases where the cold caller’s range is wider and weaker than a solver’s would be. Such overly loose opponents are common in live and smaller stakes online MTTs, so it is valuable to consider how you can adapt your own play to exploit this mistake . Overly loose opponents are common in live and smaller stakes online MTTs. In the following experiments, we will revisit the two flops – AJ6 r and 986 tt – that served as examples in the original article to see how our strategy changes when playing against overly loose callers. These exploits will not rely upon any further assumptions about how the opponent will play after the flop. If we knew, for instance, that they would also play too loose postflop, there would be additional exploitative opportunities, but for now we will focus only on exploiting their overly wide preflop range . Who Profits? First, it’s important to note that an overly loose player on your left is not necessarily good for you. Although their loose calls are mistakes with the potential to lose them EV relative to an equilibrium strategy, you are not the primary beneficiary of those mistakes. Indeed, these calls may result in a loss of EV for both the original raiser and the caller. Overly loose calls may result in a loss of EV for both the original raiser and the caller. The primary beneficiaries of this mistake are the other players still in the pot. When they wake up with hands strong enough to raise, they will win more chips, on average, as a result of the caller so rarely having a hand strong enough to stand up to a three-bet (and even if they stubbornly call again, they will be putting a lot of money into the pot with an overly weak range). Essentially, a loose cold caller takes EV from the raiser but loses an even greater amount of EV to the players behind them . One of the most essential exploits worth mentioning here, though we will not explore it further just now, is to tighten up your opening range when you have such a player behind you. This is especially important if that player is on the BTN, where they are most likely to call. This is true only if the player has position on you. If they are in the blinds, then you do not mind their loose calls

game. 4. There are no very big or small stacks. 5. We all have plenty of chips compared to the blinds and antes. This is not as unusual a set of conditions as you might think. Tournaments are so large now that it's not unusual to sit down at a table where I recognize only one or two faces. Most players who've paid out $5,000 or $10,000 to enter a major tournament tend to play conservatively, at least for a while. And the stack sizes tend to stay in a fairly close range until some players start calling the occasional all-in move. The strategy I'll describe is more aggressive than a straight conservative strategy, but more conservative than a lot of the play you will see. It's designed to keep you out of trouble, while making sure that when you do get involved in a hand, you have some solid values to play. At a live tournament this strategy will be just slightly more conservative than the average player around you. In online tournaments, you'll definitely be one of the tighter players at the table. When you implement this strategy, don't be concerned if there appear to be long stretches that you are just throwing your hands away. It happens to all players when they're playing well. If you get a little bored and anxious throwing lots of hands away, remember these two facts: 81 1. While television poker is real poker, most of the hands aren't shown. There are lots of hands that one player bets, and everyone else folds. On television, those hands don't make the cut. 2. In no-limit hold ’em, all your chips are in jeopardy every time you enter the pot. A player who splashes around in a lot of pots is much more likely to be flushed away quickly than one who enters fewer pots, but chooses them carefully. After I lay out the basic strategy, I'll describe some of the adjustments you need to make as these preconditions change. If you're a newcomer to tournaments, don't worry too much about those adjustments. If you can simply learn and implement the basic strategy, you'll already be playing better than many of the players at your table. After you're fully familiar with the strategy, you'll be ready to start making modifications based on the playing styles of the players or the changing stack sizes. As I describe the strategy, note that I refer to the player who is first to act after the blinds as being in first position, all the way around to the button, who is in seventh position. Then follow the small blind and the big blind. Although I'm describing the action at a nine-handed table, just remember that at a ten-handed table, you need to play with slightly tighter requirements. Who is in the Pot? What hands you use to raise, call, and fold depends to a huge extent on the action you have seen in front of you and your position. You need one set of criteria if everyone has folded to

I have position on him. Always remember, no-limit hold’em is a game of position and people. There’ll be a lot of times when only your good judgment will dictate the proper play. Often situations come up where a hard-and-fast rule will prove inadequate. Poker, especially no-limit hold’em, is not a game you can learn to play well in ten easy lessons. A thousand hard lessons might not be enough. There are simply too many variables involved. Nevertheless, the lessons you’ll learn below will go a long way in helping you to master no-limit hold’em. The general principles and concepts that I discuss will give you a far greater command of the game than almost all the players you could expect to be competing with. I wish I’d known all the general guidelines below when I first started to play. It would’ve made things a lot easier for me. That’s for sure. But before I get into how you should generally play specific hands, there should be a discussion of the ante, betting structure, bankroll requirements, and other considerations you’ll have to take into account before you sit in on a no-limit hold’em game. So that’s what I’ll do now. The Ante and Other Considerations If I had to choose a particular size game that would be close to perfect for nolimit hold’em, it would be eight-handed, also known as a ring or full game. Of course, I prefer to play in a shorthanded game with about four or five players, because in a shorthanded game with a high ante, you’re forced to get in there and play. You can’t just sit there and wait for the big pair, A-K, or even small connecting cards. If you do, you’ll go like Broomcorn’s uncle. So a game like that suits my style just fine. It gives me plenty of room to muscle the game. A full game with eight players is all right too. That’s just about the right amount of players for a ring game where there’ll be good action. I mean, 358 there’ll be people coming in the pots because they’ll know they won’t have to be looking at the nuts every hand. However, when that eight-handed game all of a sudden turns into a ten- or eleven-handed game, well, the complexion of the game changes completely. What was once a relatively fast and loose game becomes a thing of the past. The players no longer get in there and play as often. The game begins to screw down real tight. With eleven players, there are a lot more combinations out there on every hand than with nine players. So everyone stops playing borderline hands and starts waiting for the really good ones. In short, they don’t do as much gambling, and the action really dries up. Loosening Up a Game Many poker games are like that, and they stay that way unless something happens to change the character of the game. More than anything else, the something that changes a tight game back into a loose game happens when one of

think about so many different things when you're playing a hand and it can seem overwhelming but over time these things are going to just become second nature and and your decisions are gonna happen really quickly and easily and they'll start to come more natural with practice so question number two why is our UTD range the tightest a there are many players left to act B you don't want to play out of position with marginal hands see you only have position on the blinds D you have the least amount of information e all of the above or F none of the above so the answer is e um all of the above your utg ranges are just the tightest like I said over and over you just want to play really really tight at a position in an early position there are many players left to act behind you you can get three bet off your hand so in general just try and play your tightest range in early position so question three players to my left have been re-raising me very often how do I adjust a keep opening the same range and make and make them keep doing it sorry this was a very poorly written sentence I'm gonna have to change that uh sorry so B fold marginal hands I'd normally open C Min raise instead of a standard 3x big blind raise the raise raised to more than 3x the big blind so the answer is bold marginal hands I'd normally open so yeah unfortunately when you're at an aggressive table you just really need to tighten up a little bit more um you could sometimes start sizing up a little bit more so answer D would be okay only if it um if someone opened and it folded to you and leave position because you can't really adjust your sizing when only one or two players at the table is being super aggressive versus you um but the rest of the players are playing kind of standard so you don't want to you don't want to like start 5x and get pretty flop every hand just because one or two players are picking on you so if this is the case just tighten up a little bit and um against these aggressive players that have been re-raising you throw in some four bets to let them know that they need to stop messing with you so next question my table has shown everyone is playing extremely loose today I have Ace jack off under the gun what should I do should you hold fall raise 3x a big blind for a value or Min raise 2x the big blind so take a minute so the answer is C raised to 3x the big line for a value now I know this is a little confusing because I've said to you in the past if you're at a very aggressive table um you should tighten up a bit but Loose doesn't necessarily mean aggressive

No Limit Hold ’em Theory and Practice By David Sklansky and Ed Miller A product of Two Plus Two Publishing LLC FIRST EDITION FIRST PRINTING JUNE 2006 Printed in the United States of America

Hand Range 227: BN vs CO 4-bet (60bb) • All-in 31.1% / • Call 18.7% / • Fold 50.3%

from that and i don't understand that they really love it it's uniquely not their fault and they'll call down just to see the person's hand they'll give away their money just to see the person's hand so one option sucks but it gives you the payoff of a closed loop so you don't have to wonder at night like did that guy bluff me and the other one sucks but there's an open loop now the question is which one sucks less in which one will cost us the least amount of money and which one logically should we be pursuing so again i'm gonna say it again do not expect perfection from a game of chance there's a reason people do this at four in the morning while drinking whiskey and barely avoiding fist fights and screaming at each other it is gambling things happen now thankfully we can do it on the internet it's a little bit more hygienic than the check cashing places i played in the back of growing up but it's still gambling so do not expect it to be perfect there is no third hypothetical beautiful option that saves us from how annoying this spot is so remove that from your mind now let's get back to business he does a big bet does he value bet anything worse maybe but probably not that seems pretty odd for someone to play tens or jack 9 like that most of these players love to see showdowns and if they have a mediocre hand that's a perfect time to get to a showdown so is this a value hand we beat most likely not okay how about a draw now a lot of people are fixating on that yeah that's it he's got a diamond draw how many combos is that how many combos if you don't know it off the top of your head you probably should not be gambling on it just for reference every one of the combos is one it's one king ten of diamonds that's one eight nine in diamonds that's one how many combinations is an ace there it's a whole lot more i'd recommend you get a copy of flopzilla if you want to get down to this and it's a there's a lot more there are far far far more combinations of aces there than there are flush draws so okay could it be a flush off maybe maybe but there's not many of them okay is he turning a pair into a bluff then now that actually does happen with low six players sometimes but if you haven't seen them getting aggressive before it's unlikely to have happened and is it an absolute bluff it's the same thing asking ourselves is it an absolute bluff it's the same thing if we haven't really been noticing this person then not and one of these things you might have it right now but why would you give them the satisfaction why would you do that to yourself why would you

make this so without having a 2,000 page book. But with experience you should be able to recognize most of them when they come up. Brief Glossary If you've watched some television tournaments, you've probably picked up most of the terminology you need to read this book. But in case you've been out of touch the last couple of years, here's an explanation of some key terms, and it's also how I talk poker. All-in: A bet or raise of all the chips you have in front of you. Antes: Money placed in the pot by all players at the beginning of a hand. In a typical tournament, players don't ante up until five or six betting rounds have passed. Big blind: A forced bet made by the player to the left of the small blind, to generate even more action. Big stack: The player with the most chips at the table. If he uses his chips to push the other players around, he may be known as the table captain or table bully. Blinded away: If the player with the short stack doesn't play many pots, he may eventually lose all his chips when it comes his turn to play the blinds. Button: The player to the right of the small blind, who acts last on each betting round after the flop. The button is marked by a white disk which moves around the table counter-clockwise. Covered bet: Your all-in is covered if your opponent has more chips than you. In that case, you will be eliminated if you lose the hand, but he will not. Cut-off seat: The player to the right of the button. Domination: When two hands share a common hole card, the player with the lower other card is said to be dominated. When two players hold ace-king and ace-queen, the player with the queen is dominated. Flop: Three cards turned face up simultaneously in the center of the table. These cards are common to all hands. The flop is followed by a betting round Fifth street (also known as the "river"): The fifth and last card turned up in the center of the table, also common to all hands. Fifth street is followed by a final betting round. Fourth street (also known as the "turn"): The fourth card turned faced up in the center of the table, also common to all hands. Fourth street is followed by a betting round. Hole cards: The two down cards dealt to each player at the beginning of the hand. No other player can see these cards. Initial pot: The sum of the blinds and antes (if any) before the betting starts. Nuts: A player with the best possible hand has the nuts. Out: A card which will give you a 6 winning hand if it arrives. Short stack: The player with the fewest chips at the table. Side pot: When several players go all-in, a side pot will include those chips than cannot be covered by the smallest stack. In a few cases, there may be multiple side pots.

large spade or two spades. You assign the number depending on what your opponent thinks you have and the type of player they are. Boat – Another name for a Full House. Broadway – An Ace high Straight, also people consider face cards big Broadway cards. Bullets – A Wired Pair of aces in the hole. Button – The marker that represents where the dealer is which means that is the last person to act at the table after the flop. Calling Station – A player who only calls bets and does not take advantage of their good hands by raising. They also will not fold very often so you should not bluff them but need to show down the best hand. Case card – The fourth card of any rank that makes Four of a Kind. Check-Raise – Usually, but not always, someone in early position will check with the intention of raising if someone else bets after them. Cold Call – Is to call two or more bets at the same time. For example, if one player calls and another player raises you are forced to call two bets. Continuation Bet – A bet made after the Flop by the Pre-flop aggressor as a continuation of the original raise. Used to win the pot right there or figure out how strong the hand is after the Flop. Cowboys – The name for two wired kings in the hole. Cutoff Position – One seat to the right of the button/dealer position. Domination – When two players hold the same card rank and one player has a better kicker. For example, AK dominates AJ because they both share an Ace. The only way AJ can win is by hitting a Jack. The AK is always dominating the hand because if an Ace hits the board the AK is still winning. Therefore, the AJ has only two outs while the AK has five outs (excluding any Straight or Flush Draws). Double Belly Buster – Is the name for an inside Straight with two ways to win. Say you have 74 in the hole and the board cards are 2 5 8. You need a 3 or a 6 to catch one of your two inside Straight draws. Drawing Dead – You have no way to win the hand with further cards to be dealt. Equity – Your mathematical share of the pot and your chances of winning it. Say you have pocket Aces against two people, your pot equity is over 70 percent of the pot. EV or Expectation – Is the amount of profit or loss you would expect to make if there were no variance in poker. If you are dealt AQs three times, you are expected to win a certain amount of times with that hand. Therefore, a raise with AQs is playing the positive expectation of your cards. In the end, your AQs will show a profit due to probability. Family Pot – When everyone at the table has entered the pot. Fill Up – To make a Full

Figure 17 - The ISO Triangle As you can see, there are three points to consider in these spots just as there are three points in a triangle. The larger the area surrounding each point, the more influence that point has over our decision of whether or not to ISO. Moreover, the three points are inversely proportionate to each other in that the more of one Hero has, the less of the others he'll need. In this metaphor, for ISOing to be better than not ISOing, the triangle should be more full than empty. Let's go through the three points one by one and find out what each entails.

pay and see. Value Betting As we’ve said throughout the chapter, sheer aggression is key in limit hold’em. It is a mathematical game, one in which you want to maximize your wins while minimizing your losses. In order to maximize your wins, you’ll need to be sure that you get full value for even the most marginal of hands. To value bet in the correct spots, it’s important to think about what your opponent could have. If you put your opponent on nothing but a draw, he simply won’t call you on the river unless he makes it. Even then he probably won’t just call you, he’ll raise you! For example, say you hold A? J?, and you take the lead the whole way. The turn comes J? 9? 6? 2?. At this point, you are quite sure you have the best hand and think your opponent is on a flush or straight draw, or possibly a pair of nines or even jacks. So now the river comes with the 9?, and it‘s up to you. If your opponent was on a draw, there is little value in betting here; he’s obviously missed and will fold. If he also has a pair of jacks, there is a good chance he will bet when you check anyway. More importantly, if your opponent does have the three nines, he’ll raise you, and that will usually cost you an extra bet. These are situations where you might want to avoid value betting. Notice that in this example you are out of position. When you are in position, you will have at least twice as many opportunities to value bet than when out of position. If a player has checked the river to you, you should usually bet if you feel you have the best hand. Unless your opponent is setting a trap for you, his check on the river will mean it didn’t help him. If you had the lead going into the river, chances are you still have it. Basically, you should value bet any time you feel that your opponent will call with the worst hand more than half the time on the river. If you have bottom pair but feel your opponent would call you with ace-high, you should bet. 155 Furthermore, if you feel your opponent is calling you down with ace-high, you might even bet with as little as A-K high! That situation is rare, but not unheard of. In closing, don’t be overly worried about a check-raise. It’s not like no-limit, where a check-raise could cost you your whole bankroll. In limit poker, it’s only going to cost you another bet. You should be able to make up for a lost bet or two by picking up your fair share of value bets on the river. Bluffing Bluffing on the river is less effective than bluffing on the turn. Usually when your opponents get to the river, they are going to throw in that last bet if they have any chance of winning. As you’ve learned in this chapter,

You should try to assess most poker games in terms of your expected hourly rate by noticing what mistakes your opponents are making and how much these mistakes are costing them. Don't sit in a game with an insufficient hourly rate projection unless you think the game will become better — either because you expect some weaker players to arrive soon or because some good players in the game have a tendency to start playing badly when they are losing. If these good players jump off winners, you should quit if you can. However, it is sometimes good to continue in a game with a low hourly rate projection for political reasons — you do not want to get a reputation for gambling only when you have much the best of it. Such a reputation can make enemies, cost you money in the long run, and even get you barred from some games. Chapter Three The Fundamental Theorem of Poker There is a Fundamental Theorem of Algebra and a Fundamental Theorem of Calculus. So it's about time to introduce the Fundamental Theorem of Poker. Poker, like all card games, is a game of incomplete information, which distinguishes it from board games like chess, backgammon, and checkers, where you can always see what your opponent is doing. If everybody's cards were showing at all times, there would always be a precise, mathematically correct play for each player. Any player who deviated from his correct play would be reducing his mathematical expectation and increasing the expectation of his opponents. Of course, if all cards were exposed at all times, there wouldn't be a game of poker. The art of poker is filling the gaps in the incomplete information provided by your opponent's betting and the exposed cards in open-handed games, and at the same time preventing your opponents from discovering any more than what you want them to know about your hand. That leads us to the Fundamental Theorem of Poker: Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their 17 18 Chapter Three hands the same way they would have played if they could see all your cards, you lose. The Fundamental Theorem applies universally when a hand has been reduced to a contest between you and a single opponent. It nearly always applies to multi-way pots as well, but there are rare exceptions, which we will discuss at the end of the chapter. What does the Fundamental Theorem mean? Realize that if somehow your opponent knew your hand, there would be a correct play for him to make. If, for instance, in a draw poker game your opponent saw that you had a

Pre-flop: Not much to say about this open other than that it's standard unless we have highly aggressive 3-bettors ahead. Flop: As donk bets go, this is a huge one. This makes calling less attractive as pot odds and implied odds decrease substantially vs. a huge bet. We have little player specific information on Villain here as is so often the case with Fish. Since recreational players come and go like the wind, building up a large sample of data on them will be difficult. So often we have to go on general player type reads in these spots, lacking more specific information. As this flop texture is pretty wet, there are a vast array of draws and made-hands of varying strength that we can assume this player type is going to dissuade himself from folding should we raise. We know that fold equity and implied odds are inversely proportionate so doesn't Hero have enough implied odds to call? Sadly not. Although the few times Hero does stumble into one of his four outs on the turn, he's likely to get paid off, the price to chase with no future fold equity is too unfavourable

study aggregate reports. Apply filters to study strategically similar flops and look for general trends in the strategy at different points on the flop. Ask yourself 🤔 “What sizing does it generally use on low paired flops in this spot”? “Why is that”? Try to develop a broader heuristic that explains the cause>effect relationship. You can also study turn reports for one particular flop. Turn reports are great for developing follow-through strategies. Use the Ranges Tab to Understand the Big Picture The ranges tab lets you compare both player’s ranges at the same time. Comparing range asymmetries and equity distributions can be used to understand the motivations behind the GTO strategy. You can compare different hand classes and equity buckets. Fundamental Poker Math Poker is intuitive in practice, but mathematical in nature. Humans cannot calculate optimal strategies at the table. However, it’s imperative to learn these fundamental concepts so that you can apply them in an abstract sense. You should understand that you don’t need to defend wide when your opponent puts in more money relative to the pot. You should understand the basic shapes of ranges and how that influences your strategy. You should know the principle of indifference. You should learn how pot odds connect to the required bluffing frequency. The goal is to understand these concepts on a broad, abstract level. Expected value – Every decision you make is underpinned by one common goal – to maximize return. Equity – Equity refers to your chances of winning a hand if the pot were checked down. Range morphology – Ranges are easier to understand when you think of them as shapes. ICM basics – Learn how tournament survival pressure affects your strategy. Visualizing Implied odds – The value you expect to gain on future streets when you outdraw your opponent. What are Pot Odds in poker? – This essential risk/reward calculation tells you when a call becomes profitable. MDF & Alpha – Minimum Defence Frequency is the shield you use to prevent your opponents from running you over with bluffs. Learn how wide to defend in poker. Mathematical Misconceptions in Poker – Address common misunderstandings and develop a more nuanced understanding of these mathematical concepts. How to solve toy games – Put it all together by learning how to solve toy games. Understanding GTO Why do people want to learn “game theory optimal strategies?” What does that even mean? What if my opponents aren’t playing GTO? (Spoiler, they’re not). Read these articles to learn more about the goals and nature of GTO. What is GTO in Poker – What does GTO mean? What does GTO aim to achieve? – What is the purpose of GTO in poker? The value of fold equity – Learn about the value of relative fold equity with an experimental approach. Does your range affect your strategy? – A philosophical theory article about the nature of fixed strategies and where your EV comes from. Understanding Solvers Solvers are the engines we use to approximate optimal poker strategies. These articles cover the practical application, nuances, and limitations

six sittings of four hours each you will win five and lose once. But when you do lose, your losses should not be more than one-half of your average winnings per sitting. 'You should increase your winnings and lessen the losses by learning when to call and when to bluff. But whether you become proficient or not in the art of deceit, if you will only follow the minimum requirements to stay on you will come out winner. Remember it costs only seven cents to look at three cards. With the cost so small, why get involved on a weak hand? There is always another deal coming up. 'You must be more patient,' I told Ling, 'in seven-card stud, because I have restricted what you play on so drastically. But the pots are larger and you will win more, though not so often. The important thing is to avoid coming up with second-best hand. Be patient. Just stay in the deep freeze a bit longer.' A servant came in to tell us there was one vacant seat at the poker table. They played in one of the private rooms on the first floor on a large kitchen table. Ling and I had played there before, but I never ceased to marvel at the casual method of play. I had heard this is accepted style in the Orient, and if so, the card sharps had overlooked a lucrative field. To be sure it takes a lot of Chinese dollars to buy anything and the stakes were in Chinese money -bundles of it. The play was slovenly. No one paid attention to the rules as I know them and they often made new ones on the spot to cover a disagreement. With childish wishful thinking they disregarded all mathematical probabilities; they bet Chinese and Hong Kong money as if it had no value whatsoever, though to get it they must convert gold into Chinese or Hong Kong. And to my horror, they more often than not threw in their discards face up! They broke all the precepts on how to win at poker as known in my youth. Monty, in whose poker place I had cut my eye-teeth, would simply have passed out at the prospect of such an easy game as was afforded by the Hostel. When I entered with Ling, the table was still full. Pop Weiner greeted me with, Tm quitting in a moment, Osborn.' He owned a compound along the North River, which flows into the Yangtze. Though a Dane, he claimed German citizenship since there was no Danish Government representative in Chungking to protect him. He was about seventy-five, sported a Kaiser moustache together with a Vandyke beard, and had lived in Chungking for forty-five years. He served tiffin to a nondescript lot of Chinese and foreigners, rented rooms to couples with no questions asked, and ran a bawdy house on the side. His speciality was Chinese college girls in distress, though if the truth were known they were prostitutes who had never seen the inside of a school

So let’s stop getting so excited about flopping top pair. It’s a good start, but we’re a long way yet from home and dry. In this situation, then, it’s more important than ever to set a clear goal with the hand; it’s not like such a hand plays itself. So what’s the goal here?You can’t say it’s only to extract the most money from your opponent; in the case where your opponent has you murdered, that’s going to cost you a ton. You also can’t say it’s only to lose the least against your opponent; when you’ve murdered your opponent, that goal will cost you, too. The problem is that you really want to do both. If you knewyou had the best hand, you’d want to play the hand like a set, extracting every last penny from your opponent. If you knewyou had the worst hand, you’d fold. This is why playing top pair is so hard: We have two goals fightingagainst each other. We want to win the most money from worse hands and lose the least money to better hands. Well, here’s good news: Not only is it possible to satisfy these two goals at once, it actually conforms neatly to all of the game-theory and mathstuff we’ve been talking about, and provides nice cover for other kinds of hands to boot. This isn’t to say it’s an easy thing to think through. It’s not. Playing top pair is about the most difficult flop situation you’ll face. But it’s least difficult when the board isn’t textured, so that’s where we’ll start. Top Pair Is a Medium-Strength Hand To recap: When you flop top pair, you either have way the best or way the worst hand and you don’t know which. Looking at the hands worse than yours, you can see that they all have very few outs to beat you. If you hold AQ on an A-9-3 rainbow flop, a hand like AJ has three outs. T9 has five outs (minus your redraws). You could also face a hand like TT with two outs. Pure air, of course (a hand like J7, say), can only beat you on a bluff or some crazy runner-runner. Note, then, that on an untextured board, hands worse than yours have scant chance of catching up (at best 20% with two cards to come). On the other hand, if you’re up against AK or better, say (or AQ if you’re holding AJ), you have a maximum of three outs to win. And that’s what makes this situation so interesting and tricky. You’re either way ahead or way behind and in the absence of draws, there is no in between. This isthe fundamental fact of top-pair holdings and it’s worth searing into your brain: WITH TOP PAIR, YOU’RE EITHER WAY AHEAD OR WAY BEHIND The problem, of course, is you don’t know which. And you really can’t know which. Absent super-human reads, you have to admit that a wide range of opponents will get identically involved with AK and AJ. Players treat those two hands about

Navigating Nasty Rivers Out of Position Theory Playing out of position (OOP) is hard. It’s fundamentally disadvantageous to act on each street without knowing… 26/03/2024 14 min. / 20 sec.