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

Hand Range 261: UTG+1 vs UTG (25bb) • 3-bet 5.1% / • Call 3.6% / • Fold 91.2%

read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be a dicey proposition in single-raised pots. Cold… Dynamic Sizing: A GTO Breakthrough Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Dynamic Sizing Benchmarks Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Understanding The Impact Of Field Size On ICM In Poker When people talk about game selection in multi-table tournaments (MTTs), they invariably talk about the… Defending vs BB Check-Raise on Paired Flops This is a companion piece to Attacking Paired Flops from the BB; you will get… Mastering PKO Final Tables Final tables can be the most exciting and rewarding phase of a tournament, and being… Attacking Paired Flops From the BB Paired flops present unique challenges to both a preflop raiser and a BB caller. The… KK vs QQ vs JJ at WSOP Main Event With only fourteen players remaining in the 2023 WSOP Main Event and blinds of 400K/800K/800K,… Responding to BB Squeezes You open raise, someone calls, and the BB squeezes. How should you construct your strategy?… Crushing a Top HUNL Poker Bot In 2022, Philippe Beardsell and Marc-Antoine Provost, a team of Canadian programmers from Quebec, developed… GTO Wizard AI Explained We are excited to introduce GTO Wizard AI, formerly known as Ruse, the world’s best… GTO Wizard AI Benchmarks GTO Wizard has combined the power of artificial intelligence with traditional solving methods to bring… Table Management in PKOs Perhaps the most important strategic consideration in Progressive Knockout Tournaments (PKOs) is making sure you… Overcalling From the BB In poker, overcalling refers to calling a bet or raise after another player has also… Understanding Which Mistakes Cost You the Most Money I am fortunate enough to have worked for many years with the mental game coach… Overbetting The Flop in Cash Games Although most commonly analyzed on turns and rivers, flop overbetting can be a devastating weapon… Using New Skills at the Poker Table How many times has it happened to you that you make a mistake only to… Flatting Ace-X Hands Shortstacked Playing out of position is tricky, but it’s an essential part of tournament play. With… Playing Limped Pots as the BB in MTTs

group has usually flopped a backdoor flush draw and overcards to the board and so will float sometimes. Villain must be careful though as these overcards are often dominated and hitting them can be as much of a curse as it is a blessing vs. our uncapped linear range. We still expect to get a good amount of folds from this group. The yellow group has sufficient SDV to usually want to peel the flop but it's not unheard of for Regs to fold these hands. Finally, the red group is one pair plus and pretty much never going anywhere. The eager combo counter should take this moment to count up what percentage of Villain's range each of these groups constitutes. The result will show how much more fold equity we have than the measly target we have to surpass when we bet half pot usually with two overcards or better when called. The average Villain with these stats will certainly fold much more than 23% here. While this doesn't automatically make c-betting the highest EV line in and of itself, I can't imagine checking behind being better. C-betting everything is a good way to utilise range advantage, make lots of high EV c-bets in a vacuum and play an unexploitable strategy. Hero bets 8BB

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 GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack

What is Valor in poker? What is Valor? Long ago, the term valor described knights’ bravery on the battlefield . Zenith Poker was the first to introduce the concept of valor 🎖 Valor is your hand’s ability to bet or raise future streets for value . Qualities like the ability to continue vs aggression on later streets, or outdraw your opponent’s value range significantly increase a hand’s valor. Valor captures the quality of fighting for pots through betting and raising. High-valor hands can maximize value by putting in big bets or raises over multiple streets regardless of runout, while low-valor hands minimize losses by playing more passively. How does Valor relate to Equity, EV, and EQR? Equity (EQ) measures how often you’ll win if the hand were checked down. Expected value (EV) measures how much money you’ll actually win in the long term. Equity Realization (EQR) measures the difference between a hand’s EQ and EV performance. EQR = EV / (pot x EQ), which simply compares how much you expect to win vs how much your raw check-down equity would win. A hand that over-realizes its equity tends to capture more than its “fair share” of the pie. Valor is your hand’s ability to bet or raise future streets for value. Hands with high valor tend to over-realize their equity (EQR > 100%). In addition, hands with high valor tend to have high implied odds . Valor demonstrates how to turn equity into EV through aggressive actions! Hand Example [NL 500 Cash Game, 100BB effective] BTN v BB single raised pot: A ♠ K ♠ 6 ♦ . BTN has the option to c-bet flop. Here we can see the GTO strategy for BTN. The optimal strategy for BTN is to overbet or check. This strategy maximizes the value of BTN’s nutted hands. Strong top pair+ hands overperform with this strategy. Conversely, middle pair and pocket pairs tend to bet less frequently because they don’t retain much equity when called, and don’t fold hands that can easily outdraw them. Thus, they check back more often (unless accompanied by a draw) to get one street closer to showdown. Third pair (6x) is actually a semibluff here! Let’s compare the strategy to BTN’s equity realization : Hands with high equity realization, such as strong top pair+, flush draws, or gutshots, tend to have high valor. As a result, these hands outperform their equity and can bet multiple streets for value or outdraw the opponent’s range in the case of the semibluffs. Let’s filter for two pair and sets within BTN’s range: BTN only c-bets 40% of the time here, but sets and 2 pairs are bet frequently. These are high valor hands because they are often the best hand and we can value bet two or three streets quite often. These are pure value hands: our EV goes up when we bet and get called or raised. Now let’s filter for top pair: Top pair varies widely in EV and valor here. While it’s often the best hand, you usually need strong two pair

should generally bet out nomatter what hits on the turn or what suited cards you hold, since you can represent having either the big made hand or the flush-draw semi-bluff check-raising on the flop. Of course, if the third suited card hits and your opponent clearly shows excitement about the card, feel free to check and fold. Likewise, if theboard bricks the flush draw on the turn and your opponent looks particularly relieved to see that, feel free to check and fold as well, unless youspecifically have the ace in suit in your hand. Top Pair, Multi-Way, Out of Position, Without the Lead, Textured Board Now let’s put you out of position without the lead. Should you bet? Not just no, but hell no. That’s the pre-flop-raiser’s job. Plus, your lead-out bet can’t do you any good. If you get a bunch of callers, you’ve learned nothing about their hand strength and if you face a raise, that’s just ugly. In a multi-way pot with texture on board, is your AQ a hand worth protecting? Not really. Most people have a knee-jerk desire to protect their ace —any ace—but this hand is so fraught with problems, your bad position and your uncertainty about the next card being paramount, that you’re better off just checking and seeing what everyone behind you does. Note that if player B bets (you now being player A, right?), you actually get the right of last action. Remember that although you have AQ, your hand is medium-strength, nothing to get too excited about, especially with your bad position and all that texture. And if you do lead out, are you not defining your hand for exactly what it is? You wouldn’t be leading out bluffing into all that traffic. Maybe you have the flush draw (though most players would be trying for a free card) or a big pair, but definitely you’ve got something. Don’t giveaway that information. Plus, you really can’t stand a raise here. If you lead out with your proud little top-pair good-kicker and you get raised, you’re in a tough situation. You can sidestep that—for all these right reasons—by checking and seeing what happens next. Again, if there’s a lot of sick action behind you, you can get away from your hand—for free! But check this out: Suppose you check, B and Ccheck, and D bets. What position is he in? That’s right, the bullshit seat. So now you can raise. Think about how strong that raise looks. It looks likeyou were lurking and waiting for just the outcome you got: meek checks from the middle-position players and a reckless adventure from the player in position. It’s likely that you’ll win this pot right here. If you check and a bet comes from B, it’s a slightly different story. Let’s say B bets, and C and D fold. Now you can flat-call and play it heads-up. You know he’s got something, but you don’t know if you’re ahead or behind. From our previous discussion, we know that the best line of play is check-calling,

range, so it would have “direct” pot odds to call. However, this hand will not realize enough equity and therefore not recoup the 1.5BB call investment. This is where the concept of implied odds, reverse implied odds, and equity realization come into play. A “naive” pot odds calculation assumes equity = pot share. In reality, equity only equals pot share when no more betting occurs after the call. Read this article to learn more about implied odds! Pot odds limitations example 8Max MTT, 40BB effective, 12.5% ante BTN opens 2.3BB, BB calls. Flop: KsQh3d BB checks, BTN bets 2BB into 6BB. A “Naive” pot odds calculation would tell us to continue with any hand that has at least: 2 / 10 = 20% equity. Let’s use GTO Wizard to look at BB’s equity facing this bet: Now let’s compare that to the optimal GTO strategy: We see the solver folding hands like A7o with over 40% equity, and calling with hands like 42s which has only 18% equity. So what’s going on here? Just because a hand has 40% equity doesn’t mean it wins 40% of the pot! A7o likely has to fold to any future bets if it doesn’t turn an Ace. A7o has 0EV facing this bet. 42dd has much less equity, but it has better implied odds drawing to many backdoor flush/straight draws. 42s also has 0EV. Lastly, in the Breakdown tab , this Manhattan graph shows the entire BB strategy, sorted by equity. We’ve marked the 20% threshold below: Pot odds and Expected Value Pot odds are just a shortcut for calculating the breakeven equity required to call a shove. The shortcut we’ve outlined earlier (call/pot after you call) can be derived from an expected value equation. Call EV Example Learning how to calculate the expected value of a call is important because it tells us more than the breakeven point. It tells us exactly how profitable a call is! To calculate the expected value, we set up an EV equation like so: EV (Call) = (Win% x Win$) – (Lose% x Lose$) Win% is our equity Lose% is 1 – equity Win$ is how much we gain (relative to folding) when we call and win Lose$ is how much we lose (relative to folding) when we call and lose Note about Win$/Lose$: These are measured relative to folding at the decision point. Using the CO vs SB shove first example, how much does a call with AKs yield? Win$ = Amount we win when we call (197BB) subtract our call (75BB) = 122BB Lose$ = The amount to call = 75BB Win% = 48.4% Lose% = 51.6% EV (Call) = (48% x 122BB) – (51% x 75BB) = 21BB Or about $10.50 playing 50NL. Deriving the pot odds formula from expected value EV (Call) = (Win% x Win$) – (Lose% x Lose$) Let’s replace win/lose% with Q (for equity) and 1-Q. We’ll also replace Win$ with W, and Lose$ with L. EV (Call) = (Q x W) – ((1-Q) x L) Set EV to 0 to find

On the second draw, your opponent is pat and you draw one to the wheel. This time, you catch another 7! Unless your opponent has both the case 2 and the case 7, he doesn’t have a pat seven. Your opponent bets. What should you do? It all depends on your read of your opponent. You have a pretty good idea as to the strength of his hand, most likely an eight or a nine. Will your opponent fold? Will your opponent come off of a nine and draw? If you think there is a reasonable chance that the answer to either question is yes, then go ahead and raise. By investing one more bet, you may either win the pot right there or go from an underdog to a sizeable favorite. If it doesn’t work out, it adds more deception to your game at little cost, deception that you can exploit later. After all, you have one more draw and could still make your hand. In order for a play like this to work, you have to know your opponent. If you know him to be stubborn enough not to break or fold, save your money. However, if he is a thinking player, he’ll ask himself, “What can I beat?” Since you played the hand so aggressively before and after the first draw, a thinking player would know that you have a strong draw. If he is looking down at 3-4-6-8-9, what could he possibly break and draw to? He has to simply hope and pray that you are making a play and that you will miss on the last draw. Based on all of this, a thinking player may decide it’s not worth seeing the hand through and fold. Remember, though, do not try this play against a calling station. Trying to bluff a bad player will make you the fool. Check-Raising 312 There are times when you’ll be able to get in a check-raise after the second draw. Often, this happens when you are one card behind going into the draw, either drawing two to your opponent’s one or drawing one while your opponent stays pat. Anytime you make your hand in this situation, you should be able to check-raise. After all, if your opponent is playing properly, he’ll bet to keep from giving away a free draw. Your check and your opponent’s bet here should be automatic. You could even check in the dark, and your opponent would probably bet in the dark, but I wouldn’t recommend doing this if there are novices in the game. While it’s obvious to you and the other experienced players that these bets are automatic, a novice may not grasp it. So if there are rookies at the table, at least pretend to look before you check. If you happen to make a good eight or a seven, check-raising is probably a good idea. These hands might already be dead, but there is an excellent chance that your opponent is still drawing. Playing a rough eight or a rough nine is a

a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds are the value you expect to gain over and above your raw equity.… ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but what… What is Equity in Poker? The term “Equity” is ubiquitous throughout poker theory. Equity refers to your chances of winning… Range Morphology “Morphology” is the study of form or structure. You’ve probably heard terms thrown around such… What is Expected Value in Poker? Expected value (EV) is the most fundamental metric in poker. Every decision you make is… Why doesn’t my solution match GTO Wizard? So, you’ve got your own solutions to some spot, compared it to GTO Wizard, and… Understanding Nash Distance Understanding Nash Distance. One of the most common questions when studying with solvers is “Why… Combinatorics Poker Puzzle Today we have a special puzzle for you that will test your intuition as a… The 10 Most Important Concepts for New Poker Players The 10 Most Important Concepts for New Poker Players. Fundamentals are one of the most… What is GTO in Poker? The meaning of GTO in poker is Game Theory Optimal. Game theory is a study… What does GTO aim to achieve? So what exactly is a GTO strategy? What makes it “unexploitable”? What does it try…

combinations so the first scenario is if Ryan was being balanced if Ryan was being careful and he he said you know what if I squeeze here and either player decides to be aggressive and thinks I'm full of it then I'm going to lose a lot of my chips so you know what I'm going to use Aces and Kings for Value that's 12 combinations because of the pairs are six combinations each and then he says I'm going to use ace5 suited and that's going to be in my single Bluff so suited hand there's four combinations there so we have a three to one ratio now value value to Bluffs right so 25 of the time we win the full pot which is 150 000 but 75 of the time we're only going to have 20 Equity so in that situation we lose 80 000 chips and so if you if you take those two numbers you know 100 000 that we win 25 of the time and then we're losing 101 000 75 percent of the time that results in a net loss of 10 big blinds on average so of course we're going to want to avoid that situation um you know if we're if we're doing it way too much then it's it's not going to be good for us by uh back shopping I mean so scenario C I mean scenario B is versus old man coffee you know the the tight guy who literally never has a bluff so of course we're going to want to avoid this right so very easy math here we're losing a ton we're losing 20 big blinds but you know this this goes not only through this spot but many spots so let's say you have a really good bluff catcher on the river but the guy that is betting into you never Bluffs well it might be as good as having two napkins right it doesn't matter how good your your blockers are or how good your bluff catcher is if your hand is a bluff catcher and the guy number Bluffs so same thing here right if if he only has Aces or Kings we better let our hand go now moving on to scenario C which I think is the most likely scenario and let me explain why so scenario C are guys really really out of line so here's just a couple pictures it's it's the same thing just wanted to show you a little bit about combinations so here's his value range he has his Aces and Kings right now we we added in some Bluffs so we have four combinations of some of these Asus we have a couple combinations of this canine suited and then what you'll see here at the bottom this is uh this is the combinations of the offs you can so like I said with off suit hands there's 12 combinations and this is Ace Jack that's highlighted um and so why is this important so if

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 GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a

CHECK-RAISING 101 We have discussed elsewhere that it is often right to check (and call with) a good hand on the river as long as you think that your opponent will more likely bet (usually a bluff) a worse hand than yours than call with one. (This condition is met more often in no limit than in limit because the bigger river bet is more likely to get mediocre hands to fold.) Well the same condition often holds true with a great hand. With a merely good hand your check and call will often induce and win you an extra bet. Don’t blow that won bet just because your hand is better than merely good. Situation No.2. You have a great hand and you think your opponent will both bet and call a check-raise, but not raise if you bet or call an original bet that is approximately the size of the sum of the bet and check-raise. This second situation, while logically ironclad, suffers from the fact that in real life it comes up so rarely. You need to be awfully sure that he will bet and call a check-raise that adds up to approximately the original amount you would bet and also be fairly sure that he wouldn’t raise a smaller bet on your part. You really have to know your opponents well to pigeonhole them so specifically. The most likely situation might be where the last card completed a flush, and you have the nut flush. In theory there could be other situations where a check-raise with a great hand against an opponent’s good hand might be better than a simple bet. For instance, you might think that a check will always result in a bet of about $100 and an 80 percent chance that a $300 raise will be called. But a simple bet of $400 is only 70 percent to be called. These situations (as well as the original one specified in situation No. 2) are so rare that you really can’t go wrong making a fairly big bet almost every time when your great hand acts first against a likely good hand. There are, though, a couple of reasons to check the river occasionally with a great hand against an obvious good hand. One reason is that you don’t want him to be sure that your check indicates weakness. His uncertainty may, on a future hand, stop him from betting a slightly better hand than yours for value. His fear of a check-raise thus saves you money. The other reason you might sometimes check a great hand against an ap- parent good one is to set up a future check-raise bluff. Situation No.3. You want to bluff. A check-raise bluffon the river should be tried every once in a while against certain players in certain circumstances. The daring version of this play is doing it when there is little doubt that your opponent has a good hand. This means that you are opting not to come out bluffing with your busted hand, but instead you are

if it looks like your opponent has missed his hand, there’s usually no reason to bet any further. So you just show your hand over, or you check it and give him a chance to bluff. That’s no-limit hold’em in a nutshell, but as you know, it’s a far more complex game than that. As you continue reading, you should be aware that my advice is intended to provide you with some general guidelines. I keep emphasizing this because it’s so important that you understand it. There’s not a single play that I’ll always make with a particular hand. I’m liable to play every hand differently depending on the circumstances. The standards I have guide me in a general direction, as they should you. But sometimes, even I don’t know exactly what I’m going to do until the situation comes up. Whatever my first feeling or impression is at the time, I’d go with that. For example, I said I’d check my pair of aces one time if there were an open set of trips on the flop. On fourth street, if a man made a big bet, or if I bet and he moved-in on me, I’d probably go ahead and pay him off. If a man’s lucky enough to flop quads when I’ve got two aces, he’d have to show me— unless I’ve got a lot of money in front of me and there’s not too much money in the pot. Let’s look at a specific example, just, remember that no matter what I say now, I might do just the opposite if the situation calls for it. That depends on a lot of things, especially the guy in the pot with me. What do I know about him? So it’s back to people again. Nevertheless, here’s what I might do. Let’s say there’s $20,000 in the pot. I’ve got $70,000 on the table. My opponent has $20,000, and he moves in on me. In that case, I’d probably pay him off if I knew him to be a player, as opposed to a rock. However, if my opponent also had $70,000 and over-bet the pot by moving in his entire stack, well, then I’m not sure what I’d do. As I said, I’d go with my feelings. I’d look at him and then I’d decide. To start with, if he made a move like that I’d turn my hand face-up on the board. And I’d watch him real close. I’d want to see what his reaction was when I turned the two aces up. It would take a strong man not to show some kind of emotion. And from the emotion I saw, I’d judge whether he had quads or not. Then I’d react according to whichever way I felt. 374 Fourth and Fifth Streets As I noted, you continue to bet your big pair on fourth street when it rags off and it doesn’t look like it completed the straight or flush draw that showed on the flop. If your opponent wants to draw again, you make him

gappers, hands that can make the nut flush, etc. 7) Use Smaller Bet Sizes We’ve said it before, and we’ll say it again – defense gets much tighter multiway. Therefore, it’s very easy to overplay your range if you use large sizings . Consider your equity retention carefully in multiway pots. Equity retention is how much equity your hand retains once your bet is called . [NL500 Cash] BTN opens BB calls, flop is A ♣ T ♣ 2 ♠ . In a heads-up pot , BTN normally prefers overbetting. Here’s their equity once BB calls a 125% pot-sized bet (BB even overfolds quite a bit here!). Most of the strong top pairs are still well ahead of the calling range. As a reminder, the flop is A ♣ T ♣ 2 ♠ Now let’s compare this to a multiway spot. [NL500 Cash] BTN opens, SB calls, BB calls . We’ll use ranges from GTO Wizard . The average burden of defense is 25% per player facing this overbet (compared to 44% HU). Typically, SB would defend less than BB, but let’s just simplify and make both players call with the top quarter of their preflop calling range. As a reminder, the flop is A ♣ T ♣ 2 ♠ . Here’s BTN’s equity against the top 25% of SB and BB’s range. Surprisingly, even some two-pair like A2, or strong top pair like AK, are behind the collective calling ranges! We have effectively overplayed two-pair with a single flop bet… Note that the blinds should actually fold quite a bit more, so I’m overestimating BTN’s equity here. This is why you should typically size down in multiway pots . Your equity retention just plummets off a cliff as the collective defense facing large bets results in extremely strong ranges. That said, there are certain spots where you can overbet multiway. These strategies are reserved for scenarios where you have a significant nut advantage and can profitably play for stacks with those nutted hands. Multiway overbets are much rarer than in HU pots. 8) Positional Advantage Increases Positional advantage stems from the information gained from your opponents acting first, as well as the ability to close the action on each street. In multiway pots, positional advantage gets amplified as you have even more information , and closing the action becomes more valuable. Conversely, it’s much less profitable to play when many players are yet-to-act behind you. The simplest way to demonstrate this principle is to compare BTN’s cold-calling range to SB’s cold-calling range. In most cash games, BTN should defend wider than SB facing an open raise, despite BTN having more players left-to-act behind and a worse price on calling. Let’s cherry-pick a deepstack spot to demonstrate this principle (deep stacks further magnify positional advantage). [500NL 200bb Cash] CO opens 2.5bb . Let’s compare the BTN and SB preflop defense. BTN vs CO RFI SB vs CO RFI Note that BTN defends 8% wider than SB! This is a function of having position on the preflop raiser but also potentially having position

To be indifferent between calling or folding, P2 has to win with a frequency of: This is the exact same number as his pot odds: This result shouldn’t be surprising, as P2 wins the pot with the same frequency as P1 bluffs. We know that on the river, with no more cards to come, the pot odds simply tell a player how often a call has to be good for it to break even. So, to make P2 indifferent between calling or folding, P1 must bluff with a frequency equal to P2 pot odds.

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

The Right Way To Think About Protection Theory Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the SB. The… 08/01/2024 8 min. / 19 sec.

Hand Range 10: 60% BN Opening Range BN Calling Frequency:

and so there was little need to reduce the amount of combos we opened in the first place. In Hand 98 above, it's absolutely essential that we open tighter than any range that includes J9o. As we know, being out of position limits the amount of hands we can profitably flat a 3-bet with. Moreover, there is not one, but two very aggressive Regs waiting to pounce behind us with high 3-bet stats. If BU happens to actually 3-bet 15% in this late position battle spot and SB 13%, then we in fact face a 3-bet 1 - ((1-0.15) x (1-0.13)) = 1 - (0.85 x 0.87) = 26% of the time. This is huge and doesn't even take into account the unknown BB's 3-bet frequency, which should be assumed to be that of the average Reg in our games (normally somewhere between 5 and 8%). The EV of opening hands at the bottom of a standard or light CO range is completely decimated here. Let's summarise by saying that Hero should tighten his opening range in the face of light 3-betting whenever he doesn't have a more +EV route to exploiting the light 3-bettors that involves opening wide and defending wide. This will frequently be the case when he is out of position or facing Regs who just love to battle pre-flop. These players are nothing to fear; we just need to take a bigger weapon into the fight and play a stronger range in the first place. 2. Open Smaller Opening smaller does a few things to improve the EV of opening vs. light 3-bettors. Recall that when we open 3x and get 3-bet, there are times when calling might lose us, say, 2.6BB in EV from the point of view of the entire hand while folding of course loses us a full 3BB. In this case, our best-case scenario is to accept the 2.6BB loss. If we make the prudent preemptive adjustment of opening only 2x instead, however, then folding now loses just 2BB and this is an immense improvement on opening 3x and being forced to continue due to pot odds. In the sizing model CO vs. BU where Hero opens to 3BB and Villain 3-bets in position to 8BB. Villain risks 8BB to win 4.5BB with a raw RFE (pre-adjustment) of 64%. When we open 2BB and Villain 3-bets to 6.5BB in position then he risks 6.5BB to win 3.5BB putting his RFE at 65%. This is not a huge difference, but from this switch in sizing Hero gains one big advantage: a deeper stack to pot ratio. With more money behind in relation to what Hero has to invest to see the flop, implied odds are better and Hero has more room to make post-flop decisions and use any skill edge he might have. If Villain wants to keep his sizing larger to reduce our implied odds and force us to invest 6BB to call, then he'll have to make it 8BB. And this will shoot his RFE up from 65% to 8 / (3.5 +

Once again, there is a clear correlation between BTN’s equity and betting frequency. Most people don’t use an overbet here often enough. Since BTN bets 33% pot on the flop, BB’s check-calling range is fairly weak, and BTN has a lot of incentive to start polarizing and making bigger bets on the turn. Maybe something to look out for in your next session? The exception to the overbetting pattern occurs on a turned Ten, pairing the top card. BTN should almost never overbet; BB has more ‘nut’ combos. Instead, a 66% bet size is more profitable, even with a hand like 44 that can expect calls from Ace-highs. Putting Data Into Practice Studies like this are where a solver really shines in assisting human understanding. As humans, we can’t objectively state that a turned Queen is better than a turned 9 without using some sort of range calculation tool. If I could choose just one learning point to take away from this article, it’s that: Generally, high turn cards are going to be better for the PFR, and low cards or board-pairing cards are going to be poorer for the PFR, in an IP vs OOP caller situation. Studies like this are where a solver really shines in assisting human understanding. As humans, we can’t objectively state that a turned Queen is better than a turned 9 without using some sort of range calculation tool. If I could choose just one learning point to take away from this article, it’s that: Generally, high turn cards are going to be better for the PFR, and low cards or board-pairing cards are going to be poorer for the PFR, in an IP vs OOP caller situation. Along with the data on betting frequencies, you should now have a better idea of when we have a ‘ green light ’ to be aggressive and when we have an ‘ amber light ’ where it might be better to tone down the aggression. On the flip side, if we observe that our opponent is not respecting some turn cards where their equity is very poor, we may be able to play back at them by check-raising more or always check-calling hands that would ordinarily be indifferent bluff catchers. I would venture further and suggest that most opponents at lower stakes are not aggressive enough even on good turns. For example, on T32 T r, the solver suggests to keep betting all our 44 – 99 , which I’m confident many people don’t do. Consequently, since they removed thin value from their range, our worst bluff catchers become calls. But this is a topic for another day. Whenever we want to study exploitation, I suggest first understanding the GTO baseline, and then understanding how your opponents are falling short. Good luck at the tables everyone. 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 Darren Wee Darren is a mid to high-stakes player/coach with a passion for writing

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 GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy.

Table 104: 654r BB vs BN 30bbs Stats 654r is one of the highest donk bet flops. When the BB loses the ability to lead out on this board, they lose 1.1% of the pot or 6.5bb/100 and the EQR decreases by 2.25%. In a 5.6bb pot, playing a 100% donk bet strategy cost the BB 6.27bb/100 when playing against a minimally exploitative opponent. The value of donk betting will change depending on the SPR and what the value of the option for the OOP player to bet is. For example, on the A76r flop, OOP should donk bet about 0.4% of the time and, if we remove the BB’s option to donk bet, their overall EV remains the same. Donk betting only happens at a high frequency on a small number of flops that are also low frequency flops, so the impact of the EV loss of choosing a simpler strategy that always checks when OOP will not be significant in the grand scheme of things. Additionally, implementing donk betting strategies correctly can be difficult in-game. That said, if you play in really tough games where every possible edge counts, taking the time to study and incorporate donk bets can become a valuable tool, particularly if your opponents are not used to dealing with flop donk bets, which can result in them making more mistakes that you could potentially capitalize on. You can of course also choose to donk bet exploitatively against weaker players. For example, if you know that the Villain will c-bet at a high frequency but would never raise a donk bet without a strong hand, you can put in a small bet with some hands that will work as a blocking bet, allowing you to see the next card cheaply with some weak hands while giving you information on your opponent’s holding. Another example is if you know the Villain is overly aggressive and will almost always raise a flop donk bet. Then, you can lead out with very strong hands to induce a raise from the Villain. This would of course leave you exposed to counter exploitation, so it requires excellent knowledge about your opponent’s tendencies. The Power of Position In this section, we will use the high and low donk bet frequency flops 654r and A76r in BB vs BN situations with 30bb effective stacks. We will compare the GTO simulations against

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

our shoving range is pretty strong so we need to find some Bluffs kind of cool to see four or two shoving over nine eight though right and that's the stuff you can learn by setting the solver all right let's say instead we faced a five big blind bat now we have to fold a lot up to 70 right and now we're calling almost we're not calling all that often when we do call by the way we have pairs right we have some Aces we have some tens a lot of the sixes fold the ones with the most live kickers stick around right so that's cool to see let's suppose the turn is instead not detrimentally terrible let's put up a great turn what's a great turn for the uh for the for the big blind it's on the Flop bet small call what is a great turn I think a six is going to be a great turn because look if you look at this range they have a lot of sixes right six is going to be an excellent turn what about like a nine nine eight or a seven maybe a seven I think a seven is probably pretty good let's take a look at the six first I bet we're gonna see a lot of leads and sure enough we do see a lot of leads right because they have a lot of sixes so the sixes are leading and now when you lead with a six you're also going to lead with a bunch of Bluffs so what are bluffs at this spot now that completely lacks Showdown value usually well that's going to be the gut shots and the open endings so we see a lot of the 9798 whatever using this bet say we do bet the sixth turn the wrong button again say we do that and we get called notice not a lot of raises because you can't raise in the spot because your opponent's rage is super polarized uh notice stuff like ace high has to call here though like Ace eight calling against a two-thirds pot lead that feels dirty if your opponent's gonna fold out a lot of these hands that are calling you should actually be leading a whole lot more I actually ran this a spot similar to this in my Advanced tournament course at pokercoaching.com and you can lead almost everything if your opponent folds out a little bit too much which is fun to see anyway say they do call Rivers whatever two of Clubs we can now bet or shove basically everything basically everything we just have a few give UPS but we do get to bet basically everything what about on a uh it's not gonna be a great card because the opponent's gonna have some tens right so now we have to do more checking what about on uh Ace Ace is obviously bad we have to do a lot of checking right so you can start to see

to win poker long-term and ensure that you can continue playing in a profitable manner first we are going to discuss cash game bankroll management requirements and then we're going to discuss tournament bankroll management requirements if you're playing some sort of exotic game like um Spin and goes or a different poker variant like Po liad Omaha then you're going to need different bankroll management requirements but we're going to be discussing the two primary games that most people play no limit hold them cash games and then no limit hold them tournaments okay here are the bankroll requirements for no limit hold them Texas style cash games remember your bankroll management requirements should be determined by your win rate the variance in the game and your risk of Ruin tolerance this presumes you don't really want to go broke these are relatively cautious requirements and they presume you have this edge here I'm also presuming you're not overly insane at the poker table and not overly nitty if you're playing an overly loose aggressive battle strategy then you may need a bigger bank roll if you're playing Super nitty well you probably won't have that big of an edge so don't do that play good strong fundamentally sound poker all right how do we read this here's your win rate here's the bank roll you need this this number here presumes we are playing one two no limit hold him I know a lot of you are playing that game so that's why I wanted to list the exact amount for one two No Limit holding if you're playing 2 five well multiply the numbers by 2.5 if you're playing 510 multiply the numbers by five come on you can handle that all right if you're winning three big blinds per 100 hands which is roughly one big blind per hour in live cash games which is not a big win rate at all you're going to need about 10,000 big blinds or $20,000 for one two no limit hold them a pretty big bank roll if you don't have much of an edge if you're winning a whopping $2 per hour at one two no limit hold him you need a lot of money because you are very rarely well you just simply don't have an edge simple as that your Edge is minimal if you have a medium Edge let's say you're winning 13 big blinds per 100 hands or something like four big blinds per hour so $8 per hour at one to no limit hold them then you need something like $7,000 this is where a lot of okay poker players who are working hard on their game are going to fall and this may sound like a lot of money for one to no limit hold them 7,000 bucks or 3,500 big blinds but really it's not this is not that much money at all and this is a bigger this is actually bigger than an edge than you should expect to have online if

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 in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI upgrade already has some useful… How To Adjust When Villain Has No Bluffs “They always have it!” is a common, semi-joking expression in poker to describe the tendency… Adjusting on Later Streets After Exploiting Flop The key to exploiting opponents profitably is knowing when to stop. I’m not referring to… C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table tournament and the BB calls. Both… The Art of Bluff Catching Bluff catching—calling a bet with a modest hand which you expect to win only if… Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet… Is Limping Pimping? In a past Discord post, one of our members noted that an upside of implementing… Exploiting Excessive C-Betting by OOP A preflop raiser who continuation bets too often is always a potential target for exploitation,… Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs.… The Worst Turn Card Greetings from GTO land. In today’s article, we will use the Turn Reports feature to… Navigating Range Disadvantage as the 3-Bettor Picture this: We’re playing a NL500 6-max cash game, and we’ve won

Diagram 24 According to the EQB Charts across all 1,755 flops, almost half of the BB range is made of trash hands that have less than 33% equity, while the IP Player (BN-UTG) has on average only 6% of trash hands in their range. On the other hand, the IP Player has 22% strong hands that have at least 75% equity, while only about 7% of the BB range are strong hands. Both players have a similar number of weak hands, 23% for the BB and 29% for IP. Finally, the IP Player’s range has 43% good hands while the BB has only 25%. Post-flop Bet-sizing

position, you should stand pat with a ten or better if your opponent is still drawing, and even with a jack if it’s a showdown situation with no more betting possible. In a three-handed pot, you should always stay pat with a nine or better if your opponents are still drawing. You learned that breaking an 8-6 or 8-5 is a no-no. However, if you have an 8-7 and are reasonably certain that your opponent has you beat, you may consider breaking. If you are a novice player though, I recommend staying pat with any eight to avoid being outplayed by more sophisticated players. Play on the River Generally speaking, the river is no time to get fancy. The pots are usually so big by the river that bluffing becomes difficult. Most successful bluffs in deuce-to-seven triple draw start well before the river. When Both You and Your Opponent Are Drawing One In this situation, you rarely should bluff. Since the pots become so large, your opponent will likely call you with as little as a king. However, there are certain situations where a bluff could be profitable. You would have to have: 319 (1) The right table image; and (2) The right opponent, one who makes laydowns. Bluffing with an ace, king, or queen is just silly. You’ll get called virtually every time your opponent has you beat, and you will “bluff” your opponent when he makes a pair that you can beat anyway. I suggest that you only bluff when you make a big pair and have virtually no chance to win in a showdown. Even a pair of deuces can win in the showdown when your opponent also pairs. I suggest bluffing with pairs four and higher, and even then I would only advise you to do so every now and then. It will only work if your opponent makes a pair smaller than yours. Even then, I have seen people call bets on the river with pairs as high as 6-6! The river is the time for value betting and not for bluffing. With so many bets in the pot, all you have to do is catch an occasional bluff to make calling correct. You should always call a bet with a jack or better and call most of the time with a queen through a pair of deuces. You should also value bet hands as bad as a jack. As you learned previously, a jack is a favorite over any one-card draw, so you should bet it when you make one, regardless of your position. Since your opponent will likely call you if he makes a queen, king, or ace, or even a small pair, there is value in betting the jack. The only drawback comes when you get raised. In that case, you would have to go with your read. More often than not, your opponent won’t raise you with a 9, 10, or a jack, but he might do it with an 8 and certainly will with a 7. When Your Opponent Is Pat and

earlier raise would probably result in his reraise. This brings up an important point. Many players with a good hand, would be quick to reraise you on either the flop or the turn. However, many of these same players will not reraise on the river because they will fear that you slowplayed a "monster." Similar advice applies when you feel very strongly that your opponent is on a flush draw. Generally, in short-handed situations, it is very difficult to be sure that your opponent is merely on a draw. But occasionally you will run into someone who is quick to bet their draws, but who will check-raise with their best hands (including top pair) and check and call with their mediocre hands. If you know your opponent well, and you feel that this is the case, it is best to wait to fourth street to get the raise in. The idea of raising immediately to get maximum value on the flop is wrong. If the flush card comes on the turn, you will be happy you didn't raise. However, if a blank comes, your opponent is likely to bet again hoping that you will fold. Since you didn't raise on the flop, he will not give you credit for holding a strong hand and will often feel that one more bet may cause you to fold. Now you can raise and get him for two double size bets when he is a 4-to- 1 shot as opposed to two single size bets when he is a 2-to-1 shot. Miscellaneous Topics Afterthought We have repeatedly stressed that hold 'em is an extremely complicated game. This is easily seen by the numerous topics discussed in this section alone. In fact, it is probably fair to say that no instructional hold 'em book could cover everything, simply because so many hands are unique to themselves. Another idea to keep in mind is that you must avoid playing similar hands the same way all the time. Some variation is needed to throw off the better players. However, as we already have pointed out, a lot of deception is not necessary against the weaker players. When this is the case, solid play is usually best. It will get the money. Also, a lot of the fancier strategies that we have discussed are correct only when the situation and/or conditions are right. Don't fall into the trap of making a lot of great plays just to make great plays. You should be trying to win the most money, not to impress everyone at the table. This is an important point. Frequently the best players, and this includes us, are accused of being dull unimaginative players. Yet, in many games, this is the best style for getting the money on a consistent basis. 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 Playing in Loose Games Introduction Since the original edition

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 in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI upgrade already has some useful… How To Adjust When Villain Has No Bluffs “They always have it!” is a common, semi-joking expression in poker to describe the tendency… Adjusting on Later Streets After Exploiting Flop The key to exploiting opponents profitably is knowing when to stop. I’m not referring to… C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table tournament and the BB calls. Both…

your chips needlessly. Sometimes fold if you are not driving the betting unless you are sure the other person is betting out of place for their cards (bluffing or over-betting). I am a conservative player and if you want to play looser then increase the percentage, you will risk in any given hand. You may feel more comfortable with twenty to thirty percent of your chip stack. There is no doubt that this is the point when you will have to catch some luck from the Poker Gods. There are two things to remember if you want to win a tournament. 1. Make the least amount of mistakes. Fold if you think you are beat. Do not call raises unless you have a good hand or are getting the correct odds. 2. Get lucky when luck is needed. This you cannot control but you can put yourself into a position for luck to happen to you. There are many trees to cut down in a tournament. Do not needlessly challenge someone. Final Stage Therefore, you are in the money round or at a final table. Things get hot and heavy here. People will go all in at any time. Since everyone is going to make some money, the play gets looser. Premium cards are what you need and want when you enter a pot. You must loosen up but you must also ask yourself, would I call an all in raise with these cards? If the answer is no then throw them away. A majority of the hands will have all-in bets pre-flop or on fourth street. This is why you should not panic in the middle part of the tournament if you are not the chip leader or even in the top 20. If you have the average amount of chips then a double up or a triple up from a pivotal hand will happen. After the first bubble pops, the all-in bets get more frequent until the next bubble level. Usually at this time, the blinds are very large and many of the players will not be able to last one or two rotations. This is another reason people will go all in at any time. If someone commits all of their chips, look and see if they are in first position right before the blinds hit them. Look at their chip stack. If it is small, then this is probably an inferior hand. For the rest of the tournament the battle between a made hand and an overcard drawing hand really appears. The starting hand showdowns of AK vs. QQ or AA vs. JJ are typical showdowns in the late stages of a tournament. If you have a strong starting hand, you should raise with authority. You should try to steal the blinds as often as possible in favorable position. Since the bets are such a large percentage of a players chip stack, one hand can bust someone out of the tournament or cripple them severely. The other players will not contest your raise unless they have a very

These models do not take into account the future game . In the future, we want to win the bounties of the player who cover us right now, which requires having to think a few moves ahead. The HJ is in the middle of the pack with 42BBs, covering UTG1, UTG, and the BB. In a regular MTT, the middle-of-the-pack players have to play tight and avoid big confrontations. However, in this spot the HJ might be best advised to take a big risk to double up . By big risk, I mean a high variance play – taking a very small edge or even a slightly minus EV gamble. illustration They have a pretty bad seat at the table. When the shorter players are in the blinds, if the HJ wants to target them they have to get through the three biggest stacks. If the HJ is the Big Blind and one of the shorter players enters the pot, there is a very good chance the player currently in the LJ with 58BBs will isolate them. Crucially, if the HJ doubles up, they will have at least 84BBs and thus will cover everyone at the table . While not in a great chip position, the current BB is in a reasonable table position. They are third lowest in chips but the two players who are lower are to the BB’s immediate left. The BB is out of position to them, which is not ideal, but the stacks are short enough that the BB could bet/call a resteal against either of them very profitably. If they took a big risk to get a big stack, it would not put them in a spectacular position . Doubling up would get them around 68BBs, which means they would still be covered by the BTN or SB (assuming it was not them who doubled them up). So ironically it might be better for the BB to bide their time and enjoy covering two players right next to them. The current SB is the chip leader and will be looking to play as many pots as possible to win bounties. However, if the BTN or CO got aggressive with them, this might be a spot to pass some small edges. Losing an all-in to either of these players would make the SB the shortest stack at the table. It might be more prudent to avoid close spots with the two other big stacks if it means maintaining their overall lead. Other than this exact hand, the SB also enjoys position over the other two big stacks. Another reason not to punt off light against them when they could instead grind them down in small to medium pots. illustration The BTN is in a similar position; they cover everyone but the SB. Generally speaking, it might be a good plan to avoid tangling in big pots with the two other big stacks, because they can still win six bounties immediately. However, the BTN has a terrible seat , they are to the immediate right of the chip

BLUFFING ON THE TURN AND RIVER 50 to a +$1,000 success) only 5 percent of the time. But there’s a more subtle reason that’s just as important. The less you bet on the river, the more you can bet on your turn bluff. Betting more on your turn bluffserves two purposes: • Increases your chance of success, at least somewhat • Improves your potential reward on the river bluffif you get called on the turn Say you have $4,000 to distribute between bluffs on the t11rn and river. The pot on the turn is $1,000. You are trying to choose between $1,000 and $3,000 bets or $500 and $3,500 bets. You think a $500 bluffwill succeed on the turn about 30 percent of the time, and a $1,000 bluffabout 50 percent. If you’ve bluffed $1,000 on the turn, then you think a $3,000 river bluffinto the now $3,000 pot will work about 70 percent of the time. If you bluffed $500 on the turn, then you think a $3,500 river bluff into the now $2,000 pot will work about 80 percent of the time. Which series is better? When you bluff$500 and $3,500, you can have one of three outcomes: you can win the initial $1,000 if your turn bluffsucceeds, you can win $1,500 if your turn blufffails, but your river bluffsucceeds, or you can lose $4,000 if you get called down. You’ll win $1,000 30 percent of the time. You’ll win $1,500 80 percent of 70 percent of the time, or (0.8)(0.7) = 56 percent of the time. You’ll lose $4,000 the other 14 percent. Thus, the EV of this sequence (assuming you have no chance to win by making the best hand) is $580. $580 = (0.3)($1, 000) + (0.56)($1, 500) + (0.14)(−$4, 000) When you bluff$1,000 and $3,000, you can also have one of three outcomes: you can win the initial $1,000, you can win $2,000, or you can lose $4,000. You’ll win $1,000 50 percent of the time. You’ll win $2,000 70 percent of 50 percent of the time, or (0.7)(0.5) = 35 percent of the time, and you’ll lose $4,000 the other 15 percent of the time. (Note that we’ve set the numbers so that both sequences ultimately succeed roughly 85 percent of the time.) The EV of this sequence is, thus $600. $600 = (0.50)($1, 000) + (0.35)($2, 000) + (0.15)(−$4, 000) Betting somewhat more on the turn and somewhat less on the river increases your overall EV by $20 even though, the way we set the numbers, your total chance of success drops slightly from 86 to 85 percent. It’s because your turn bluffsucceeds more often and because you win a bigger pot, $2,000 versus $1,500, when your river bluffsucceeds. You have to find the sweet spot. Dividing the bets $2,000 and $2,000 wouldn’t work at all: It would violate the first principle by not leaving a credible blufffor the river.

Steal: Raise First In from BN, CO or SB. Isolate: Raising after someone has entered the pot with the intention of playing heads-up post- flop vs that player. Minraise: When a player raises the minimum allowed, which is two times the last bet amount. Minbet: Making the minimum bet allowed. Post-flop, this is one big blind. Overbet: Making a bet that is larger than the size of the pot. Three Bet (3-bet or 3b): Making a re-raise, which is to increase the bet after someone else raised. Resteal: 3-betting after someone else steals. All-in or Push: Betting all of your chips. Open Shove or Open Jam: Going all-in when no one else has entered the pot before you. 3-bet-Jam, 3-bet-Shove, Reshove, or Rejam: Moving all-in after someone else has already raised. Four-bet (4-bet or 4b), 5-bet and any subsequent number of bets: Refers to the number of bets that have been made during the current betting round. Cold 4-bet: 4-betting when the player making the 4-bet was not the initial raiser. For example: UTG opens to 2bb, BN 3-bets to 5bb and the BB cold 4-bets to 12.5bb. Cold Calling (cc): Calling a single raise when in position, or calling a 3-bet or 4-bet when you have not previously voluntarily put money in the pot. For example, MP opens to 2bb, CO 3-bets to 6bb, BN folds and SB cold calls. Squeeze (sqz): 3-betting after someone raised and someone else called. For example, UTG1 opens to 2bb, CO cold calls, BN squeezes to 9bb. Continuation Bet (C-bet): Post-flop bet made by the player who was the last aggressor in the previous betting round. Donk Bet or Lead Out (DK): When the player who is OOP bets into the aggressor on the previous betting round, denying the option to C-bet. Slow Play or Trap: To play a premium holding in a passive manner, hoping to induce a value- bet from an inferior hand or a bluff. Action Lines A “line” is a specific sequence of betting actions taken by a player. Limp/Fold (l/f): A player enters the pot by limping (calling the big blind) and then folds to a raise.

between playing in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI upgrade already has some useful… How To Adjust When Villain Has No Bluffs “They always have it!” is a common, semi-joking expression in poker to describe the tendency… Adjusting on Later Streets After Exploiting Flop The key to exploiting opponents profitably is knowing when to stop. I’m not referring to… C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table tournament and the BB calls. Both… The Art of Bluff Catching Bluff catching—calling a bet with a modest hand which you expect to win only if… Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet… Is Limping Pimping? In a past Discord post, one of our members noted that an upside of implementing… Exploiting Excessive C-Betting by OOP A preflop raiser who continuation bets too often is always a potential target for exploitation,… Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs.… The Worst Turn Card Greetings from GTO land. In today’s article, we will use the Turn Reports feature to… Navigating Range Disadvantage as the 3-Bettor Picture this: We’re playing a NL500 6-max cash game, and we’ve won a few pots,… Mastering Three-Bet Pots In Position in MTTs Playing in position against a three-better is a lesson in playing to your advantages. As… Mastering Three-Bet Pots Out of Position in MTTs Three-bet pots are scary. Playing out of position is scary. Put them together, and you’ve… The Greatest Final Table in Triton History Today, we’ll examine one of the most epic final table battles I’ve ever witnessed! Our… Mastering Thin Value Bets in Checked-Down Pots Valuing your hand appropriately—determining whether it’s strong enough to value bet or so weak you… Maximizing Value on Monotone Flops Monotone flops tend to provoke great anxiety among poker players. It’s easy to imagine that… How to Defend Against Turn Donk Bets Responding effectively to donk bets on the turn is tricky;, there’s no getting around that.… How and Why You Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns of phrase have entered the poker… Should You Ever Cold Call a 3-Bet? When there’s been a raise and re-raise before the action is

MULTIPLE LEVEL THINKING 115 that would be both time-consuming and prone to error (not just the calculation, but the assumptions you’d have to make along the way). So think a little on the second level. What might he think you have? You opened preflop from late position, something you probably do with a fair range of hands, but one tilted toward the big hands. That is, he’d expect to see pocket aces more often than nine-trey, even though you’re dealt nine-trey more than twice as often as pocket aces. You bet the T♠8♠5♣flop when checked to. You might do this if you hit the flop, but you also might do this as a continuation bluff. He’d know that. When you check the K♢on the turn, he will naturally assume you have a marginal or semi-weak hand. Perhaps you have a flush or straight draw, or maybe you have a pair smaller than kings. Or maybe you have ace-queen or another hand that missed entirely. The river K♣doesn’t help any of those hands. So if you were weak on the turn, you’re still probably weak. Given the action throughout the hand, it would be natural to assume that this first-level thinker would “put you on” a modest holding. Given that knowledge, why would he make an extra large bet? He probably expects you to fold. If he has a big hand himseIf, surely he’d rather you call $100 than fold to $250. And if he has a decent, but not great, hand like A♡T♢, he’d probably either check or make a modest value bet, as a big bet would rarely get better hands to fold and also rarely get called by a weaker hand. (Remember, he’s not stupid, just not a deep thinker.) So the bigger than average bet here is likely to be a bluff. With big and mediocre hands alike, you’d expect a smallish bet because he probably puts you on a modest hand. The big bet is designed to blow you out. Perhaps he called the flop with Q♠7♠or 9♣7♣and now has no chance to win by checking. He’s worried you have enough to call a $100 bet, so he makes it big enough to scare you out. If your assumptions are right, if your opponent is a decent player and first level thinker, you have a clear call. You have second level thinking to thank for making that decision so clear.30 If your assumptions are wrong, however, and your opponent actually thinks on the third level, then your second level thinking might be your downfall. If he thinks on the third level, then he might realize that you know he would put you on a modest hand due to your turn check. He would also know that sometimes you would check behind on the turn with a king or other hands you might call with on the river. With a big hand, he might make an extra big bet, knowing that you would interpret it as a sign of weakness in this situation. That way he gets the best

Run good A prolonged winning streak where a player encounters significant positive variance and an extended period of results above expectation. The opposite of run bad.

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 GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds

Adjusting to Loose Games and Players Some of your most profitable no limit opponents are the loose players. Loose players play too many hands and go too far with them. Sometimes they don’t raise much, but call too often (loose and passive), and sometimes they raise and call too often (loose and aggressive), but their main characteristic is that they put way too much money in the pot with hands that are too weak. Before we discuss how to beat these players (and it isn’t very hard), we want to distinguish truly loose and aggressive players from dangerous seemingly loose and aggressive players. Some very good players will play a style that, to a lightly trained observer, might appear loose and aggressive. They play lots of hands preflop, and they bet and raise liberally. The difference is that they play recklessly only for the small preflop and flop betting. Once the betting gets big on the turn and river, they play a very tough game, and with superior hand reading and manipulation skills, they trick others into playing too loosely against them. Truly loose and aggressive players aren’t so cunning. They simply play too many hands and bet and raise too often with them, both early in the hand and for the big money. Here’s an example of the difference. With $1,000 stacks in a $5–$10 blind game, you open for $40 with Q♣Q♢from middle position. Everyone folds to the big blind, a truly loose and aggressive player, who calls. The big blind has K♡3♡. The flop comes A♡A♠Q♡giving you a full house and your opponent a flush draw. He checks, you bet $60, and he raises $240 more to $300. You know your opponent is reckless, so you simply move allin now, $660 more. He calls in an instant. You roll over your full house, and he realizes he’s drawing dead to a runner- runner royal flush. Your opponent’s flop play was atrocious, but truly loose and aggressive players periodically make enormous mistakes like this one. A dangerous loose and aggressive player would never play a hand like that. Instead, they play hands like this one: With $1,000 stacks in a $5–$10 blind game, you open for $40 with K♡J♡ from middle position. The dangerous player calls on the button, and the blinds 122

a premium made hand a draw a marginal made hand or junk you should always consider how every single hand in your range lines up uh premium made hands are hands that are usually just good enough to bet and get all the money in draws are are going to vary in strength from very high Equity draws all the way down to junky draws and the hands that are classified as a draw depend on your rain comp range composition and the board for example on Ace 93 there's not a whole lot of actual draws right so an ace 93 maybe a hand like Jack 10 with a back door flush draw counts as a draw even though it's not a particularly good one right then you're going to have your marginal made hands these are hands that want a little bit of money to go in the pot but not a lot usually you'll betting these hands once either on the Flop or the turn and then look to see a somewhat cheap showdown from there these are going to be weak top pairs all the way down to something like ace high maybe King High if there's an ace on the board and then you have junk this is just hands with little to no potential hands that cannot really improve hands that you're just giving up with at least on the Flop now if the Flop goes check check and then your opponent checks again on the turn sometimes this junk is going to turn into a bad draw or maybe just decide to Bluff it because you don't have any other logical Bluff so I want to make it clear you're not just totally giving up with your junk but quite often if you're not betting with your entire range on the Flop the junk often does not get BET next range Advantage remember frequency is determined by hand types range advantage and position the range Advantage is this idea that one player's likely range has more equity on a particular flop than the other players range and you're going to find that on all flops the pre-f flop razor almost always has an absolute range advantage over the pre- Flop caller and your decision to bet frequently or infrequently is going to be based on how big that Advantage is if the range Advantage is small you're usually going to be betting less often if the range Advantage is Big you're usually going to be betting more often let me give you an example of this there's a program called equilab you can get that can calculate range versus Range so you can see who has the advantage um in various scenarios so here what we have is I have given this is roughly a lowjack or highjack raising range looks like a lowjack raising range doesn't really matter an early position raising range versus a big blind callers range notice the big blind is missing Aces kings queens Jacks Etc this is probably 40

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 GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds are the value you expect to gain over and above your raw equity.… ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but what… What is Equity in Poker? The term “Equity” is ubiquitous throughout poker theory. Equity refers to your chances of winning… Range Morphology “Morphology” is the study of form or structure. You’ve probably heard terms thrown around such… What is Expected Value in Poker? Expected value (EV) is the most fundamental metric in

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

Table 34: MTT Results of Great Players in the Mid-high Stakes Players 6-10 are great players who play the mid-high stakes (Table 34). This type of player has the potential to become one of the best players in the world. Some of them are still working towards that goal while others are content with just printing money at the mid-stakes. Table 35: MTT Results of Low- and Mid-stakes Regulars Players 11-15 are low and mid stakes regulars (Table 35). In this group we start to see lower Avg ROIs and also a wider spread in their results, with some of them winning small amounts or even losing. These type of players should spend more time working on their game, making sure they have all the fundamentals well covered. They should actively be looking for a poker mentor/coach, or join a group of players who study together and support each other. Players 11 and 14 are clearly playing too high for their current skill level.

you should bet — or raise — with a semi-bluffing hand, especially as the pot gets larger. 9. It is usually better to make a semi-bluff bet when you are first to act; when you are last, you have the opportunity of giving yourself a free card, and you may not want to risk the chance of an opponent check-raising you. Chapter Twelve Defense Against the Semi-Bluff The Power of the Semi-Bluff Let's say you're playing seven-card stud. You have a pair of jacks, and on fifth street your opponent bets. You know he has a big hand. So your response is easy: You fold. Suppose you know your opponent is bluffing with nothing. Again your response is easy: You raise. Suppose you think he has you beat with two small pair, but you're getting sufficient pot odds for a call. So you call. Straightforward bets, straightforward responses. But what if your opponent is not so straightforward? What if he's the kind of player who might be betting with a legitimate hand but might also be semi-bluffing? He's not always semibluffing, of course. That would also make it too easy to respond, because if you know an opponent is semi-bluffing when he bets, you can simply raise with anything, and he will probably fold. The problem arises when you think an opponent may be semi-bluffing but can't be sure he does not have a legitimate hand. What's more, if he doesn't have a legitimate hand now, he may get it later — or he may look like he's gotten it later. It turns out there aren't many defenses against the semi-bluff, which is why it is such a powerful play. Frequently the best play against a possible semi-bluff is to fold, especially when the pot is small. All right, your opponent has beaten you. He may even have made you throw away the best hand. But if you call his bet, he has three other ways of beating you. He may in fact have had the best hand when he bet. He may have been semi-bluffing, but he now outdraws you. Or he may have been semi-bluffing, but he 106 Chapter Twelve proceeds to catch scare cards that force you to fold. Therefore, though you may have thrown away what was the best hand at the moment, still your opponent had too many ways of beating you to justify your calling his bet. Even when you think you are favored to have the best hand, it may be correct to fold. Let's say you think it's a little better than even money that your opponent is semi-bluffing. For convenience, we'll say you think there's a 52 percent chance he's semi-bluffing and a 48 percent chance he has a good hand. If he is semibluffing, you figure you're a 6-to-5 favorite to beat him. However, if he isn't semi-bluffing and has the hand he's representing, you're virtually locked out. Thus, 52 percent of the time you're a favorite to win. Should you call his bet? Many professionals as well as amateurs make the

right um and that's usually what you're going to see also we have some weak ax doing a decent amount of checking which makes some sense also some Queens doing some checking which also makes some sense right the medium Str hands whereas a hand like Ace Jack and Ace Queen and Ace King are betting almost every time all right what should the button do against a bet of 4.9 big blinds well they should not fold much at all also because this board actually does favor the initial razor a decent amount you also don't get to raise all that much at all so take a look at what's folding in this scenario what is folding is literally only King High Jack High 10 high nine High and some eight High also under pairs are folding sometimes sixes and fives are folding sometimes but notice you have to call a ton and that's because you're getting really good odds a lot of people in this spot fold out hands like pocket Jacks every time they just ditch them they just put them right in the muck oh Jacks are in bad shape I got to fold but no no no no no facing a 4.9 25% pot bet you have to continue incredibly wide notice our raising range includes Jack's 10 I'm sorry Ace Jack Ace 10 ace9 and then a few nonsense Bluffs these races are small Races by the way they are not all in these are going to be to like 2.3 times the opponent's bet um so we're raising very polarized again hands that can easily get it in aack A10 A9 you are raising in getting those in and then you're raising the absolute garbage down here with the intention of folding to a shove what about against a big bet a pot siiz bet now you get to fold a ton cuz now you're getting way worse odds in this spot you plan to call with with all your acex and all your queen X and some of your 9x I'm sorry some of your 7x on the Flop and then you're going to fold out the 7x and some of the queen X to a turn betat and then you're going to fold out all of it except for the ax to a river shove okay if the opponent does rip it all in on the turn you're going to call it off with again all the ax and some of the queen X so this is a rather interesting scenario where a lot of people they get really really scared they have a like Ace to and they just fold or they have a hand like king queen and they just fold but as you can see here that's not what you're supposed to do what are you supposed to do if they check we saw that happening about 20% of the time anytime you're check to in three bet pots you're going to find that you usually want to be betting

to a flush or straight, and you don’t have any of it. With a big pair in that spot, it’s back to judgment again. You have to evaluate what you think your opponent was drawing at and whether or not he’s got one of the cards that would complete the straight or flush. You should never bet in that situation. If he’s first and he checks, you should just show it down. If you are first, you’d check it. If he bets, well, you’re back to people. You’d just have to evaluate your player. That situation brings to mind a play I often make. I’ve played a lot of pots against tight players when I’ve made a very weak call on fourth street, hoping the last card will make a four-card straight or flush on the board so I could represent the straight or flush by making a big bet. For example, my tight opponent has raised before the flop and I feel he has a big pair in the pocket. The situation might look like this: My opponent bets on the flop, and I call. The next card is the 2?, and if my opponent bets again, I’ll call—not because I think I have the best hand, but because of the tremendous bluffing opportunity I’ll have if the last card is a 3, 4, 8, or 9. Any one of those four cards will mean the board is one card off of a straight. I’ll almost certainly win the pot if, as in the example, a 4 fell on fifth and I represent the straight by making a substantial bet on the end. 377 There’s also a chance that I’ll catch a 10 or 7 on the end. I’d win a nice pot in that case as well, so I’m justified in calling on fourth street. I do a lot of gambling like that on fourth and on the end. And they’re good gambles because I know a tight player wouldn’t jeopardize all his money when one card would beat him. It’s not only tough for a tight player to make a call for all his money in a situation like that, it’s tough for anyone to do it. But if you know your opponent, it does make it easier. If the straight or flush is made on fourth and fifth streets, a backdoor job, then you may want to reconstruct the play of the entire hand and try to determine whether that particular player would have gone as far as he did to make the hand. Of course, a lot of times a player will literally back into a hand like that. For example, he may have started with a small pair on the flop, picked up a straight or flush draw on fourth, and got there on the end without really trying. With two aces or kings, you’re going to have to use a lot of judgment when all the cards are out and your hand never got better. You’d have to go back to what you originally felt

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 GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds are the value you expect to gain over and above your raw equity.… ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but

the radio direction finder I had brought with me, which was more accurate than those of the Service. I set it at 13 kcs, the position of the suspected radio. 'I'll put this in a suitcase. Take it to your room in the consulate, turn on the switch, and put on the earphones. If you hear signals, watch this hand. It will point towards the sending radio. You understand?' She nodded dubiously. 'You want to get to Shanghai ?' I asked. 'Oh, yes, more than anything else. It means I'll be reunited with my family in Germany.' "Then do as I say. Whether you are successful or not, I’ll see that you get to Shanghai. Furthermore the Chinese Government will be grateful and will repay you. The car will wait for you. No matter what time of night it is, if you hear signals come back to tell us - and watch the little hand. 'Clean that money off the table before the servants see it,' I told Ling after Maria had gone. He returned my $2000 loan and I put it back in my money belt while he counted the rest like a miser. 'Quite a haul,' I said and poured two drinks of the Hatchet Man's best brandy. His lips curled in a silly grin. 'You think I play better than in Hong Kong?' 'You graduated with honours,' I said gravely. 'But you'd have been a sick cat if that last card hadn't been an ace.' 'Chinese like to gamble,' he said. 'But as you say, the odds favoured me. The ace of spades was next to the ace of diamonds. The German didn't shuffle the cards much.' Ling took a deck of cards from his pocket and began to deal to himself, while I lay stretched on the couch. 'Ling,' I said, 'wasn't your ass puckering a little before you caught that ace of spades?' III Time dragged on and I fell asleep. Suddenly there was a commotion in the hall and Maria rushed in unannounced. I jumped from the couch. 'Well?' I asked. She was out of breath. 'The little hand points at the Hostel.' 'What time did you hear the signals?' 'At 12.15.' 'How long did they transmit?' 'About five minutes.' 'Here, take a drink of brandy. You need it.' 'Prosit' she said, gulping it down, 'You have any trouble getting out?' 'No, I came down the back stairs.' 'Adviser, what do we do now?' Ling asked. 'Keep the German under surveillance and move some of our good equipment up close to the Hostel and intercept his messages. If he has made contact with the enemy I want no one to bother him but let him continue to send and receive. His code will not be too difficult to break. When we have enough of it I think I can read it. He must be one of a group of agents and we want to catch the whole crowd. Let him become suspicious and we fail to break up the plot, whatever it is.' 'The Donkey won't

and descriptions of selected sites that are particularly useful and rich in content. General Information httv://www.intelli~ent~oker.com-is the companion Web site for this book. Changes that occur after this book is published will be posted on the Web site. Availability and offerings for online cardrooms is especially time sensitive and will be updated. Included are links to join online cardrooms, links to purchase books, and links to the home pages of most of the public cardrooms listed in Chapter 10. httv://www.vokemages.com -is one of the top-ranked poker portals on the Web. It has comprehensive and up-to-date information for poker worldwide. The site offers: a database of poker establishments, daily-updated events and results, tips, seminars, and player profiles. Listen to live-audio broadcasts. Practice in free play-money tournaments. Communicate globally via forum and chat rooms. There is even a section for women in poker. http://www.vokerschoolonline.com-is an online school for poker (presented by Pokerpages described above). For $14.95 per month membership, you receive instruction-beginner through advanced levels-from poker professionals. Also, compete in play-money Multi-Table Tournaments, Satellites, and Ring Games, where over $100,000 worth of sponsorship points are available. Players who accumulate enough sponsorship points at the play-money games are awarded seats in real-money tournaments. The Poker School games are among the closest to the real world with the safety of play-money. This is a great way to learn tournament play without having to open a real-money account. 128 THE INTELLIGENT GUIDE TO TEXAS HOLD'EM POKER http://www.pokerl .corn-is the site for Mike Caro Unversity of Poker, a school for poker that is affiliated with Hollywood Park Casino (see Southern California Cardrooms on Page 147). Mike Caro, the legendary "Mad Genius" of poker, has many of his articles, columns, and lectures posted at this Web site. Also affiliated with Caro's site is United Poker Forum, which is an online message board for discussing any question, opinion, or issue related to poker. Sources for Articles and News on Poker Commitment to poker excellence reqtiires continued reading and analysis of what others write. Here are some sites that have free articles on poker: http://www.cardplaver.com-has many online articles by the most influential writers on poker. The site is also a great source for poker news and current events, including extensive coverage of tournaments throughout the United States. http://www.pla~winninmoker.com-poker professional Steve Badger maintains a large site with dozens of articles on strategy and online poker. His many subjects include Omaha strategy (see Appendix I for an explanation of Omaha), and the differences between online poker and in-person cardrooms. Selected articles are posted in multiple languages (Spanish, French, German, etc.). http://www.~oker.net-is an attractive site with articles, news, discussion forums, and links. They have a comprehensive directory of online cardrooms with ratings and profiles of each. htt~://www.~okersearch.com-has online articles and a discussion forum. The site lists the locations and contact information for hundreds of cardrooms throughout the United States and assists in travel planning, including air and hotel reservations. RESOURCES 129 http://www.seriouspoker.com-is the companion web site for Dan Kimberg's book, Serious Poker. Go here to learn more about his book and read his articles

Hand history The description of how a hand occurred, or in online poker, a copy of the hand as recorded by a tracking software.

try to like target their 10x to to find some phones so um you can see that king jack queen jack we are just saying all them most of the time i do sex is bluffing which makes sense right we're blocking some of their value um with the pocket deuces type stuff we're also blocking straights which is now huge this is kind of why we use this hand type it gives us board coverage on like straight completing rivers and turns um deuce knives blocking the straights right that's huge um sandwich queen deuce so we're bluffing these hands and then we see that our king three and our spade draws are blocking the spot and we don't love it right it's not great blocking their auto folds but we just don't have um a ton of board coverage on a run out like this such that we can have a perfect buffing canvas on every street so we go all in uh here's their autofolds right these king highs that are going to autofold but what we're targeting with this are their 10x so we're essentially targeting their king 100 their low suited 10s also ace king is queen high holding is is pretty nice so um overall pretty happy with this hand hopefully that helps you um develop strong check raising strategies as well as understanding when to better overturn um we'll keep working on like rare strategies and some of that and some of the other hands so we can we can talk more on that the last thing i want to say about the stand is uh at the start of the video i mentioned how difficult it is to defend a really wide range and i think this is a really good example of it because we look at this bet 25 raise 85 you have to peel so much like you just do have to peel all your king high back to flush draws excuse me king four king five all your acid back to flush draws and then you get barreled for about 16 the turn you're just not holding that much you know you're still calling your screen x king high um you're never folding a 10 unless that's bad blockers like 10 9 8 they're blocking some of my bluffs right uh 43s through nines but in rowdy you have to fight really hard for pots here and then we're 40 big blinds deep in a big event and you get chuck raised you get barreled for about 60 and then you get jammed on the river and you just have to look at your jack three and it's worth a lot it's like a snap on the spot um and then you have to mix calls through ten three ten four ten seven etcetera so in general i think these spots are really really difficult to defend against um so i would i would really look to be very aggressive in the big blind against wide ranges um use some

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

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72 Chapter Nine odds are 5-to-1 against your opponent making a hand that beats yours. By betting $20 into a $ 150 pot, you are offering that player 8 1 /2-to-l odds ($170-to-$20), and so he is correct to call the $20. But by betting nothing, you are offering him infinite odds, in that he has to call zero dollars for the chance to win $150. Therefore, when the pot is large — even though you are offering your opponent favorable odds — it is always correct to bet with the best hand. The opponent's odds are not so favorable as they would be if you didn't bet at all. Furthermore, there is always the outside chance he might give up and fold. (See the next chapter for an extensive discussion on the free card.) In no-limit and pot-limit games it is easier to win the big pots right away because you have the luxury of being able to bet almost any amount. So you can choose what odds to give your opponent. For example, with a $150 pot in a pot-limit game and your opponent a 5-to-1 underdog, betting the maximum $150 allows you to offer your opponent 2-to-l odds ($300 to $150) on a 5-to-1 shot. If your opponent calls, he is taking the worst of it, and you are not unhappy with the call. Whenever possible, then, with the best hand, bet an amount large enough so that by calling, your opponent is not making the correct play. Furthermore, in no-limit and pot-limit games, you must be careful, as we saw in Chapter Seven, to bet a sufficiently large amount so that your opponent is not getting sufficiently good implied odds to make a call correct. By definition, in limit games you are not free to bet whatever you want, and when the pot gets large, it's hard to make a player fold. However, unless you have the pure nuts, you should give your opponent every opportunity to fold and make it as expensive as you can for him to call, even when by calling he is still getting favorable odds. Win the Big Pots Right Away 73 Betting (or Raising) to Drive Opponents Out One step toward winning a big pot is driving out as many opponents as possible. Let's say you are playing seven-card stud, and there has been a lot of raising on the first three cards, which has created a big pot. You have three-of-a-kind, a powerful hand, and now on fourth street the man to your right bets. Should you call or raise? You should definitely raise even though you are driving out all the weaker hands behind you. Indeed that is precisely the purpose of your raise. The pot has become sufficiently large for you to try to win it right now, forsaking any future bets you might win. If everybody folds after you raise, you are delighted. If your raise succeeds only in cutting down the number of opponents, that's still pretty good. Most people don't think in terms of this special

than the Golden Nugget in which to spread a game. The Golden Nugget didn’t exactly attract the same number of high roller casino patrons that the Strip casinos reeled in by the thousands. This meant there was very little opportunity to catch a drop-in player or producer at the poker room. But in 1969, Sid Wyman, the boss of the Dunes Hotel and Casino, today the site of the Bellagio, invited us to spread a high-stakes no-limit game just outside the entrance to his main showroom, where we were able to catch lots of dropins, including the late Major Riddle, the majority owner of the Dunes. Remember, Nevadans and Californians were primarily five-card stud players. And although he was originally from Lockhart, Texas, Riddle was by now a transplanted Nevadan. As such, he had no experience playing a game that required such sublime strategy, and it is fair to say that he and others new to the game were faced with a steep learning curve. Their inexperience helped fill the lockboxes of the outside gamblers from Texas who brought the game west. One such incident took place at the legendary poker table in the Dunes. On one hand, all but Texan Johnny Moss and Major Riddle folded, leaving a huge heads-up pot. Johnny was in the lead and never checked his hand; Riddle never hesitated to call Johnny’s bets from before the flop or after the river. When all the cards were out, the board was K-K-9-9-J. Moss moved in on Riddle, and Riddle called him. Moss rolled a pair of nines out of the hole for four of a kind. Major Riddle rolled a pair of deuces out of the hole. See 39 what I mean about the five-card stud players and their learning curve? Riddle had a wired pair, and he was not about to lay them down, not realizing that he had the worst hand possible in this situation and could not even beat the five cards on the board. One player, Joe Rubino, who was from Alabama and a good Kansas City lowball player (but not much of a Texas hold’em player), went so far as to register an objection to Johnny winning the pot. Rubino claimed that since Riddle could not beat the board with his two deuces, he should be able to take his last call back. It didn’t take Johnny but a second to tell him that sometimes the board is the best possible hand in Texas hold’em and that his comment showed how little he knew about the game. He also told him a couple of other things about minding his own business when he was not involved in a pot. As the game began to catch on in Las Vegas during the late sixties and early seventies, high stakes no-limit Texas hold’em games ranged from $10,000 to $100,000 change-in (that’s about $60,000 - $600,000 in terms of today’s dollar). In 1968, Tom and Lafayne Moore decided to hold a table games tournament in order to promote the Holiday Hotel in Reno. They designed

reduced risk of moving all in . With short stacks behind you, you must play somewhat tighter than you otherwise would because of the risk of one of them moving all in. When you are one of the shorter stacks at the table, you can move all in somewhat wider than you would if everyone had a stack of your size, because players who call your shove will not be all in themselves. When all players have 9BB , the CO shoves 31.6% of hands: MTT cEV – CO 31.6% Push – 9BB Symmetrical When the players behind have deeper stacks (29, 21, and 32BB, respectively), the CO can shove 35.3% of hands. CO risks the same 9BB in both scenarios, but the players behind must take on greater risk when they have more chips. If the SB calls the shove, they are putting in nearly half their stack and so effectively committing 21BB to the pot should the BB wake up with a strong hand. MTT cEV – CO 35.3% Push – Stacks: CO 9, BTN 29, SB 21, BB 33 Notice that CO pushes wider when players behind them are deeper? 🤔‼ The BTN has room to call and still fold some hands to a BB shove, but even that comes at a cost. Those hands the BTN folds have a chance of winning, which means they lose equity when they fold to BB. The risk of being denied that equity discourages calls from some hands that could have called if BTN also had just 9BB. This does not mean a short stack is more valuable than a larger one. On the contrary, a player with more chips is more likely to win a larger prize, so the cash value of their stack is greater. However, when contesting a pot, the short stack does enjoy some advantages that make it a bit easier for them to accumulate chips. Folding is +EV In a cash game, if you fold, you win nothing. That means any play with a positive expectation, no matter how small, is better than folding. In a tournament, survival has value. That means folding has a positive expectation, not $0 as in a cash game. In a tournament, survival has value. Whenever another player is eliminated, the value of your stack increases, even if you were not the player who took their chips . You are now that much closer to locking up the next prize. The closer you are to a pay jump, the more it’s worth it to you to fold and let other players take risks against each other. You should only contest a pot by calling or raising if you believe the EV of doing so to be greater than the EV of folding. Although you will not be able to calculate these values precisely at the table, you can build intuition around them by studying charts calculated using the Independent Chip Model, or ICM. Here is the CO’s opening strategy with 20BB stacks and 50% of the field remaining , which raises 30.7%

aggressive actions if they sense weakness they're kind of like a shark they just try to they just go nuts raise too frequently try to make you fold too often their calls tend to be looser because they don't want to give up they tend to value it's in their nature to value winning pots above all else so the way that they the way that a volatile wreck thinks about poker is that if they win the hand then that means they're playing winning poker and if they lost the hand well that means they're playing losing poker right and that is a very dangerous position to be in because eventually you're just going to bomb off stacks you're going to be losing way too much money in pots you have no business in playing so that is a volatile wreck and they're predictable they're predictable in that they just take way too many aggressive actions they're driven by winning the pots i'm sure most of us know players just like this who just want to win hands like let's just play cards and win hands and if i fold well folding that means that i lost the hand and that that doesn't feel good right number three so variable number three is bet sizes so larger bets tend to be tighter which forces tighter calls and raises smaller bets tend to be looser which forces looser calls and raises people are scared to lose a lot when they bluff right like it's really as simple as that it there's they're driven by emotion um that we're going to get into but larger bets as in cash games a larger c bet tends to be tighter smaller sea bets tend to be looser let's imagine you open pre-flop from the cutoff you got one caller a wreck out of the blinds and are now faced with a post-flop decision so here we have king seven deuce why do you choose to bet smaller with your bluffs on king seven deuce right risk aversion pure human emotion why risk more when one one-third gets the job done right why risk more when less gets the job done this is a very simple thought but very very relevant um on the flip side here greed when you have a strong hand you think why i bet less when my opponent's continuing range is inflexible right so the two emotions that make this true larger bets tend to be tighter smaller bets tend to be looser risk aversion and greed just pure human emotions human tendencies it's uh this is backed up by mass data and really just backed up by common sense right like our intuition can tell us exactly why greed comes into play when we have a hand like ace king when we have you know king seven of diamonds on king seven deuce or pocket deuces yeah we wanna play a bigger pot right we're just greedy we wanna we wanna put more money in in the middle and when

This doesn’t mean raising before the flop is incorrect in a no fold-em game; rather, a raise should be made only when you are looking to play a bigger pot against several opponents. When is a raise likely to narrow the field? Typically, if the table is fairly tight or most of the players are trying to play decent starting hands, which tends to be the case as limits progress in size, raising will thin the crowd. The raise should be even more effective if no one has entered the pot yet. Also, if your opponents perceive you to be a tight, solid player, they may be less likely to call your raise. Poker games are almost always in a state of flux, so it’s important to pay attention to how the game is playing. The addition or subtraction of just one player is often enough to dramatically alter the entire complexion of the game. Hands that should be protected with a raise are those that fare best against fewer opponents. These include most hands with two aces, as two aces with 174 any two other cards are a favorite against nearly all other hands in a one-onone situation. Other hands that have both low and high potential, such as A2-K-x, A-3-5-K, or A-2-Q-Q, play well against few opponents, although they also play fine multiway. Holding an A-K combination frequently comes in handy in pots against only one or two opponents. When only a couple of players see the flop, the deck is often richer in aces than normal. This assumption is based on the tendency of Omaha eight-or-better players to play hands with an ace in them. If both you and your opponent are holding an ace and an ace flops, your king may wind up playing as a kicker, enabling you to win the high side of the pot with A-K. Also, you generally won’t need as strong of a hand to win a heads-up pot, so flopping a king or kings up has definite value. Not unlike hold’em, the value of the A-K combination declines as more players contest the pot, since stronger hands—such as straights, flushes, or full houses—will typically be needed to win the high portion of the pot. Great Omaha eight-or-better hands like A-2-3-4 can be raising hands before the flop as well, but for another reason. Raising in spots that are likely to produce a short field is a mistake with this sort of hand, due to its lack of high-hand potential. However, in a pot contested by several players, this hand is excellent. If a low hand is possible—and a low hand will be possible most of the time—you will most likely be holding the nuts. Due to this hand’s high probability of making the nut low, go ahead and raise to build a big pot if several players have already entered the hand. Additionally, if your opponents seem to have no respect for raises, go ahead and raise regardless of your position. You should still get plenty of action. Other good hands to

What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the flop or turn, you are not guaranteed to see a showdown. Leverage can make it correct to fold despite getting a good price on the current street, because you might face a difficult decision and lose EV on a future street. Hands that can bet as part of a polarized range profit from leverage . Betting the turn, whether for value or as a bluff, is more profitable if you anticipate profitably betting the river. Conversely, the medium-strength hands in a condensed range lose value to leverage. Calling the turn is less profitable when it risks another tough decision on the river. Equity Realization and Indifference Leverage is related to the concept of equity realization . There is extra value in growing the pot when you hold a hand that stands to benefit from future action, whether through value betting or bluffing. It’s fairly intuitive that when you have a hand strong enough to win a large pot at showdown, you benefit from betting multiple times. But it is also true that if you anticipate bluffing many rivers, you can bluff even more on the turn. These situations are related: when your range contains many strong candidates for value betting, that is what enables you to bluff more often without fear of exploitation. To understand why let’s revisit the concept of indifference . You may know that the right ratio of value bets to bluffs in a river betting range makes your opponent indifferent between calling and folding with their bluff-catchers. For example, if you make a pot-sized bet with a range that includes 1 bluff for every 2 value bets, calling with a bluff-catcher has an EV of 0 for your opponent, just as folding would. Likewise, their calling frequency should make you indifferent to bluffing. This requires calling at a ratio of 1 – Bet/(Bet+Pot), also known as the Minimum Defense Frequency . Things get more interesting when we carry this concept back to the turn. Turn play is more complicated because all the board cards have yet to be revealed, so hands can change value. But the general concept holds: most of your bets should be clearly identifiable as value bets or bluffs , and at least one of the goals of your betting range is to give your opponent a tough decision when they hold the sort of hand that can beat a bluff but will lose to a value bet. Indifferent to what, though? Unlike on the river, a turn call does not end the action. Both you and your opponent must continue to be unpredictable on the river. That is, they should not be able to predict that you will or will not bet again with your bluffs, nor should you be able to predict that they will or will not call again with their bluff-catchers. The only way to arrive at an equilibrium is if you sometimes give up your bluffs on the turn, sometimes

six suited you want to be three betting these hands that are playing much better a very deep stack depth that can make straights and flushes and give you some board coverage now at fifty big blinds the range is going to change a lot in terms of where we draw our three bit Bluff strong and this is one of the biggest mistakes that players make plain short stack from Louis ya hands like ace Queen off ace Jack suited we would be just calling with on the button this is just the hands that are gonna be rear AZ with and from Stan our ace deuce suited and ace three suited that much worse than H four student H five student or do they just add too many Bluffs into our range it's kind of a combination of both like I said before in the types of hands you can definitely three about a three and ace to student but you have that little added equity with the ace five and H four Souter when our opponent has deuces and threes they are better hands you're gonna make slightly you're gonna make a pair of fives you're gonna have dominated a little bit more when he has five six suited or five seven suited and the five comes on the flop just you know a little bit stronger hand you just don't want to you can't be bluffing every combination but it's just combination of both we don't want to be bluffing too much in 85 student is stronger than ace deuce and has some more equity when called so at 50 big blinds the bigger a sec suited hands are gonna be part of our bluffing range and offs you Broadway heavy range so we're gonna have a wider value range at 50 big blinds so when we're three betting off of 50 big blinds we need less of a the value threshold is lower so when you're three betting at a hundred or 150 big blind you need a stronger hand to stack off because you're risking 150 big blinds when you three about fifty big blinds you can stock off with a little bit less of a hand because you're only risking 50 big blinds so you can have more hands for value which also means you can have some more hands for Bluffs so in this value range we've added a hand like pocket tens ace Queen suited ace Jack suited ace Queen off king queen suited kind of Anor value range and our Bluffs have changed drastically we no longer are three bit bluffing these smaller suited connectors are three that bluffing range has gotten stronger in terms of now with three betting these ace nine ace ace five suited and then this region here the ace Jack King Jack ace 10 off in King 10 off and the reason why do we want to start now three betting these ace jacks King tens ace 10 King Jack off there's a couple of reasons first

OOP does well on the average turn card, with 48% equity, and over-realizes it to win 53% of the pot. The worst possible turn cards for OOP are offsuit aces such as A♠/A♣ where their EV decreases to 25.8%. The best possible turn cards are offsuit 5x such as 5♠/5♣ where their EV increases to 64.17% of the pot. Notice how there is a correlation between OOP’s EQ and EV, although the highest EQ card is not necessarily the highest EV card (Tables 134-137). Diagram 118 The EQB charts for the A♠ and the 5♠ turn cards demonstrate just how much range morphology can vary according to the runout, even after the same action line on the same flop (Diagram 118). This has a substantial impact on the players’ equilibrium strategies.

Hand Range 172: BB vs LJ 4-bet (40bb) • Call 48.8% / • Fold 51.2%

about those players Emily if you want the just basics basics of how to win it No Limit Hold'em play big pots vs. wide ranges and just try to get them to fold their high cards if you get one person heads up the thing they're gonna have most the time is high cards almost any see that will be profitable do not try to get people to fold pairs in low to mid stakes that is a great way to go broke fast what you're gonna do when when a bunch of people limp you gotta raise big right we're talking like 4x + 2 X for each limb per pot plus the big blind right you get a heads up versus one player you see bet you just trying to get their high cards out if they call you they've got a pair it's most likely one of the pairs on the board and they're not folding it so if you have a pair that's better than that pair get every cent you can from them never hit the brakes but if you've missed you just gotta accept reality on reality's terms and wave through your time so there's a lot of questions while I just went on that tirade so let me keep going how would you start playing the first few levels in the W so P in big 50 aggressive or passive I show up I am aggressive from the start because you know what everybody plays like it's me let me ask you this dog lift how many times have you played a live tournament played one hour look down at your stack and went where did 15 percent of my stack go I want to be the guy getting everybody's 15 percent of the stack because most people they open whatever they feel like III bet it doesn't seem like that much they call and then they're in this pot out of position that they didn't really prepare for I want to be the initiator in every one of those pots that's where I want to be I look for the guy I think is opening too much almost everybody opens too much from the low Jack hi jack cut off now and I'm just 3betting from the start it seems that one of the biggest things for me to focus on the most is proper best sizing any advice on how to optimize this Chad it the fastest way I could do that is if you think your opponent as a big range you can bet bigger just forget a lot of the high cards to fold out if you think it's a tight range usually you should bet smaller just because if they are folding they're probably they were folding to whatever right people that play tight ranges tend to have a specific way they play poker so betting big since they don't have many high cards anyway that's not gonna fold them out a time you should just take a little shot

basic effectively um in the 10 of Hearts Let's actually can look at here it's better uh there's there's a lot of betting for the small bet size the bigger bet size um is mostly only used in medium cards looks like yeah um so here on the 10 in general unless the 10 of clubes you won't see really much bigger bed size the of clubs difference is that it brings a second flusher of course and then now you actually want to just Jam uh a lot of hands here but um with the 10 of Hearts there's no need you can just bet small and keep betting your range uh you wouldn't be raised that much the St to p ratio is very very shallow so even if the building has a queen here he shouldn't be yamming all that often to us almost like never at all and if he does then yeah you you have to fold some of your two PA type hands but we should have the hero should have here so many Straits right and top two pair and sets that it doesn't matter even if he jams we still have a pretty Prett strong range that can call almost 60% of the time here and with this to put ratio it will be a rather easy call with um ajck you know fold King Jack you f some more often than that and then a then uh you can probably call like um 50/50 or something like that all right so um by betting small what we mostly accomplished is um just um f get value um from a lot of a ax and also F some um and get Val from flos and set up a river yam that's effectively what we want to do in this C because it's very for a range we have um an advantage here when just want to keep putting money into the pot and force the in position player to keep putting money with you know um two pairs and stuff like that if we look at the range Explorer here um on this turn straights the out of position player will have 27 combos which is 1/3 of his range while um the in position player will only have a straight um 15 Combos and that's 23% of of um his range with this difference um it of course makes sense that now um the out position player wants to keep uh start building a keep building the pot and just viral for three streets a very high frequency and also because of of how often uh the her has a straight here compared to the villain we uh that's why we don't see much racing by the imposition player even if he has a queen he shouldn't be racing at all um because then if he raises every single queen he has a queen on the river and we can just you know keep yamming on him very very aggressively uh some of

that respect. Making matters worse, people expect the big blind to get jiggy in order to retard aggression. Raises from the big blind not only get less respect, but in fact invite the nasty possibility of a re-bluff push from the original raiser, especially one canny enough to see that the big blind will re-raise as adefense against getting bullied. What falls out of this is that if you’re going to bluff-re-raise, presumably against a late-position opener, it’s much wiser to do it from the small blind than the big blind. Remember, if you raise with a hand that can’t call, you have to believe you will win the pot about 70% of the time. Because of the lack of respect that re-raises out of the big blind garner, that 70% is a tough mark to hit. To be sure, sometimes in bubble situations or against super-tight and timid opponents, you can hit that mark even out of the big blind. But it’s a much easier mark to hit from the small blind, where your opponent is much less likely to put you on a bluff. So lean toward flat-calling with your playable hands from the big blind. Your raises usually won’t do much except create a big pot that you’ll have to attack out of position for the rest of the hand. Similarly, you should be more likely to re-raise on a complete bluff from the small blind than from the big blind, leveraging the respect that small-blind raises naturally accrue. As a last thought, let’s talk about the concept of defending your big blind. Players love to talk about how they call with a wide range of hands fromthe big blind in order to defend it. Thing is, that blind doesn’t belong to you, so there’s nothing to defend. Once your chips go into a pot, they ain’t yours. They’re part of the pot and only relevant inasmuch as they help determine the pot size. Calling with weak hands because you somehow want to protect chips that no longer belong to you is the very definition of throwing good money after bad. It’s okay to be pushed around on your big blind. Don’t get your knickers in a twist. Not playing certain hands is part of correct play, too. Now, I imagine you’re thinking, “But can’t I call with weak hands since I’m getting such a good price on my money?” Let’s consider it. Are you getting a better price to call? Absolutely. That’s why you can be a little looser on your calls in the big blind, but only a little. In a 100/200 game with a raise to 600, you’re calling 400 to win 900, so that’s a little better than 2-to-1. To show profit, you have to win from this point forward over about a third of the time, hard to do out of position and without the lead or a legitimate hand. And yes, you always hear players quote the odds that if you take two undercards (like 96) versus two overcards (like AK), the undercards

Hand Range 250: HJ vs UTG (25bb) • All-in 1.1% / • 3-bet 3.9% / • Call 8% / • Fold 87%

be too strong for 4-bet calling TT or AQs to be feasible on Hero's part. This calling range is much wider than in the hand before and this is down to Villain having a wider range and being a weaker player. It encompasses 224 combos. Each hand defended in this range is estimated to be higher EV to defend than to fold, or in others word, better than -2BB in EV from the point of view of the entire hand. The 4-bet bluff range spans 88 combos and roughly makes up the 2:1 bluff to value ratio we were aiming for. These bluffs are chosen using the same criteria as before - they're the best of a relatively bad bunch of remaining combos. Playability is not such an issue here though given that Villain is unlikely to be calling too many 4-bets with a VPIP/PFR so close together and such a high fold to 4-bet stat. Hero folds the rest of his opening range happily, knowing that overall he is only mucking 266 combos / 618 combos = 43% of his range. This is comfortably less than MDF would have him fold, and just as well. Villain is playing in such a way that this strategy is much better than striving for balance would be. The exploitative strategy is complete. Villain can expect to loose quite a bit of money playing like this against Hero for the foreseeable future. Completely Unbalanced Defending In Hand 96, balance was less of an issue than in Hand 95, but it was still an issue. We expected a dramatic shift in our strategy to cause an undesired adjustment from Villain, ruining our long-term chances of exploiting the hole we'd found in his game. However, when we're against Fish or other unaware player types too unsophisticated to adjust at all to hugely exploitative strategies, any strategies which are best in a vacuum, will also be best in the long-term. This hand is a great example:

chips invested. The higher your Bubble Factor, the more disastrous it would be to lose. As a result, the higher it is, the tighter you should play. As the name suggests, most of the time it would be catastrophic to get your money in bad on the bubble of a tournament. What you lose, in real money terms, massively outweighs what you gain if you find yourself all-in for your tournament life on the bubble or at a final table. Bubble Factor is a relative measure, however . If you are the 2nd chip leader, your Bubble Factor is low against all the other players, but if you take on the overall chip leader it is extremely high. Busting to the chip leader is a disaster when you could otherwise bully all the medium stacks and coast to a big payout. Middle stack vs. middle stack is a very high Bubble Factor spot, as is short stack vs. short stack. However, big vs. short stack tends to play closer to ChipEV. The big stack can play loose because they have very little to lose. The short stack must make a move soon, so they are better off making it against the player who will call them the widest (especially as the other stacks will avoid playing a 3-way pot with the big stack). Now that we have skimmed over Bubble Factor, how does this apply in postflop ICM spots? The answer is that covering players get to be more aggressive postflop . If you play bubble/final table chip leader vs big/middle stack pots the same way you would a ChipEV spot, you are torching money. Big stacks can bet more often, even when out of position. They can be more aggressive even when the other player has range and nutted advantage. It is not uncommon to see the bigger stack donk lead on flops that clearly favor the other player because the shorter-stacked player must play so much more cautiously. You don’t have to be one of the outright leaders, you just have to be the covering player. The 2nd shortest stack gets to be more aggressive against the shortest stack at the table, just as the big stack gets to be aggressive with medium stacks, and so on. However, it is important to note that the degree to which you cover the other player determines how aggressive you can be . If you have three times as many chips as your opponent, you can take some really loose lines, if you have 40 big blinds and they have 36 big blinds, you both have to play carefully because neither of you wants to lose an all-in pot. Big stack vs. second biggest stack Let’s look at an example to illustrate what we are talking about. In this example, we have a player with 40 big blinds open on the BTN and get called by the BB with 70 big blinds. The flop is A ♣ 8 ♦ 3 ♠ . We are at a final table with stacks and potential payouts

has earned 50 cents. If you can manage 500 flips of the coin per hour, your hourly rate is now $250, because on average you will lose one dollar 250 10 Chapter Two times and win two dollars 250 times. $500 minus $250 equals a $250 net win. Notice again that your mathematical expectation, which is the amount you will average winning per bet, is 50 cents. You have won $250 after betting a dollar 500 times: That works out to be 50 cents per bet. Mathematical expectation has nothing to do with results. The imbecile might win the first ten coin flips in a row, but getting 2-to-l odds on an even-money proposition, you still earn 50 cents per $1 bet. It makes no difference whether you win or lose a specific bet or series of bets as long as you have a bankroll to cover your losses easily. If you continue to make these bets, you will win, and in the long run your win will approach specifically the sum of your expectations. Anytime you make a bet with the best of it, where the odds are in your favor, you have earned something on that bet, whether you actually win or lose the bet. By the same token, when you make a bet with the worst of it, where the odds are not in your favor, you have lost something, whether you actually win or lose the bet. You have the best of it when you have a positive expectation, and you have a positive expectation when the odds are in your favor. You have the worst of it when you have a negative expectation, and you have a negative expectation when the odds are against you. Serious gamblers bet only when they have the best of it; when they have the worst of it, they pass. What does it mean to have the odds in your favor? It means winning more on a result than the true odds warrant. The true odds of a coin's coming up heads are 1-to-l, but you're getting 2-to-l for your money. The odds in this instance are in your favor. You have the best of it with a positive expectation of 50 cents per bet. Here is a slightly more complicated example of mathematical expectation. A person writes down a number from one to five and bets $5 against your $ 1 that you cannot guessthe number. Should you take the bet? What is your mathematical expectation? Four guesses will be wrong, and one will be right, on average. Therefore, the odds against your guessing correctly are Expectation and Hourly Rate 11 4-to-1 • Chances are that in a single try you will lose the dollar, However, you are getting $5-to-$ 1 on a 4-to-1 proposition. So the odds are in your favor, you have the best of it, and you should take the bet. If you make that bet five times, on average you will lose $1 four times and win $5 once. You have earned $1 on five bets for

Hand Range 23: BN Nash Equilibrium

Diagram 74 The texture most c-bet is trips. Hero has more overpairs and premium overcards that will turn big pairs more often than IP, and IP’s range has many suited, connected type hands that are complete trash and often have to fold. Paired boards are c-bet very often and, contrary to IP vs BB situations, Hero as OOP uses big bet-sizes on paired boards, particularly on low rank flops. When the Villain is in the BB, their range is much wider and can connect with trips in multiple ways, but when they are on the BN, the number of hands that make trips is way lower. This creates a situation where IP’s range will be capped, while OOP is uncapped, allowing OOP to use a large bet-size, particularly on low and middle boards. The OOP player has a significant polarization advantage on rainbow flops, allowing them to use bigger sizes more often. On the two-tone flops, the equity and EQR of many of OOP’s strong hands gets reduced due to the presence of the flush draw, resulting in a reduced c-betting frequency. Monotone boards improve IP’s equity distribution substantially. This results in OOP using a small bet and c-betting only about 50% of hands.

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three you check they bet you check raise let's say you've been check raising them constantly you want to know they'll freak out with one pair that tends to be a youth thing but there will be times you just piss off someone who's older enough that they're gonna do it by the way guys like anyone can play any way they want every time i play people get really pissy because they want to see flops it's not pie gal it like people are allowed to do whatever they want it's essentially well it's a it's a strategy game with chips and cards the chips and cards are there to trick you so we call and the board comes jack of spades eight of clubs five of spades would you like to check or bet here i'm gonna give you a few seconds we're gonna go ahead and check and this player bets 21 000 here would you like to fold call or raise 10 seconds if you did say raise what did you want to raise too i don't know why this works live but live right after the person bets look right at the dealer and wave your hand in and go i'm all in and for whatever reason people will just scream and they'll table queen a to hearts like it's the nuts and i don't know if that's normally people do that with a draw or what but it does seem to work i here's a cooler right like he should bet call there because nine ten hearts would be getting it in and hands like that some weaker flush was but if you want to get max value from this after this is one of these weird hands where you can almost play it anyway if you said donkly on this flop okay that's fine i i do donk lead there a lot but when you check jam there if you check jam the second it's on them that a lot of people want here's the thing nobody wants to fold their hand they did not show up two-fold why do people play poker people play poker for the thrill of it they they save the money the money is part of it but they wouldn't show up every single day even when they're not making money a lot of those days if there wasn't something else they're getting out of it and what they're getting out of it a lot of the time is just the thrill of playing it's true like the the days i get to play cards are some of the best days of the month some of the best days of the week so people want to play and that means they don't want to fold because folding is not playing folding is observing if you can master folding you'll make money at this game usually people who get really good at folding are there because they really need the money when i came into this game with missing teeth living

a second Barrel here with A6 suited on this board straight draws have improved to either a pair or a straight flush draws still willing to continue in this case flush draws have improved so the one hand he could get to fold is a pair of fives but a pair of eights going over a pair of jacks going nowhere a pair of 10 is going nowhere everything better going nowhere and dairy poker just having little to no equity with E6 of hearts on a board with nothing but the other suits it's probably just going to be given up with the handle now on this River could go for a bluff yeah flush gets there straight gets there so now on this River he could get a pair of eights to fold maybe you can get a pair of tens to fold so nice job there dairy poker recognizing that on most rivers it would be a give up but on that perfect River where he can get a lot of one pair of hands to fold that are beating his A6 nice spot to go for a chunky Bluff take it down great play there from dairy poker all right we'll see an open here from welcome Inferno with King 3 suited for sure and off of 14 blinds this is another easy reshuff for monsman he's getting a lot of these optimal spots that you want when you're sitting on that 12 to 25 big blind stack which is a loose opener opening from late position when you have a medium to strong strength hand that being those pocket pairs the bigger the better and those asexes the bigger the better and of course your king queen suited your king queens and your suited Broadways as well but welcome Inferno not going to be slowing down we'll see another open Dairy poker very playable hand here with king queen question is how to play it there are two shorter Stacks but with how wide welcome inferno's going I wouldn't be surprised if we just see this one going all in I guess he could conceivably flat um and commit more chips when he improves his hands we can keep in those dominated King x's and queen axes oh he does decide to fold actually probably due to the fact that these two stacks are both shorter and the fact that welcome Inferno is opening from first position or maybe it was because welcome Inferno has just been running so hot with all ends and every time someone re-jams welcome just seems to have it and dairy poker didn't want to be the next one to uh Fall by the wayside either way dirty poker folding what was technically the second best hand but what certainly would have been a strong enough uh and to to make a play with and while Queen Inferno would have been folding that he's four suited for that many big blinds did johnik opening A7 Suited welcome to Inferno getting a great

Chop A pot where, at showdown, two or more players are tied because they have hands of the same strength, and therefore share, or “chop” the pot.

gave more examples and offered more detailed explanations. But the basic concepts from the first edition remained the same. It is now a new century, and we have decided to continue the process that we began in 1994. But we have taken it one step further, we are going to cover much new territory. Many of you have complained that while Hold 'em Poker for Advanced Players was the "advanced" text, it did not explain in enough detail how to play in loose, low limit games. This has now been thoroughly addressed and those of you who are familiar with the so called "low limit" texts will see that our approach is very different and much more profitable. In addition, some of you felt that the section on short-handed play was not complete; this has also been addressed. We have also added many new concepts into the "body" of the manual. And, as we have said many times before, if you study hard, get a proper amount of experience, and do a great deal of thinking about the game, you should be well on the road to success. 4 Introduction Finally, we would like to express our appreciation to Irving Sklansky for editing this work. Thanks to him our ideas are now more clearly stated and thus should be more easily understood. In addition, we would like to also thank Charmaine Dadian for her typing, proof reading, and assistance in the overall production of this text. Using This Book As stated in the introduction, this book will require you to do a great deal ofthinking. It is recommended that the whole book be read first, then you can return to those sections that require more study. Also, if you are new to hold 'em you should memorize the hand rankings and how to play the first two cards. We see no better way to master this area of play. However, after you have gained the requisite experience, you will begin to see where it is appropriate to deviate from "correct" strategy and you will begin to think in terms of the actual hand itself rather than hand "groups." Almost all top players do this, although you should not get carried away. The text will supply plenty of discussion in this area. We also recommend that you not jump right into a $40-$80 or higher limit game. Even though the strategies in this book will win their share at the $40-$80 limit, especially if your opposition is not too tough, it is still better to start lower and work your way up. In a game as complex as Texas hold 'em, there is no substitute for experience. Keep in mind, when trying to master hold 'em, that at times many of the following concepts will seem to contradict each other. For example, some concepts might recommend that you bet your hand right out, while other concepts will advise you to go for a check-raise. One of She keys to successful hold 'em play is to balance these ideas, which will help you select

Pot committed A situation where a player is unlikely to fold because the amount they have contributed to the pot thus far is large, relative to their stack. However, there is no mathematical rule or consensus as to what is considered pot committed, and usage of the term varies from player to player.

Ace track Ace 10 Ace nine Ace five four three two all offsuits shove a lot king queen offsuit shelves King jack off suit shoves sometimes King seven suited King six through the King five Suited like the shav and then we again see the best hands re-raising right ace and student better Jackson better few suited connectors but then a nice mixture of asex king or sorry King X Queen X Jack X and 10x Bluffs a lot of players do not re-raise these hands with Bluffs ever and it makes them very easy to play against if you only re-raise with the nuts you become super duper easy to play against I want to make it really clear if you look at all these charts all of these charts have some non all in re-raise Bluffs and they're almost entirely from King X asex Queen X Type junk like King four Queen four Jack four get in there with the Jack four have fun with GTO approved now when we get down to 15 big wines this is when we are going to defend very wide but also we're going to shovel and a lot and now we can no longer re-raise less than all in and still fold if we get shoved on because if someone raises to two and we make it let's say five and a half and they shove now we're getting two to one pot odds we only need to win about 33 of the time and most hands went about 33 of the time against decently wide ranges so and all the deeper Stacks so far we've seen non-reays our non-all in re-raises but now at this stack depth we are going to be shoving or calling no more small re-rays all in and we're gonna see the hands that like the shove are usually the pears pears love to shove and then a lot of asex and maybe some King ex suited so let's take a look against under the gun we're gonna be pretty tight here we're shoving all our pairs except for five four threes and twos those calls sometimes Aces slow plays one thing when you're playing a little bit shallower stacked from the big blind Ace of slow plays when you get very very shallow because by slow playing Aces it lets you defend a little bit wider because your range is a Little Bit Stronger notice we are calling a lot right we're calling with all except for the worst offsuit hands in all these scenarios are all in Rage Against under the gun is Ace Queen and better all the pairs a state suit a seven suit a five suit is four suited and King ten suited and some jack 10 suited that's it still a pretty tight shoving range right but a pretty wide defending range because remember when they raise a new call if you flop any pair you check they bat you're just not folding if you make a pair it's not hard to

All in This Is Where It folds around to the small blind they rip it all in in the big blind we have to call off pretty wide King 3 suited and better King seven off suit and better Queen eight suited Queen nine off suit Jack ten off suit Jack nine Suited tough spot dicey spot most people don't call quite enough here um and again when there are payout implications you probably should call a little bit tighter but this is a spot where you do need to call off pretty wide because your opponent's open shoving range should be pretty wide now let's discuss another major strategic change you're gonna have to make as you get even shallower down to 10 big wines now at this point for Simplicity I recommend using the push or fold app we have in the poker coaching app it's completely free check it out and the reason for this is because while you can use a Min raise or shove strategy at the stack depth it doesn't really gain you that much Equity it gets really tricky to play especially after the Flop if you raise and someone calls because then you got to get it in pretty wide due to your amazing products if you just rip it in pre-flop You're Gonna Lose a little bit of EV compared to perfect GTO poker but not much and it's going to be super duper easy to implement the main exception to this is when you're playing blind versus blind because you should be limping from the small blind still again because you have to put in half a big blind to try to win three realize your opponents may use all sorts of strategies 10 big lines deep I do think most people opt to just use a shove or fold strategy especially in the non-super high stakes games because it's easy and these charts are freely available on my site and everywhere else so let's take a look at pre-flop shoving ranges okay under the gun 10 big wines deep this presumes there is an ante in play so if there's no anti you're going to shove tighter but you see what's shoving here freezing better Ace five suited a seven suited and better any two suited cards nine or higher hasten offsuit and king queen notice King Jack Queen Jack Ace nine nine eight suited eight seven suited A6 suited Ace three suited these hands are not good enough to shove for 10 big lines under the gun in this scenario under the gun is eight-handed I believe in this chart looking up in the app all right hijack gets the shove much much wider right we see almost any Ace twos and better lots of high suited connected taipans and any offsuit Broadway hands are opting to shove now and then from the button you get to shove really wide right a much wider range of suited hands Queen Force suited and better King five off suit and better any

nine of diamonds things like that so we're actually not going to bluff our diamonds very much as you can see a sport of diamonds plays a pure check we are blocking their auto bones that's terrible when we're river blocking right whereas if you compare it to our lower diamonds you're finding a little bit more blocks right but even your jacket is not good enough you just have to check back and it doesn't feel good right you you take jack eight of diamonds that flop your bed turn you shouldn't have jackpot in the river but the bottom line is you have really bad card removal it's a really it's two really bad cards to hold in your hand because when you jam you're blocking the ace jack of diamonds you're blocking the ace eight of diamonds these are pure bowls right so river bluffing is all about blockers and our hand 86 of spades fits perfectly into a river block we have eight high so we benefit a ton from bluffing our hand and getting anything to fold and we're not blocking any of the folds really right when we have eight six of spades um as we talked about earlier the a6 is still bluffing here because it's blocking many fewer of uh of the opponent's boats than like the jack high ones but when you have the h3 of clubs it's a perfect hand to bluff off with you because you're unblocking all the opponents um hopefully that shows you how to approach turn barreling uh turn range construction when you're in position and then another example of how to structure your river blocking ring all right the last hand uh part one we're going to go back to a oop big blind spot uh the button play raises from a recent uh 15k from a few days ago um called the five three off suit we queen six six rainbow jack turn off super so i think that this hand fits nicely into uh what we've been talking about over the previous two hands because it's a really good example of how op you're gonna mostly just want to have equity when you you know we talk about barely in return with check raise how you want equity when you put money in the pot the same thing happens with turn probes um and so most of your range is going to want to have extra equity because you're out of position uh putting a lot of money in the pot so we think about what that size we want to use when probing this term well what does our value feel like it wants to how much money does our value want to put in are we going to be really polar or is the board is so good for us that we're gonna be betting small well in this fight we're gonna be really bolder right because when we bet we're saying i have a six or i have a queen right we're

Satellite A tournament that awards seats to another tournament, typically one of the higher buy-in. They provide a way to enter a tournament cheaper.

Diagram 82 Trips and rainbow paired flops are the most frequently c-bet textures, with two-tone and monotone flops being the least frequently c-bet. On two-tone flops, OOP has a great spot to x/r with many flush draws, which would force Hero off the pot. For this reason, two-tone flops are checked back at a high frequency, allowing many of IP’s good and weak hands to realize equity.

hand that's probably the best hand but if you bet and your opponent calls you you may not we will be giving some examples of this later in this course and also we discuss this thoroughly in the homework challenges at pokercoaching.com so make sure you check those out when you are vetting you can either be betting a premium hand like the nuts or a decent but marginal hand this is referred to as betting for thin value when you bet for thin value you're betting a hand let's say someone raises before the flop and you decide to re-raise with a hand like ace queen right if you re-raise ace queen and the initial razor then re-re-raises you at that point you're not really loving it anymore right but if you raise with ace queen and they just call you now they're probably going to have a whole lot of hands worse than ace queen because they would have re-raised with the better hands right so in that scenario you are re-raising for thin value the next reason is for essentially protection this is a broad concept that sometimes gets put into the value category but there are many times where you have a hand like top pair bad kicker after the flop where you have the best hand but a bad kicker and you're betting because if your opponents fold they're usually folding out some hands that could outdraw you some portion of the time like let's say the board comes 983 and you have queen nine in that scenario if you bet and your opponents fold out a hand like king jack yeah you had the best hand at the moment but if they get a king or a jack they beat you so you don't really care if they fold because they are gonna outdraw you sometimes and if they fold out that hand that's a reasonable success the final reason to bet is as a bluff and when you are bluffing you are betting because you want better hands to fold um before the flop the hands near the bottom of the range of hands that you are going to play are essentially considered to be a bluff we'll be discussing which hands you should play in all positions in the very next section of this class so stay tuned for that when you are bluffing it can either be a pure bluff or a semi bluff a pure bluff is when if you bet and your opponent calls you just always lose this is usually going to be occurring on the river on the last betting round where you get to the river you have perhaps a draw that did not improve to a straight or flush on the river and you're betting knowing that if you get called and you lose well you lose the hand but when you bet with a pure bluff and your opponent folds they're usually folding out a better hand which is a huge success the other reason it

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Villain could have all kinds of low pairs, flush draws, straight draws, pair + draws etc. when he calls the first two c-bets. This range largely misses the turn and river and these cards strengthen Hero's flop bluffing range substantially. Hero should therefore expect more fold equity than normal on this type of run out and, all else being equal, should probably favour a bluff-heavy range full of hands with very poor SDV against most opponents. If Villain is skilled enough to react to such a strategy well then Hero can always retreat into balance, which will still involve a fair bit of bluffing - Hero can value bet thinly here as Villain's range is quite weak and could well be capped. Example Hands Let's put what we've just learned into practice with a few examples. Try to decide whether Hero should triple barrel bluff in the following spots.

Reverse implied odds The opposite of implied odds. They estimate the amount a player could lose when they make their hand but their opponent makes an even stronger hand, thus making it likely they will lose a significant amount of chips.

flop, which will reduce their share of the pot. Ranges in Play The following hand ranges identify the ranges in play for the subsequent analysis (Hand Ranges 341-348) Hand Range 341: CO RFI 40bb • Open 2.3x 36.4% / • Fold 63.6%

Pre-flop: By now this should jump out as a very obvious spot to set mine vs. a tight Fish's opening range, in position, getting a phenomenal price to bolster implied odds even more. Enough said really. Flop: This is a fairly mandatory raise for three reasons: The passive Fish can't be trusted to carry on betting on future streets even with a strong hand like an overpair, especially with say QQ on unfavourable turns like a K or A. If the Fish doesn't bet, Hero can't raise and he needs to raise at some point to get this pot growing. The c-bet is relatively small leaving a lot of pot building work to be done. The Fish's range is just very strong here. He's opened UTG then c-bet three-way. Given his c-bet stat is so low, this indicates an overpair as opposed to overcards the majority of the time. Hero also doesn't care about calling his sets to protect the weaker hands in his range since this player will simply never be adjusting by applying more pressure on later streets, even if he were aware of Hero's strategy. Slowplaying is unnecessary and not the best line here.

in a little bit more checking especially from out of position a little bit more folding from out of position and also using more polarized bets when you are betting right especially when you're in position you're usually going for big bet sizes because when you have the nuts you won't be able to get the money in the pot and if you're betting very polarized you get to include a lot of bluffs and also nut advantage matters very much as we get deeper and deeper and the ability to make the nuts and or block the nuts like we saw that king 10 with king of spades or tennis fades goes up in value so keep these three things in mind when you're playing deep stacked and besides these three things for the most part you play very similarly similarly to when you are playing 100 big blinds deep

first three cards and no other cards seen, you will make a spade flush in seven cards 18 percent of the time. Now, suppose when you look around the table, you see that exactly one of your seven opponents shows a spade. What does this do to your chances of making a flush? If you say it increases them, you are right. True, one of your needed cards is gone, but so too are six unneeded cards. Therefore, there are more spades proportionally among the unseen cards than you would assume if you had seen no cards at all. Generally, though, it's not so much the total number of exposed cards that people ignore but the number of cards among them that they need. It is very important to pay attention to these cards because their presence can change a playable hand into an unplayable one. Let's say you start with three spades on your first three cards in seven-card stud, and you have seen seven other cards. The following table shows the effect of the other cards on your making a flush. Chances For a Flush % 23.6 19.6 15.8 12.3 9.1 Number of 5s and Aces Seen Besides Your Own 0 1 2 3 4 You start with Chances For Aces Up Or Three-of-a-Kind (%) 41.0 34.1 26.5 18.3 10.5 Pot Odds 39 With no spades out, you have a strong hand. With two out, your hand becomes marginally playable. With four or more out, it becomes a hand not worth a call. Here are a few more examples from seven-card stud and seven-card razz to demonstrate the effect of exposed cards on the chances of making a hand. You start with on your first three cards in seven-card stud. You have seen seven other cards. Number of Spades Besides Your Own 0 1 2 3 4 40 Chapter Five on your first four cards in seven-card stud and have seen eight other cards. Pot Odds 41 Though you're a favorite to make an 8 low or better with as many as eight of your needed cards among the ten exposed, notice how much harder it is to make a 7 low. Number of 5s and 10s Seen 0 1 2 3 4 Chances For a Straight (%) 49.8 44.8 39.4 33.8 27.8 Number of 5s, 6s, and 7s Seen 0 4 8 Chances For a 7 Low or Better (%) 69.2 51.9 29.1 on your first four cards in seven-card razz. You have seen ten other cards. Number of 5s, 6s, Chances For an 8 7s, and 8s Seen Low or Better (%; 0 81.8 2 76.0 3 72.7 4 69.2 5 65.3 6 61.2 7 56.7 8 51.9 You start with These tables indicate the importance of taking the cards you see in other players' hands into account before you compare the pot odds you are getting to your chances of making your hand. Position Just as the number of needed cards you see reduces your chances of improving your hand, your position in the sequence of betting

Table 103: High Donk Bet Frequency Flops On the high donk frequency flops, the BB has an average of 50% equity and is able to over- realize that equity (103% EQR), capturing an average of 52% of the pot (Table 103). The main reason why the BB over-realizes equity is the way the equity is distributed (Diagram 26). Diagram 26: EQB on High Donk Bet Frequency Flops Here, the BB’s range is more polarized than IP’s range. The BB has the advantage in both strong and good hands, while 50% of IP’s range are weak hands that will have a more difficult time realizing equity and will therefore benefit from playing passively. This range construction resembles the Clairvoyance Toy game, with the IP having the more depolarized range, which makes the BB want to take the betting lead.

a play that makes you a ton of money and small six cash games where the Flop aggressor just wins the pot when the opponent doesn't have anything and setting yourself up to be in situations like this over and over again especially against weak ranges and especially when you are in position is going to be very very valuable okay I have one more hand straightforward limper limps the button small blind lengths we have Jack free off suit most players think check we don't have anything but I disagree this is a pretty excellent spot to raise our hand is terrible and for that reason it's not going to realize that much equity on the flop even if you get top pair you don't love it it's but if we are against a button limper who's going to be limping with mostly trash because they're going to raise all their good hands we can raise in this spot if we make it big enough most players in the situation will fold almost everything so in this situation we already have two dollars in the pot if we make it something like 15 we're risking 13 to try to win six which is actually an okay risk award ratio especially if you think your opponent is going to fold a large portion of the time and even if they do call sometimes you make a hand not too often but sometimes you do here though we make it 15. they just let it go and that's fine fine and good and easy that is what we are going for here we want to put ourselves in situations where we have nice easy decisions and here we've ended up winning six dollars from this pot with the Jack 3 off suit which is very very good some of the best hands to use as Bluffs by the way are going to be hands like king with a low card Queen with a low card and Jack with a low card those are very very good hands to use as Bluffs against very weak ranges let's discuss when your limp gets raised 100 big lines deep you're going to want to ask yourself what pot odds am I getting and what implied odds am I getting am I getting the correct implied odds to draw to my hand in general with small Pairs and medium pairs you're going to want to be getting something like ten to one implied odds meaning you're putting in some amount of money and you want to be able to win roughly 10 times that amount so if you put in two dollars and someone makes it ten dollars you're putting in eight more dollars to see the flops you need to be able to win at least eighty dollars more from your opponent to justify calling again these are rough numbers but it's easy enough to remember if you have a suited connector or suited Ace usually want to be getting something like 20 to 1 in

get stacked is you know when you both flop prepare your your ticker yeah Dan I the premium though should be some more information here in the coming week I would think Nate yeah training sites now it's so much easier now to get really good at poker than it was 10 years ago when I started I had a lot of access to you know I remember when Johnny backs opened their first site I'm gonna stop the recording right now just we're going a little long

3. Fourth street is the 8♥. Again you bet, and again you get called. 4. Fifth street is the 9♥. Should you bet? Answer: Now the answer is clearly no (except in rare cases as a possible bluff). From the way the hand has developed, there's a very large possibility that your opponent has been drawing to a straight or a flush, or both, and may now have hit his hand. If he has been drawing and he actually missed his hand, he'll fold your bet. If he hit, he will raise you. It's very unlikely that he will call and then show down a hand you can beat, so you must check. If he bets, you'll have to fold unless the pot odds are just too tempting. All-in on Fourth and Fifth Street Among good players, all-in moves are a rare occurrence until they start getting short-stacked. The reason is pretty simple. When you go all-in, you're putting your whole tournament life at risk. Good players don't like to do this. They're confident of their ability to keep outplaying their opponents and accumulating chips, so they see time as being on their side. A certain segment of newcomers and weak players, however, like shoving all their chips in the pot. These players see no-limit hold ’em as a game of big bluffs and big moves, and they're thrilled to catch a hand and bet all their chips. On the first day of a major tournament, a significant portion of the field will be playing this way, and when a bunch of these folks butt heads at the same table, watch out! Not only will several players get knocked out, but whoever survives the melee will have a really big stack. These phantom chip leaders, however, usually don't hold up well as the tournament goes on. 160 In the last 20 years, the opening-day chip leader at the World Series of Poker has never won the tournament!8 Compare the merits of an all-in bet to the merits of betting just the size of the pot. If you have a strong hand and your opponent has a weak hand, either play will chase him away and claim the pot. If you have a strong hand, and your opponent has a weaker hand, but one which he still wants to play, a pot-sized bet is more likely to win some extra money than an all-in move. And if you have a good hand, but your opponent has a well-concealed monster, a pot-sized bet will give you at least one more chance to reconsider before you lose all your chips. Having said all that, there are a few circumstances where I'll make an all-in play. Usually three conditions have to apply: 1. I'm a little short on chips, but not yet desperate. 2. I have a good, but not great hand, which still rates to be the best at the table right now. A typical example might be Q♠ T♦ in my hand, and a board of T♥ 9♣ 3♠ 2♠ (with no obvious flush

Pre-flop: With a hand likely to be in such good shape vs the opener's range and the added incentive of a Fish in the BB, calling this open is by far the best play. As we'll see in Chapter 10, a 3-bet here would not clearly be for value since Hero can't be sure that HJ continues with enough worse hands out of position. 3-betting also narrows the Fish's range considerably and Hero would love for this player to come along with his wide assortment of worse Ax and Qx and likely desire to never fold the weak top pair hands that those commonly flop. Flop: Another spot where folding is clearly out of the question. Hero's equity is huge and not of the ghost variety at all. He can get to showdown here pretty frequently on most board run outs. Should he raise though? There are two possible reasons that Hero could raise for here: value and protection, (clearly his raise would never be a bluff as villain is very unlikely to fold better). It turns out that raising for either reason is a severe blunder in EV .

time he does make hisflush he’ll win the 1,250 pot. His net profit, over five theoretical tries, is 250. It looks like you just gave him free money. It’s bad enough to give the right price to someone who would fold if you offered the wrong price. It’s even worse when you offer the right price tosomeone who would have called even for the wrong price. If you have an opponent who’ll call any bet with a flush draw, even a money-losing bet, why offer him a call that’s good math? That’s a disaster. And that’s why you bet at least half-pot instead. You put at least 500 into a pot that has 1,000 in it and send it back to your drawing opponent at a price of at best 1,500-to-500 or 3-to-1. In calling 500 to win 1,500, your opponent is nowmaking a bad mathematical decision with a flush draw. The four times he doesn’t complete his flush, he’ll lose 500 x 4, or 2,000. And the one time he complete his flush, he’ll win only 1,500. Now he’s giving you free money and life is good again. Therefore, by sizing your bet correctly, you hand your opponent a lousy choice. He can do the correct thing and fold (and you win) or he can do theincorrect thing and call (and you win). You might think it’s better to bet more, just to make sure your opponent either does the right thing or pays a bigger penalty for doing the wrong thing. While that’s true, up to a point, remember that any time you put more chips in the pot, you’re also putting more mathematical pressure onyourself; you have to be right more often. The more you put in the pot, the more you risk. If you bet 500 into a 1,000 pot, you can lose your bet twicefor every one time you win the pot and still break even. But if you bet 1,000 into a 1,000 pot, now you have to win as often as you lose in order tobreak even. So if you can bet less to get the same result (winning the pot or causing bad math), your profit will be greater in the long run.And it turns out that people who’d fold for a three-quarters-pot or pot-size bet are likely to fold for a half-pot bet as well. Either they know they’re not getting theright price or they’re just done with the hand. There are only two times when it’s appropriate to bet more than the pot. One is when the amount you’re thinking about betting is such a highpercentage of your stack that you’re pot-committed anyhow, so you might as well move all-in. The other has to do with decreasing the difficulty of your decision-making, which we’ll discuss in the fullness of time. For now, just set your sights on betting about half the pot (I usually land on 60%) and start adjusting upward if that half-pot bet doesn’t do the job you want it to do. Think in terms of betting the least you

position we aren't going to be able to get all in you know by the turn or maybe the river and therefore the player in position has a big advantage over us so rather than three betting and building up a pot that we're gonna play out of position where the player in position has a bigger advantage as the stacks get deeper it is actually correct to flat call more of your hands from the big blind and three bet fewer hands and it actually gets to the point where once you're three four five hundred big blinds deep many professionals consider it incorrect to three bet even a hand as strong as aces unless you know the game is playing so huge where people are opening for you know eight blinds on the button and you can three bet two like 40 blinds and they'll still call but if we're talking standard sizes you know to and after three and a half opens and three bets to you know seven and a half to ten big blinds because there's still so much play behind and your hand is becoming pretty clearly defined it's better to not three about those hands and put yourself in position and actually just flat to defend with majority of your range if not all of it and you're yeah you're playing a smaller pop but your hand is disguised and when you're that deep out of position it's very hard to stack your opponent anyway you're much more likely to get stacked and therefore better to keep the size of the pot small with hands even as strong as aces was what we were discussing there and that's something that I learned from the 2012 Main Event champion and Player of the Year Greg Merson who was a mentor of mine and also a good friend as we lived in an apartment together in Toronto in 2011 after meeting at the World Series of Poker the summer before you might say it was a match made in heaven that's applicable when it's deep stack when the body it's applicable when it's deep stacked because when the blinds are huge the stacks are actually shallow so it's not so much about what the blinds are it's about how deep the stacks are okay well done and well-spoken clear concise info Thank You Jay Regan okay last chance to get questions in people coming up on my bedtime so if there are no more questions I am ready to crash what's my favorite color well some people would say it's not a color it's a shade my favorite color is white the most rich color of them all it contains all of them it's the color of the Sun some might say it looks like it even though if you do and it looks orange but it's the color of the moon which is one of my favorite things in the universe and I've just always loved the color white I find it just such a soothing

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

= 1 (we’ve normalized the pot since s = bet/pot) Call% = c Win and lose% = q and (1-q) respectively. EV (value bet) = c(q(1+s) – s(1-q)) + (1-c) We can take this a step further and substitute q, but this isn’t required unless you want to solve this analytically. EV (value bet) = 1+s(c-2t) – t Step 4) Graph the expected value by bet size The easiest way to find the optimal bet size is to simply graph the expected value against the bet size and then pick the highest point on the graph! Play with the graph! I’ve created a simple calculator you can use to graph the EV as we plug in different values for the number of traps. Simply drag the t slider. Graphing this function shows that if villain has 10% traps, then our optimal bet size is 123% pot. Although realistically, anything between 100%-150% gives us close to the same EV. Now some of you may want an analytical solution. To solve that, you’d need to use calculus. More specifically, you’d want to find the argmax ‘s’ that maximizes EV (value bet). Calculus is beyond this video’s scope, and I think simply graphing the EV is much easier. But for completion: Watch the full video! The full video goes over many other toy games, including: Polar vs bluffcatcher Polar vs bluffcatcher with traps Bluffing with draws Multistreet polar game [0, 1] game Further reading Learning toy games can be fun while providing you a deep knowledge of game theory that can translate into better play. We’ve only skimmed the surface today. Check out these books to learn more about how to solve toy games: Expert Heads Up No Limit Hold’em, Volumes 1 & 2 by Will Tipton Play Optimal Poker, Volumes 1 & 2 by Andrew Brokos Modern Poker Theory by Michael Acevedo Mathematics of Poker by Chen & Ankenman 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 Tombos21 Tom is a long time poker theory enthusiast, GTO Wizard coach and YouTuber, and author of the Daily Dose of GTO. 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