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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 Success as the BB in limped pots begins before the flop. The BB’s equilibrium strategy… The Absurd Game Theory of Chopped Boards A “chopped board” in poker is one where the community cards make up the best… Playing Limped Pots as the SB in MTTs MTT confrontations between the small blind and big blind force no-limit players into uncomfortable situations,… The Art of Learning Poker In his book The Art of Learning, chess and Push Hands champion Josh Waitzkin describes… Is Donk Betting for Donkeys? “Donk betting”, or betting from out of position into the player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals
Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) 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 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 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…
Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet too often . The unexploitable, solver-approved strategy is already to bet their entire range. In other cases, it is close enough that simplifying to betting their entire range does not open them up to significant exploitability (though it does make it all the more important for the blinds to respond with appropriate aggression). However, the raiser is not supposed to bet even half their range on less favorable flops. If they bet too often in these spots, their opponent can exploit them in multiple ways, some more intuitive than others. In this article, we will conduct several experiments using the nodelocking feature to learn how to exploit over-aggressive continuation bettors . The Experiment These simulations are based on 30bb ChipEV preflop ranges in a single-raised pot between a BTN raiser and a BB caller . While the general principles of how to exploit an in position opponent who bets too often apply to other scenarios as well, these stack depths and positions bring the principles into a particularly clear focus. The BB, acting first, may check or bet 33%, 66%, or 100% pot. The BTN’s only continuation bet size is 33%, and we will experiment with what happens when we nodelock them to bet their entire range . The BB may respond to this bet by calling, folding, or raising 33%, 66%, or 100% pot. If they raise, BTN has the same options. Options on later streets are determined using the Automatic feature . The Low Connected Flop At equilibrium, donk betting is an important part of BB’s strategy on 6 ♥ 3 ♦ 2 ♣ . They have a lot of 6-x, which is strong enough to play a fairly big pot on the flop but will lose a lot of value on later streets, as the turn and river will almost certainly bring overcards. BB’s Donk Betting Strategy If BB checks, BTN bets 62.5% of their range, after which BB responds mostly by calling , raising just 11% of their range. So many of their best hands went into their donk betting range that they do not have enough value left to balance a wider check-raising range . BB donk bets to prevent BTN from checking behind the flop. If BTN is never going to do that, then BB prefers checking to induce bets. When we nodelock BTN to bet their entire range , BB has no incentive to donk bet. The main reason to bet a hand like J6 would be to prevent BTN from checking behind the flop. If BTN is never going to do that, then BB prefers checking to induce bets from the many weaker hands in BTN’s range. Then, they can raise all those top pair hands to get even more money into the pot and deny equity to BTN’s live overcards: Notice that BB’s primary exploit is raising more , not calling more. Calls do not really “punish” BTN for betting too often because
they will still get to realize the equity of their bluffs on the turn and perhaps the river as well. Nor are these raises pure bluffs. Indeed, BB still has a folding range, suggesting that raising any two cards is not necessarily profitable. Rather, it’s a value-heavy raising range centered around top pair (BB raises literally all their top pair), second pair with a good kicker, and bottom pair with a gutshot. These hands are not bluffs, but they still benefit from fold equity because they are so vulnerable to getting outdrawn. Raising top pair here is a bit like raising AK preflop: you probably have the best hand, but you’re still happy to get folds. You are so far ahead that the profitability of the raise does not depend upon your opponent’s response . If they fold often, you profit from denying equity to many hands with a 25% chance or so of drawing out on you. If they call often, they are putting in money from way behind. And if they raise often, your hand is strong enough to go to the felt. The one thing they can’t do is consistently have a hand better than yours. Check-raising top pair capitalizes on a mistake they already made —betting the flop too often—not on a mistake you’re hoping they’ll make in response to the raise. Raising top pair here is a bit like raising AK preflop: you probably have the best hand, but you’re still happy to get folds. That said, after betting this often, it would be easy for BTN to make a mistake in response to a BB raise. Specifically, it would be easy for them to over-fold because the GTO response for them entails some awfully ambitious and counterintuitive calls and raises: Is your typical opponent going to call a check-raise with K ♠ J ♠ ? Are they going to shove AJ o? If we introduce an additional nodelock to make BTN fold 50% of hands to this check-raise rather than 44%, then BB can profitably raise any two cards : To summarize the exploits against an opponent who continuation bets too much: Stop donk betting . Check-raise more aggressively for thin value and protection. If they will over-fold to your raise, which is easy to do once they’ve made the mistake of betting so many weak hands, then you can also check-raise bluff more . The Medium Coordinated Flop J75 r is another board where BTN ’s equilibrium strategy involves a lot of checking, with about 40% of their range. Unlike on 632 r, BB does not do any donk betting. When facing a 33% pot continuation bet, BB check-raises at a moderate frequency, with an emphasis on top pair with a good kicker. Although top pair is less vulnerable to overcards on this board than on 632 r, it is more vulnerable to straight-completing turns that may result in winning less, even if they do not cost them the pot. They fold the bottom 30% of their range. When we nodelock BTN to range-bet ,
BB folds a bit less, but as on 632 r, the major change is their raising frequency, which nearly triples. They raise all their top pair, plus a lot more backdoor straight and flush draws. They still mostly slowplay two pair, which wants BTN to turn top pair. As for those folds , they could easily become profitable bluff raises. GTO Wizard’s response to a 66% pot check-raise entails pure calling KQ o and bottom pair. Against human opponents who are less likely to find those calls, you should raise rather than fold your worst hands. High Card, Low Pair This effect is most pronounced on K44tt , where BTN ’s equilibrium continuation betting frequency is just 42.8%. Even so, BB responds with an aggressive strategy of small raises with more than a third of their range, including most of their trips and King-x. When we nodelock the BTN to bet their entire range , we once again see no donk betting from BB (they donk bet about 13% at equilibrium). We also see no calling . Almost all of the increase in BB’s raising frequency comes from hands that called at equilibrium, not hands that folded: Deeper Stacks For this final experiment, we keep the same betting options but change the effective stacks to 100bb . Will this make calling more appealing on the K44tt board if the weaker top pairs are no longer strong enough to play for stacks? Will it make larger raises more appealing, as BB will want to force bigger pots with their trips? Let’s find out. The unlocked solution with 100bb does not feature any larger raises, but it does include a small donk betting range of about 6% of hands, centered around 4-x: BTN bets 47.4% of their range after BB checks, a slight increase from 42.8% in the 30bb scenario. BB still prefers the small size when they raise, but as predicted, top pair (King-x) does a lot more calling now that stacking off is not so appealing (due to the higher SPR) . This supports a wide calling range that also includes some pocket pairs, high card hands, and backdoor hands: Most of those calls drop out when we nodelock BTN to range-bet , as does the donk betting. BB still uses the small raise size almost exclusively, but most of their calls have become raises : Hands like QT with a backdoor flush draw and A8 o have too much equity to fold on this flop. Raising is tempting because they benefit from denying equity even when they’re ahead, but it’s risky because these hands perform very poorly against BTN’s best hands. Once we expand BTN’s betting range, those best hands are a much smaller proportion of it. BTN’s equilibrium betting range already included most of their best hands, so those “extra” bets come almost entirely from weaker holdings. This shifts the incentive for hands like A8 and QT , which face little additional risk but stand to gain a much greater reward from raising into so many more weak hands. Conclusion
The main takeaway from this article is to fight fire with fire! Raising is the essential exploit against overly aggressive opponents . This is especially true on early streets and when you are out of position . Calling instead of raising enables them to realize the value of both their hand and their position on later streets, mitigating the magnitude of their mistake. Few hands you could hold are strong enough to take on that risk, and even when you do have such a hand, you are incentivized to raise so many other hands anyway that you should have no trouble getting action. Fight Fire With Fire! The best candidates for these “extra” raises are not your worst hands but rather the middle of your range , hands that might otherwise have called against a less aggressive opponent. Much like AK before the flop, these hands benefit from folds while still performing reasonably well against calls. Bluff raising could easily be profitable as well, but it requires your opponent to make the additional mistake of over-folding, which is easier to do after betting too many weak hands. Finally, it is important to understand the theory behind why donk betting is a mistake if your opponent will continuation bet too often because it gets at a more general point about exploitation. Few hands you could hold are strong enough to take on that risk, and even when you do have such a hand, you are incentivized to raise so many other hands anyway that you should have no trouble getting action. The best candidates for these “extra” raises are not your worst hands but rather the middle of your range , hands that might otherwise have called against a less aggressive opponent. Much like AK before the flop, these hands benefit from folds while still performing reasonably well against calls. Bluff raising could easily be profitable as well, but it requires your opponent to make the additional mistake of over-folding, which is easier to do after betting too many weak hands. Finally, it is important to understand the theory behind why donk betting is a mistake if your opponent will continuation bet too often because it gets at a more general point about exploitation. Fight Fire With Fire! If you expect your opponent will make a mistake at some future node in the game tree, you have extra incentive to adapt your play at earlier decision points to increase the likelihood your opponent will end up in the situation where they are likely to make the mistake you intend to exploit . GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Navigating Nasty Rivers Out of Position Playing out of position (OOP) is hard. It’s fundamentally disadvantageous
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no-limit players into uncomfortable situations,… The Art of Learning Poker In his book The Art of Learning, chess and Push Hands champion Josh Waitzkin describes… Is Donk Betting for Donkeys? “Donk betting”, or betting from out of position into the player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and
explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) 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 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 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…
Exploitative Dynamics GTO solutions are designed to be unexploitable , performing reasonably well no matter how your opponents play. They achieve this by assuming that when there is a best option with a given hand, your opponents will make that play. Thus, the GTO approach is to play in a way that minimizes the amount and profitability of good options available to your opponents. In other words, GTO solutions do not incorporate or rely upon any assumptions about mistakes your opponents will make . This makes them robust against any strategy, no matter how unpredictable, your opponents might throw at you. However, it also limits their ability to profit from any mistakes your opponents do make. To be clear, GTO strategies will profit from many common mistakes; they just won’t profit as much as an exploitable strategy designed to take maximum advantage of those mistakes. GTO strategies will profit from many common mistakes; they just won’t profit as much as an exploitable strategy designed to take maximum advantage of those mistakes. When you can predict specific mistakes your opponents will make, you should deviate from unexploitable play in order to take advantage of those mistakes. This is not a violation of GTO . It is the same thing a solver would do if you were to “teach” it about the mistakes you planned to exploit (which you can via nodelocking ). For more on the differences between GTO and exploitative approaches, see this piece . Mixed Strategies and Sensitivity Some parts of a GTO strategy are more sensitive to your opponents’ response than others . For example, raising AA on the BTN will certainly be the best play in a 100bb cash game, regardless of who’s in the blinds. Folding 72o in the same spot will also be the best play, absent some very big mistakes from the players in the blinds. But hands like A3o or T4 ♠ could go either way, depending on how the blinds react to your raise. How do we know this? Have a look at the chart below, which shows BTN’s opening range . The number in the lower right of each box is the EV of that hand if your opponents respond perfectly. Of course, with Aces the decision is not close, but this is true for many lesser hands as well. ATo and J8 ♠ are such profitable opens at equilibrium that they show a profit no matter how the blinds respond. Even if the blinds call or three-bet more than a solver would, these opens will still be profitable. They may even gain EV! Conversely, 72o is so far from being a profitable open that even if the blinds call or three-bet somewhat less than optimally, you are still unlikely to show a profit with it. For many hands, however, raising and folding have similar EVs at equilibrium, which means either option could be superior if your opponents do not respond perfectly. For any mixed strategy, the EV of all options in the mix must be identical. If they weren’t, the solver would
prefer one action over the other. This means even a slight deviation from your opponents could make one option more profitable. Even pure strategies can be quite sensitive, however. Notice the EV of opening T4 ♠ into blinds who will play perfectly is only -0.01 bb. If the blinds fold too often, or if they do not three-bet enough, allowing you to realize more equity than the solver expects, this could become a profitable open. Conversely, even T6 ♠ , which the solver shows as a pure open, could become unprofitable and therefore a pure fold against blinds who 3-bet too often. The closer the hand is to the thresholds, the more sensitive it is to the responses of the players behind you. The Four-Step Exploitative Process In my book, Play Optimal Poker , I recommend a four-step process for exploitative thinking: 1) Envision the Equilibrium Ask yourself, “How would this hand play out if my opponents and I were replaced by game theoretically optimal supercomputers?” You aren’t a game theoretically optimal supercomputer, so you won’t be able to answer this precisely, but you should consider factors like: Which player should be more inclined to bet? What kind of range should each player bet? Which are the best hands for each player to value bet? If I bet, what should my opponent’s raising range look like? What are the weakest hands with which my opponent ought to commit his entire stack? Once you have a sense of what your opponent’s equilibrium strategy ought to look like, it will be easier to envision how they are likely to deviate from it. Then, you can think about how to take advantage of those deviations. Once you have a sense of what your opponent’s equilibrium strategy ought to look like, it will be easier to envision how they are likely to deviate from it. If you’re new to game theory, this will probably be the hardest step in the entire process. The good news is that it’s not an all-or-nothing proposition: even if you get only the rough contours correct (“I should mostly check, and my opponent should mostly bet”) that’s still a big step up from not thinking about the equilibrium at all. With practice, experience, and study, you’ll get better and better at envisioning equilibria. 2) Make a Read Ask yourself, “ How is my opponent deviating from the equilibrium? ” Be explicit about this, and as specific as you can. “They’re calling too often with pure bluff-catchers on the river,” is more useful than “They’re too loose” or “They’re a fish.” It’s OK if all you have are hunches. It’s rare to have a surefire read, just as it’s rare to have a surefire winning hand. Poker is fundamentally a game about making decisions under conditions of uncertainty. Later in the process, we’ll account for your confidence in your read. 3) Identify the Exploits Once you identify a likely deviation from the equilibrium strategy, ask yourself, “ What can I do to exploit this mistake? ” Once again, you want to be
as precise and specific as possible. You also want to be creative, as there is often more than one potential exploit for a particular mistake. 4) Determine the Degree of Deviation Ask yourself, “ How far should I deviate from the equilibrium? “ Suppose your opponent doesn’t seem to bluff enough on the river, and you plan to exploit them by folding more often. The next step is to determine how much more often. Does this just mean folding when the decision would otherwise be close? Is it as extreme as folding the second nuts ? Or is it somewhere in between? There’s a strong situational component to this – it’s harder to find bluffs on some rivers than on others – but two factors you can consider in advance are the magnitude of your opponent’s mistake and the degree of confidence you have in your read. Remember that in order to exploit an opponent who seems to be deviating from his equilibrium strategy, you must deviate from your own equilibrium. This, in turn, raises the possibility that you will be exploited if you are wrong about your read. The larger your deviation from the equilibrium, the greater the penalty for being wrong, which is why larger deviations require stronger reads. Demonstration Let’s consider a simplified river scenario where the final board is 22223. The IP player has a range of 44-AA, while OOP has only the middling hands in that range, 77-JJ. There is $100 in the pot. IP may either bet $100 or check. If they bet, OOP may call or fold (even if they were allowed to bet or raise, they would never want to do so). IP’s equilibrium or GTO strategy is to bet anything JJ or better and to bluff with some combination of 44, 55, and 66 (it doesn’t matter which, as all are equally worthless) at a frequency that makes OOP indifferent to bluff-catching. The value bets are all pure strategies , which means betting is definitively better than checking. Even JJ, the thinnest value bet, makes $133.92 by betting as opposed to $98 from checking (it does not win quite the full pot by checking because it occasionally chops with OOP’s JJ). The bluffs are all mixed strategies, which means betting must have the same EV as checking, $0 in this case. OOP must reach a calling frequency of 50% to make IP indifferent to bluffing (very slightly less here because of the blocking effect from JJ). JJ is a profitable call because it blocks some of IP’s value bets, the rest are pure bluff-catchers and indifferent between calling and folding. Although both players have 50% equity, IP’s EV in this game is $67.70, well over half the $50 pot. This is true despite OOP playing as well as they possibly could. The opportunity to bet a polarized range is inherently valuable, no matter how your opponent responds . What do you expect to happen if we node lock OP’s strategy to call at a frequency of 52% rather than 50%? How will IP
change their strategy to exploit this slightly too loose calling strategy? Do you expect them to change not at all, to bluff slightly less, or to bluff dramatically less? You can see for yourself in the solution here. This very small increase in OP’s calling frequency caused IP to stop bluffing altogether! This is because all those mixed strategies were extremely sensitive to OP’s response. Notice that none of the pure strategies have changed. TT remains most profitable as a check, because this was not an especially close decision at equilibrium. If we turn OOP into a huge calling station who calls 100% of the time, that makes TT a value bet for IP, but 99 still plays best as a check. Even when you choose to exploit an opponent’s mistakes, it’s useful to start with an idea of the baseline or GTO strategy . Once you understand which parts of that strategy depend most on your opponent’s response, you can make more informed and profitable decisions about how to deviate and exploit that response. Adapting on Early Streets When you anticipate an opponent making a mistake at a future node, the value of reaching that node with hands that will profit from that mistake increases, and you may be incentivized to play differently on early streets in hopes of profiting from that mistake later. Suppose you had a read that a certain opponent called too often on the turn. Bluffing less on the turn would seem to be the obvious exploit, but what if they also folded too often on the river? In that case, you might actually be incentivized to bluff more often on the turn in anticipation of growing a pot you expect to steal later . Similarly, if your opponent who bluffs too often on the river, you should factor that into your turn (and earlier street) decisions. Mostly this will mean calling more turn bets, anticipating extra value from bluff-catching rivers. But if your hand is an especially poor candidate for calling rivers, you are likely better off folding it immediately on the turn, even if it’s a hand that would be a profitable GTO call. The GTO strategy for such a hand would anticipate more checking and showing down on the river than you expect from this opponent. These exploits can extend all the way back to pre-flop decisions. The more mistakes you anticipate an opponent making after the flop, the more incentive you have to get into pots with them in order to profit from those mistakes. There’s a big caveat here, though… Multiway Pots Before the flop, or any time there are multiple players with live hands, you are limited in your ability to exploit a specific opponent . Suppose you know, before the flop, that the player in the BB is a nit who will fold their blind too often to a small raise. If you are UTG at a nine-handed table, you might be able to open very slightly wider than you otherwise would, but you still can’t get too out of
line because of the seven other players who might call or three-bet you. If the action folded to you on the BTN, you’d have a lot more leeway to open more hands, as the BB is now the primary constraint on your opening range. Even so, you’d be somewhat constrained by the threat of three-bets from the SB, especially if they were a savvy player who expected you to open wider against a tight BB. A similar dynamic can occur after the flop. Suppose UTG opens, you call on the BTN, and the BB calls. UTG is an overly straightforward player who will reliably bet their strong hands and check their weak ones after the flop, but BB is a tough and savvy opponent whom you expect to be aware of UTG’s mistake and your likely adaptations to it. Should UTG check to you, you would want to bet somewhat more often than a GTO strategy would to take advantage of extra fold equity from UTG, but you should expect BB to call and check-raise you somewhat more often as well. As with the pre-flop example, both you and BB can adapt to exploit UTG’s mistake without becoming exploitable by one another . It is UTG who could exploit both of you, should they ever get wise and check some strong hands or check-raise some bluffs. That latter case can best be thought of as a blend of GTO and exploitative dynamics, where both you and the SB are claiming a larger share of the pot by adapting to the BB’s mistake while trying to remain balanced against one another. This will entail you opening somewhat wider than you otherwise would, the SB calling and three-betting somewhat wider, and you calling or four-betting those three-bets with somewhat weaker hands than you otherwise would. A new equilibrium emerges, with the BB’s mistake enabling both you and the SB to play more hands without becoming exploitable against one another . The player who could profit from your deviations would be the BB, if they were to wake up to what was going on and increase their own calling, three-betting, and four-betting frequencies. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Navigating Nasty Rivers Out of Position Playing out of position (OOP) is hard. It’s fundamentally disadvantageous to act on each street… Crack the Shell of Nut Draw Strategy Nut draws hold obvious appeal as betting and raising candidates. They benefit from fold equity,… 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
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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 Success as the BB in limped pots begins before the flop. The BB’s equilibrium strategy… The Absurd Game Theory of Chopped Boards A “chopped board” in poker is one where the community cards make up the best… Playing Limped Pots as the SB in MTTs MTT confrontations between the small blind and big blind force no-limit players into uncomfortable situations,… The Art of Learning Poker In his book The Art of Learning, chess and Push Hands champion Josh Waitzkin describes… Is Donk Betting for Donkeys? “Donk betting”, or betting from out of position into the player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go
in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) 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…
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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…
When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody asked me whether it was correct because it involved a very surprising range . Preflop Setup 75% of the field remains in this Progressive Knockout (PKO) Tournament Progressive Knockout Tournament (PKO) In poker, a PKO (Progressive Knockout) tournament is a tournament format where a portion of the buy-in goes toward a bounty on each player’s head. In PKO tournaments, when a player eliminates another player, they typically receive a cash prize for half of the eliminated player’s bounty. The remaining half of the bounty is added to their own head for other players to try to claim. When two or more players win, in a split pot, the bounty is divided equally across all winners. Note, some sites such as Pokerstars run PKO tournaments where ⅔ or even the full prize pool are dedicated to bounty prizes. . Action folds to the CO with 69bb and a $75 bounty. The BTN has 37bb, the SB has 13bb, and the BB has 21bb. All of these players behind the CO have $50 bounties. The CO opens with this range: So far, so good. But this BTN response is unusual: You are not looking at an error, nor have the color settings in GTO Wizard changed. The BTN continues 39% of the time, and when they do, they only call ; they never raise . I have never seen a pure flatting range like this before, but I have seen very similar ranges in PKOs before. Once you understand the format well, this range will make sense. The shape of the range looks like an opening range if BTN were first to act . It’s rare to see linear Linear A range construction that consists of the top-down strongest hands. A linear range might contain nutted to medium-strength hands, or value to thin value. flatting ranges like this in any format. It’s always helpful to compare PKO ranges to their nearest ChipEV equivalent. Here is the 35bb effective BTN response to a CO open : The continuing range’s overall shape is similar , but it is much wider in the PKO . The BTN continues with 27.6% of hands here compared to 39% of hands in the PKO, which is not a great surprise. There is a significant 3-betting range in the non-PKO solution, however. All the big overpairs are 3-bet to some degree, as does AK . The value hands are accompanied by an assortment of bluff hands, giving us board coverage. Pay Attention to Whom You Cover in PKOs The answer to why the BTN only calls reveals perhaps the most important strategic adjustment in PKO tournaments. As discussed in our article on Table Management in PKOs , knowing who you cover is the most critical consideration in Progressive Knockout Tournaments. How often you enter the pot and whether you open, raise, or call should be determined by how the players you cover may respond. This is all because of
the bounty. You should always be paying attention to whom you cover in PKOs. If you presently don’t cover many people , it can be correct to deviate from GTO and take on extra risk to cover more people in the future. If you do cover many people , as the chip leader for example, it can be correct to pass a slight edge to avoid losing your advantage. How often you enter the pot and whether you open, raise, or call should be determined by how the players you cover may respond. This is all because of the bounty and the potential to unlock it. As we have discussed before, when you win a bounty, you win 4 types of equity : The ICM equity from the ‘regular payout’ portion of the prize pool The immediately realized equity for winning the opponent’s bounty The potential future equity of winning more bounties because you cover more people at the table The potential future equity of winning your own bounty when you win the whole tournament Winning a bounty is so much more valuable than winning a big pot. Most of the time, winning the bounty is preferable to winning a pot several times larger with no bounty. Particularly in the early stages, before ICM is a significant factor in PKOs , the bounties are worth a lot. In terms of immediately realized equity, they are usually worth at least 25% of your buy-in. This is demonstrated by the Bubble Factor in PKOs, which usually starts at less than 1, something you never see in regular MTTs. With that in mind, why is the BTN flatting so much in this example? Adjust for the Bounties You Can Win The CO covers the BTN, so the BTN cannot win the CO’s $75 bounty this hand. The BTN does cover both the SB and the BB, however. The BTN can win both of these bounties, and they won’t even have to risk all their chips in the process. Preflop Setup It would be very nice to double up against the CO; that would put the BTN second in chips at the table. But there is still the chip leading LJ who covers them comfortably. The LJ should be playing very loose and aggressive at this table, making it tougher for whoever else has a big stack to win bounties. Instead of doubling up, the best outcome for the BTN would be to win one (or two) bounties! Suppose the BTN 3-bets in this spot, the SB and the BB would be incentivized to fold a lot. However, when the BTN flat-calls , the blinds are getting a better price to continue. Indeed, look at the SB ’s response to a BU flat-call: SB response vs CO open-raise and BU flat-call Against a BTN 3-bet , the SB would fold 86.9% of the time , compared to only 72.8% folding versus a flat. The SB only has 13bb, so calling a shove is easy for most hands in the BTN’s range when you factor in the
bounty, assuming everyone else folds. SB Squeezes All-in However, another crucial factor in this hand is that the BB covers the SB . The BB has the 2nd shortest stack at the table, so the SB is their only shot at a bounty right now. When the SB shoves , this is how the BB responds: BB response vs SB’s squeeze all-in (13bb) (vs CO and BU) This is a very wide range to call a squeeze Squeeze A preflop play whereby a player raises after one player has made an open-raise, and the second player has called that raise. The idea is to “squeeze” the caller out of the hand, thus increasing the dead money in the pot. , and it showcases what we discussed in our article on multiway strategy in PKOs . Ranges get wider, not tighter, in multiway pots in Progressive Knockout Tournaments . This is because of the bounties , especially when there is a shot at multiple bounties. Also, don’t forget that the CO and BTN ranges were wide to begin with. The BB’s range here—mostly suited high cards—plays very well against three opponents. Notice hands like A8 o and 22 fold, but all the suited high cards that can make straights, flushes, and good one pair hands go hunting for the bounty. When the BB shoves as well , the CO proceeds as follows: CO response vs SB all-in (13bb), BB all-in (21bb) They put the BTN all-in with most of their range, only folding the really weak hands that don’t play so well multiway and calling with a very small portion of their range (there are no pure calls either, every hand that calls also puts the BTN all-in at some frequency). When they do put the BTN all-in, this is how the BTN responds: BTN response vs SB all-in (13bb), BB all-in (21bb), CO all-in (37bb effective) The BTN calls 77.6% of their original flat-calling range. Notice that, once again, the shape of the range is geared towards hands that play well multiway against wide ranges, which is mostly suited broadway hands that can often hold up if they make one pair, but have outs if they run into a monster. If you are new to PKOs, this calling range might be hard to understand. This is one of the aspects of PKOs that make it quite a bonkers format. It is correct to set up situations where you find yourself calling off multiway for your tournament life with hands like Q9 s. PKOs are not for the faint-hearted. SB Overcalls Let’s rewind the hand two steps and see what happens when the SB overcalls instead of shoves . This is BB ‘s response: BB response vs SB’s overcall (of CO and BU) They continue with almost 100% of hands. Their raising range is almost identical to that in the last example. If this is what happens, BTN will have a very profitable situation. They now find themselves in a postflop spot with the positional advantage against four very wide ranges with two
bounties they can potentially win, and it would only take a bit more than a pot-sized bet to put them in play. SB Fold Even when SB folds , the BB continues this way: BB response vs CO open-raise and BU flat-call The BB continues almost as often, even though they cannot win a bounty. This is because the CO and BTN’s ranges are so wide that it becomes very profitable for them to continue, especially when they close the action. What happens when SB folds and BB shoves ? This is CO ’s strategy: CO response vs BB’s squeeze all-in (21bb) (vs CO and BU) The CO still continues fairly frequently, but much tighter now that there are only two—rather than three—bounties they can win. When CO shoves , the BTN responds like this: BU response vs CO all-in (37bb effective), BB all-in (21bb) Likewise, the BTN folds much more in this example. The prospect of risking their tournament life for only a single bounty as a reward has shifted them towards folding most of the time. When the CO calls instead of shoves, it is just a formality, the BTN shoves the exact same range, and then the CO calls. Conclusion The most important consideration in PKOs , particularly at the start, is how many players you cover . Always be aware in every hand how many players you can win a bounty from and how many could win one from you. Also, pay attention to where they are at the table. A player you cover seated next to you is worth a lot more than a player you cover four positions away. In this hand example , there was a perfect storm that led to the exclusively flatting range of the BTN. It was early in the MTT, so bounties were worth the most in terms of equity. The LJ with the chip lead had gotten out of the way, meaning the CO became the de facto chip leader. The CO with the next biggest stack was in a late position, so they could open a very wide range. Our Hero had the BTN, meaning they always have position postflop. They covered the blinds but not the CO. Just flatting increases the likelihood of the SB entering the pot and eventually putting their bounty into play. Three reasons to flat instead of raise. The SB was short stacked, so they had a natural squeezing stack when the BTN flats, and their bounty would be put immediately into play. Finally, the SB was the only bounty that the BB, who was also short, could win. Take out one or two of these variables out of the equation and the BTN probably does not flat their whole range. Multiway pots are very profitable in PKOs when you cover multiple players, even if you are covered yourself. The common response in online games is to see a lot of isolation raises from the covering players, trying to win a single bounty without any resistance. The big takeaway here is perhaps that passive
play can be preferable to aggressive play in PKOs when it can encourage opponents whom you cover and can win a bounty from to enter the pot behind you, not isolating to thin the field . 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 Barry Carter Barry Carter has been a poker writer for 16 years. He is the co-author of six poker books, including The Mental Game of Poker , Endgame Poker Strategy: The ICM Book , and GTO Poker Simplified . Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players,… C-Betting As the OOP Preflop Raiser Position is an extremely valuable advantage in poker. Most players would describe the comfort zone… Overchoice: Making Sense of Multiple Sizings Solver solutions with multiple bet sizes often involve a lot of mixing between those sizes,… River
Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing 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 on you, you will… When ICM Breaks Down If you have 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 Success as the BB in limped pots begins before the flop. The BB’s equilibrium strategy… The Absurd Game Theory of Chopped Boards A “chopped board” in poker is one where the community cards make up the best… Playing Limped Pots as the SB in MTTs MTT confrontations between the small blind and big blind force no-limit players into uncomfortable situations,… The Art of Learning Poker In his book The Art of Learning, chess and Push Hands champion Josh Waitzkin describes… Is Donk Betting for Donkeys? “Donk betting”, or betting from out of position into the player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is
how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) 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 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 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…
Combinatorics Poker Puzzle Today we have a special puzzle for you that will test your intuition as a poker player, and challenge your understanding of combinatorics. Six players go all-in preflop with a range of (QQ+, AK). Questions: Can QQ win the pot? If so, how? Can KK win the pot? If so, how? Would you rather hold QQ, KK, or AKo in this scenario? A spectator places a side bet. They win the side bet if any A/K/Q lands on the board postflop. What are the chances that they win? Please note that you do not need an equity calculator or any special software to answer these questions. Answers: Correct answer The trick to answering these questions is to ask yourself how it is possible that 6 different players ended up with (QQ+, AK). When you consider card removal, the possibilities become quite limited. There are only 12 cards in the deck that contain a Queen, King or an Ace. 6 players with two cards each will use up every king, queen, and ace in the deck. Now let’s ask how many ways can 6 players actually have these ranges. There are only 3 possibilities: Can QQ win the pot? If so, how? Yes, but only if it makes a straight flush! Two players are guaranteed to have QQ in all scenarios . All the aces and kings are in play, so winning with a regular flush is impossible. All queens are in play, making it impossible to outdraw better pairs. Can KK win the pot? If so, how? No, KK cannot win the pot . KK is always trying to outdraw AA. To do this, it must make a straight, a flush, or use a 3rd king. All the kings are in play, so it can’t use a 3rd king. All the queens are in play, so a straight is impossible. All the Aces are in play, so it can’t win with a flush. Therefore, KK cannot win the pot. Would you rather hold QQ, KK, or AKo in this scenario? QQ has substantially more equity than the other hands. Winning isn’t the only way to win the pot, you can also chop. ⅓ of the time QQ ends up in scenario 1, where you’re up against another QQ and 4 players with AK. This is very profitable for QQ since the AK block each other’s outs. The only way KK can chop is if all 6 players chop via a straight on board. AK is always up against 1 or 3 other AK’s. It can win with an ace-flush, and it can chop with a wheel straight. However, these events are far less likely to happen compared to QQ’s 1 in 3 chance of running into scenario 1. If we run a simple equity calculation, we see that QQ has substantially more equity than KK or AKo. However, this comes from the fact that QQ chops with the other QQ over 20% of the time. A spectator places a side bet. They win the side bet if any A/K/Q
lands on the board postflop. What are the chances that they win? The probability is exactly zero, since all the aces, kings, and queens must be held by the 6 players. 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 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… 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 on you, you will… When ICM Breaks Down If you
have 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 Success as the BB in limped pots begins before the flop. The BB’s equilibrium strategy… The Absurd Game Theory of Chopped Boards A “chopped board” in poker is one where the community cards make up the best… Playing Limped Pots as the SB in MTTs MTT confrontations between the small blind and big blind force no-limit players into uncomfortable situations,… The Art of Learning Poker In his book The Art of Learning, chess and Push Hands champion Josh Waitzkin describes… Is Donk Betting for Donkeys? “Donk betting”, or betting from out of position into the player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first introduction to the Independent Chip Model (ICM) is not from studying bubble… How does ICM impact PKO strategy? If you have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no
further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) 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 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 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…
Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy, we frequently rely on heuristics or “rules of thumb.” In this article, we will utilize GTO Wizard’s aggregate reports to create heuristics that aid our defense of the blinds in tournaments. Donk Betting Donk betting refers to a bet from an out-of-position player who was not the aggressor on the previous street . For example, a player in the BB who calls a raise from the BTN preflop then leads the flop is donk betting. So is a player who checks and calls a flop bet and then bets the turn. Had the flop checked through, an out-of-position player betting the turn would not be donk betting, because there was no aggressor on the previous street. Donk betting acquired its pejorative name long before the advent of solvers or the rigorous application of game theory to poker. Even in those dark days, smart poker players understood that it was generally correct to “check to the raiser”. Now, we can prove it with the help of GTO Wizard’s aggregate flop reports! Here’s a 40bb BN vs BB MTT scenario . The solver’s average donk betting frequency across all flops is 2%. Its donk betting is concentrated almost entirely on connected flops, where a straight is possible. Even there, it donk bets barely 7% of the time: By getting even more specific, we can see the donk betting occurs mostly on low connected flops (but not 432): This is not a fluke of stack sizes or position: the BB’s donk betting frequency is lower still against an early position raiser, and it remains minuscule at all stack sizes . A preflop raiser’s range is much stronger than a BB caller’s. The reason for this phenomenon is simple: a preflop raiser’s range is much stronger than a BB caller’s. The following chart displays the BB’s donk betting strategy across all flops, ranked by how much equity the BB has on each flop. The boards at the far left are the very best for the BB. Even there, BB barely clears 50% equity. Not coincidentally, most of BB’s donk betting occurs on these few flops where equities run close : On most flops, BB has less than 45% equity, and on the worst, they have barely 35%. When at such an equity disadvantage , they have little interest in putting more money into the pot than is necessary, so they do their part to keep the pot small by checking. Even on the rare occasion they do have a strong hand, they can count on the BTN having a lot of incentive to bet, at which point the BB can check-raise. The SB suffers from a similar dynamic. Though their calling range is stronger than the BB’s would be, they are still quite capped after calling preflop. Consequently, they, too, will be at an equity disadvantage on the flop and should mostly check to the raiser: By utilizing this aggregate data, we can
generate a simple heuristic: The Blinds should check to the aggressor on all but the most advantageous flops. Responding to a Continuation Bet as the Big Blind We can use GTO Wizard’s interface to examine how BB’s average response facing the 33% pot-sized bet . In this chart, each flop is grouped together by high card . We can observe BB defending less often on broadway flops in general that hit the aggressor’s range: Using this grouping method, we can also visualize the expected value of different flops: The BB’s response to a continuation bet depends at least as much on the size of the bet as it does on the board texture . Let’s examine how BTN’s sizing impacts our defense next. The chart below shows the BB’s average response to continuation bets of various sizes in the 40bb BTN v BB MTT scenario we’ve focused on so far. A few patterns emerge: The larger the BTN bets, the more BB folds . That may seem obvious – larger bets offer worse odds and make bluffing a riskier proposition for the BTN–but it contradicts the popular belief that big bets “look bluffy”. In fact, bigger bets should be more polar, consisting of more very strong and very weak hands and fewer thin value/protection bets. This brings us to the second key takeaway… The larger the BTN bets, the less BB raises . Raising is less effective against a more polar range. The strong hands are happy to continue, while the weak hands don’t lose much when they fold, and fewer hands in the middle will face tough decisions. The BTN’s smaller continuation bet ranges should contain more medium-strength hands, so BB raises them more often. The larger the BTN bets, the smaller BB raises . A small raise of a small bet offers extremely good pot odds. It also does little to grow the pot. When the BTN bets 20 into a pot of 100, a 33% pot raise would offer calling odds of 46:186, roughly 4:1. BB mostly prefers to raise larger in order to get more fold equity on their bluffs and more money into the pot with their value hands. As the BTN’s bet gets larger, a proportionately smaller raise offers similar odds, and larger raises are no longer required to get stacks in by the river . Responding to a Continuation Bet as the Small Blind The same patterns appear in the SB’s response to a BTN continuation bet, as shown in the following chart: The SB folds somewhat less often to similarly-sized bets because they don’t see the flop with nearly as many weak hands as the BB . The Big Blind’s preflop calling range is much wider than Small Blind’s because they get a better price and close the action. SB’s calling range tends to be more condensed , containing less trash compared to the BB. Therefore, the SB tends to continue more often facing a flop c-bet. The SB does not check-raise much more than the BB, however, which might come as a surprise
given their stronger range. This is largely because the BTN bets less often into a SB caller than into a BB caller . The BTN’s average continuation betting frequency (regardless of size) against a BB caller is roughly 75%, compared to roughly 50% against a SB caller. Essentially, the BTN compensates for SB’s stronger range (relative to a BB caller) by betting less often in the first place . Exploitative Responses In theory, arguments along the lines of “my SB calling range is strong so I get to check-raise more often” or “this is a good flop for me so I get to check-raise more often” are of limited utility because these range disparities ought to be built into the preflop raiser’s continuation betting strategy . That is, they should bet somewhat less often when the caller’s range is stronger. If you suspect someone is not doing this – if you suspect they are betting most or all of their range even when they do not enjoy a large range advantage – the best exploit is usually to raise them more often than a solver would suggest. If you suspect someone is betting most or all of their range even when they do not enjoy a large range advantage, the best exploit is usually to raise them more often. The best way to identify such opportunities is to study continuation betting strategy with an eye toward which boards/situations incentivize the preflop raiser to have a lower betting frequency. These are generally the best spots to increase your check-raising exploitatively against a player who bets too often. Donk betting is most valuable as an exploit against players who do not continuation bet enough (a less common type than those who bet too often). To capitalize on this exploit, look for spots where you would check-raise most aggressively at equilibrium. Against opponents who are less likely to give you the opportunity to check-raise, you have more incentive to take the initiative and bet yourself . Adapting to Earlier Positions The details of the above examples are specific to the positions and stack sizes investigated, but it is not difficult to extrapolate to other positions and stack sizes. Against an UTG raiser , BB’s response is remarkably similar to their response to a continuation bet from a BTN raiser. The following chart compares Big Blind’s defense frequencies facing BTN and UTG C-bets: Comparing Stack Depths When examining shorter-stacked play, there is another confounding variable to consider, which is the increased weakness of the BB’s calling range. With 20bb stacks , the BB shoves more of their strongest hands preflop and also calls with hands that were too weak to call with 40bb stacks, when the BTN’s raise was slightly larger and being out of position was a greater liability. Consequently, we see more folds and comparable raising frequency in response to smaller bets. Facing a larger continuation bet, the BB still folds more than at 40bb but also raises more often , since such bets constitute a much larger fraction of the effective stack. The
following table compares Big Blind’s defense frequencies at 40bb and 20bb effective stack depths: Conclusion After calling a raise from the blinds, you should almost always check to the preflop raiser, regardless of whether you are in the BB or the SB. The major exceptions are on very specific flops or as an exploit against players who do not bet often enough. When facing a bet, you should recognize you are at a significant range disadvantage. Unless the bet constitutes a large fraction of the effective stack, your choice is mostly between calling and folding, though you should raise somewhat more often against smaller continuation bets. But beware of the “Jedi mind trick” where you anchor the size of your raise as a multiple of your opponent’s bet . Against a very small bet, it is generally correct to raise a larger percentage of the pot to avoid offering extremely good odds. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping
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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 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…
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 I didn’t provide enough information to answer that question. Let’s say we’re 100bb deep in a single-raised MTT pot , and it’s early in the tournament, so we’re looking at ChipEV ranges. The CO has just continuation bet 33% pot with K ♠ T ♣ on the K ♥ 8 ♦ 5 ♦ flop, and the BTN holds 7 ♥ 6 ♥ . Who has the higher EV? Perhaps you deduced that I wouldn’t be asking this question unless the answer was 7 ♥ 6 ♥ . Despite being “just” a draw, it has an EV of 5.81bb, while K ♠ T ♣ has an EV of 5.36bb. This is not merely a function of position. K ♠ T ♣ has an almost identical EV (5.37bb) in BTN’s hands. In other words, even in the same position, facing the same bet, the draw performs better than the “made hand.” This is a function of stack depth because K ♠ T ♣ is, of course, the higher-equity hand, with about 63% equity in a mano-a-mano matchup. The equity-vs-range difference is even more dramatic. CO’s K ♠ T ♣ has about 75% equity vs BTN’s range, while 7 ♥ 6 ♥ has only about 40% equity vs CO’s betting range. If there were no more money to wager, you’d rather have the top pair . In our example, 7 ♥ 6 ♥ benefits from “visibility.” The player with 76 will more frequently know whether they have the best hand, enabling them to over-realize their equity by value betting or bluffing. The player with KT hates facing these bets, because they will generally not have visibility. That means they will have tough decisions on future streets. On blank turns, they will have to choose whether to risk betting into stronger hands, against which they are way behind, in order to deny equity and get value from the many weaker hands in the opponent’s range. When draws complete, they will often face big bets and are forced to make no-win decisions about whether to bluff catch or surrender the pot. Underscoring this point, KT ’s EV improves by more than 10%, from 5.36bb to 5.99bb, if we give them the T ♦ instead of the T ♣ . The diamond provides more than just a flush draw; it’s also a blocker that makes value betting and bluff catching more profitable on three-diamond boards. Even the T ♥ improves their EV to 5.42bb. What’s Your Kicker? What really improves the EV of top pair is having a stronger kicker. This image shows the EVs for CO, but BTN’s range follows a similar pattern: What really improves the EV of top pair is having a stronger kicker. What we see here is that KT does not perform much better than K9 , but after that, the improvements are dramatic, with KJ doing about 0.5bb better than KT
, KQ doing another 0.8bb better yet, and AK getting another 1.2bb on top of that! (Suits make a difference as well, as we saw before, but the general trend remains the same.) Top pair with a stronger kicker performs disproportionately better than the lower kickers. It’s not exactly headline news to observe that better hands are better, but this is not just a matter of having more equity. Top pair with a stronger kicker performs disproportionately better than the lower kickers. These hands both have more equity and realize that equity better : All these top pair hands will have similar difficulties vis-a-vis the draws in BTN’s range. On the flop, they do not gain terribly much from growing the pot against hands like 7 ♥ 6 ♥ . The difference for AK and KQ is that they will benefit from growing the pot against the King-x portion of BTN’s range, while their own weaker King-x is dominated by most of these hands. Hands like K9 and KT often win the pot, regardless of whether they bet or check, but are not likely to win more than that because they are not favored as the pot gets larger. The profit garnered by AK and KQ above and beyond their equity comes not primarily from the draws in BTN’s range but from the dominated pairs . That this board offers so many draws is a big part of why CO does not c-bet frequently, only about 30% of the time. Let’s see how our example hands, K ♠ T ♣ and 7 ♥ 6 ♥ , stack up on various turns after a 33% pot continuation bet from CO. For comparison, here’s a chart showing the relevant metrics on the flop: A Blank Turn ( 2♠ ) A modest made hand can be thought of as a draw to a blank turn. A modest made hand like KT can be thought of as, in part, a “draw” to a blank turn. Despite not improving in rank, KT gains a lot of EV when draws miss. Some of this EV gain is also attributable to the pot being larger than it was on the flop, but even as a percentage share of the pot, KT ’s EV is greater on the 2 ♠ turn than it was on the flop. However, it still does not over-realize its equity. The threat of putting money in from way behind remains significant, and it will face tough decisions on many rivers. Indeed, even checking and facing a 20% pot bet yields a slight decline in pot share. Against larger bets, KT fares much worse. Blank turns, of course, are bad for draws. They lose equity and EV but continue to dramatically over-realize equity because of their ability to bluff or value bet rivers. Indeed, 7 ♥ 6 ♥ retains much of its EV even when facing a 200% pot turn bet , whereas K ♠ T ♣ drops to 0 EV and becomes indifferent between calling and folding. A Flush Turn ( 2♦ ) A diamond
is bad for both of these hands, but it is worse for 7 ♥ 6 ♥ , which loses not only much of its equity but also its equity over-realization. Yes, it can bluff to represent the flush, but it no longer has any draws to the nuts. Two of its straight outs put four diamonds on the board, which is a disaster, but even on a 4 ♠ river, the risk of a flush reduces the opponent’s incentive to pay off with worse. KT , meanwhile, has good showdown value as long as the pot remains small. Its EV starts to drop off when facing bets or raises. A Heart Turn ( 2♥ ) For KT , the 2 ♥ is good for the same reasons as the 2 ♠ . It doesn’t improve many hands that weren’t already ahead, though the second draw on the board will lead to more tricky river situations. For 7 ♥ 6 ♥ , picking up a flush draw is, of course, better than not, but any turn that doesn’t make it a straight represents a net loss of pot share. That even one of the best non-straight turn cards results in a loss of pot share hints at just how much this hand depends on making a straight for its EV. On that note… The 6♠ Turning third pair is actually less good for 7 ♥ 6 ♥ than turning a flush draw. It’s a bump in equity, but the equity is extremely difficult to realize . When this hand does not river a straight, it will face value bets from many better hands as well as bluffs from most worst hands, which will bury its EV beneath a pile of no-win decisions. Straight equity is low but dramatically over-realized. Pair equity is higher but dramatically under-realized. The EQR of 80-90% is misleading, as this hand really has two different sources of equity. It has the straight equity, which is low but dramatically over-realized, and the pair equity, which is higher but dramatically under-realized. For KT , this is a fairly neutral card. It presents a few new threats in the form of straights and two pairs, but it also fades the most imminent threat of the flush draw. The 4♠ Turning the nuts is an excellent poker strategy, extremely good for one’s equity and equity realization. This is not a bad card for KT , either. Straights are a very small part of BTN’s range, which is why the reward for making one is so high . The 4 ♠ does not improve flush draws or make as many two pairs as the 6 ♠ , so it’s actually a pretty neutral turn for KT . Chasing and Implied Odds We’ll conclude by returning to the K ♥ 8 ♦ 5 ♦ 2 ♠ board. Suppose you were BTN facing a 200% pot continuation bet from CO. Which hand would you rather have: Q ♦ 7 ♦ or 7 ♥ 6 ♥ ? The Q7 has nine outs to a flush and 35%
equity, while the 76 has eight outs to a straight, two of which also make flushes possible, and just 23.4% equity. Once again, however, I wouldn’t ask if the answer was obvious. Q ♦ 7 ♦ actually has 0EV, making it indifferent between calling and folding, while 7 ♥ 6 ♥ has 4.38bb in EV. Q ♦ 7 ♦ faces the same problem as 7 ♥ 6 ♥ on diamond rivers: it’s a strong hand , but not the nuts . BTN has too many flush draws to call with all of them at this price. Such a strategy could be exploited by an opponent who simply check-folded diamond rivers, as BTN would not have enough bluffing candidates to balance all their flushes. BTN never folds Ace- or King-high flush draws to this bet, and they never fold combo draws. But Queen- and Jack-high flushes are indifferent. And T ♦ 7 ♦ is a pure fold even though it, too, has better equity than 7 ♥ 6 ♥ . As we saw on the 4 ♠ turn, 7 ♥ 6 ♥ realizes equity well precisely because the open-ended straight draw is a much smaller part of BTN’s range than flushes are on diamond rivers . This hand performs a function few others can, which is to make a monster on a relatively innocuous river card. It also provides bluffs on diamond rivers , when bluffing candidates are otherwise hard to find. These bluffs are not terribly profitable at equilibrium, earning roughly 1% of the pot, but they are +EV, which is not always the case with river bluffs. Conclusion Q ♦ 7 ♦ suffers from the same problem we’ve seen with K ♠ T ♣ throughout this article. Both make reasonably strong hands that will often win the pot when they “hit.” But they will struggle to put more money into the pot as a big favorite after getting there, and that matters in deep-stacked scenarios. With a lot of money still to be wagered, a hand’s value comes not primarily from its rank but from being “best in class.” On King-high flops, CO has many top pair hands, and the best ones earn disproportionately more than the worst. On diamond rivers, BTN has many flushes, and the best ones earn disproportionately more than the worst. Thus, in deep-stacked scenarios, draws to rare monsters can be worth more than draws to higher-ranked but more common monsters . They can even be worth more than so-called “made hands,” a distinction which should appear largely meaningless after digesting the analysis here. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit
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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 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 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…
Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players, particularly those that play large field MTTs, only rarely experience heads up play. This article will examine three common examples of how our opponents, in the Small Blind, may vary their preflop HU strategies in-game and how we, as the Big Blind, can take advantage of these variations . Over-folding Small Blinds Some players don’t play the bottom of the range they’re supposed to play when heads up. Using the AI Heads Up preflop solver , we can simulate this deviation and develop a counterstrategy for the Big Blind. Before we look at this specific example, let’s set the standard of SB’s optimal opening range when playing 50bb effective. Note that the ranges used in this article are based on a Chip EV game with a 0.12bb ante . SB range at 50bb with a 0.12bb ante Because of the relatively high Stack-to-Pot Ratio Stack-to-pot ratio (SPR) The effective stack divided by the size of the pot. SPR is commonly used to gauge the value of implied odds and the relative value of made hands. ( SPR ), we can see most hands open-raising at a high frequency with some limping included to balance the bottom of SB’s range. Overall, the SB only folds 4% of hands. Given this wide opening range, how does the BB respond? BB response to an open-limp BB response to an open-raise of 2.1bb The BB attacks the SB’s relatively weak limping range by raising 34% of their range, mainly balancing the bottom of their suited hands and low offsuit connectors with the strongest hands to maintain a balanced range postflop. Against a 2.1bb open , the BB will 3-bet a stronger range, mixing in weaker offsuit face card hands that block part of the SB’s 3-bet calling range. With this baseline in mind, what should the BB do if the SB deviates from this strategy? Let’s examine three potential SB deviations and BB exploits . As an example, let’s use nodelocking to double SB’s fold frequency from 4 to 8% and see how this affects BB’s strategy. SB range at 50bb folding 8% of range BB’s response to an open-limp against 8% folds (left) and 4% folds (right) One big adjustment is that BB uses a smaller raise size , 4bb instead of 6bb, because of the SB’s stronger limping range. However, we also see a big increase in the raising range from 34% to 48% of hands due to the smaller raise size. When we commit fewer chips with our raise, we can use a wider range as there’s less risk in raise-folding. BB’s response to an open-raise against 8% folds (left) and 4% folds (right) We can also see that BB’s response to raises has changed by 3-betting 0.7% more often to 7.4bb, rather than 8.4bb, while calling 2% less. This matches our adapted response to a limp strategy of using a smaller raise sizing more frequently. When our opponent over-folds their small
blind deep stacked, we begin raising and 3-betting to a smaller size more frequently. Small Blinds Who Raise Large In the previous examples, we saw the SB using a 2.5bb open size, but sometimes a player may prefer a larger open size. This could be due to a perceived skill disadvantage where they want to increase variance or simply a lack of experience in heads up play. To simulate this, let’s give them a larger 3.5bb open size instead and see what happens. SB range with a 3.5bb open size The biggest adjustment for the SB is to increase their limping range even further when their open size is increased. Because they are committing more chips, their opening range becomes much more polarized Polarized Describes a range that is mainly very strong made hands or bluffs, with very few middle strength hands. with a mix of weaker suited and offsuit face card hands. This leads to BB defending a tighter range due to playing a larger pot postflop. BB’s response to an open-raise of 2.1bb BB’s response to an open-raise of 3.5bb BB Equity Realization when SB opens 2.1bb BB Equity Realization when SB opens 3.5bb With a larger open size and lower potential equity realization Equity realization (EQr) The ability of a hand to “realize” it’s raw equity. Generally, equity realization has come to mean the translation of raw equity to expected value. A hand that wins more than it’s equity would suggest is said to “over-realize” its equity. A hand that wins less often than its equity suggests is said to “under-realize” its equity. Mathematically, equity realization is typically defined as EQr = Pot-share/Equity, where pot-share is the expected percentage of the pot a hand will win according to its expected value, and equity is the raw equity of a hand if checked to showdown. For example, a hand that wins (on average) 70% of the pot, which only has 40% raw equity, has an equity realization factor (EQr) of 0.7/0.4 = 175%. as shown in the graphics above, the SB forces the BB to play a stronger range to avoid committing chips with hands that can’t realize their equity well enough. The flip side is BB can now 3-bet more with their stronger hands , as well as Ace and King blockers to take advantage of the bloated pot. If you look carefully, another hint of the tendency to be more aggressive can also be noticed by the slight increase in shoving frequency from marginal hands such as AJo and 98s to fold out some stronger hands while locking up their equity. When the SB increases their open size, the best adjustment for BB’s range is to fold more often while 3-betting less frequently. Small Blinds Who Raise Too Often Finally, let’s look at opponents who raise with an even wider range than the equilibrium strategy suggests. Some players may choose to open-raise even their worst playable hands, either to balance their full range or to take advantage of an opponent they expect to fold their big blind too
often. In this example, we’ll expand SB’s open range from 64 to 72% and see how BB responds. SB’s range when open-raising 72% of hands (left) instead of 64% (right) When increasing their opening range, SB prefers to do so by increasing the frequencies of mixing hands because the pure limping hands don’t gain anything from adding opens. It is important to note here that the SB is no longer limping any of their ‘Best’ hands (and limping less with their ‘Good’ hands). BB’s response to a limp when SB open-raises 72% of their range (left) and 64% (right) Similar to our over-folding example, BB adjusts to a SB limp with a wider raising range while reducing their raise sizing . In this case, SB has capped their limping range even further by removing all strong hands from their limping range, incentivizing BB to raise more aggressively. BB’s response to a raise when SB open-raises 72% of their range (left) and 64% (right) Again, we see a parallel with our first example, where the BB strategy remains unchanged when the SB opens an 8% wider range . Because the SB is just adjusting frequencies of hands that were already in the range, instead of adding new hands to their opening range, BB is still calling and 3-betting a nearly identical range. When our opponent begins open-raising more often, we should respond by raising their (weaker) limps more often, using a smaller raise size. Conclusion For tournament players that enter larger field games regularly, heads up can be a situation where strategies deviate from a GTO approach. While many players are experienced with the early through late stages of a standard MTT, few players have significant heads up experience. Because of this, we can find many players making exploitable plays heads up, such as the ones shown in this article. Below is a summary of the three examples we looked at: When SB folds or opens too frequently , we should adjust by raising more regularly over their limps with a smaller raise size . If the SB uses a larger open size , we should adjust by folding more often and 3-betting a stronger range . What are some plays that you have seen heads up that seemed out of the ordinary? Let us know in the comments for further analysis in future articles. 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 JonnyLaw John Lawford AKA “JonnyLaw” is a midstakes online MTT regular with a passion for the Progressive Knockout format. 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 &
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The Absurd Game Theory of Chopped Boards illustration A “chopped board” in poker is one where the community cards make up the best 5-card hand for the majority of hands in both players’ ranges. This is often called “playing the board”. Chopped boards lead to fascinating, often counterintuitive strategies. In this article, we’ll dive into the absurd mathematics of chopped boards. Before we get started, watch this video by Qing Yang to learn more about the theory of “Playing the board”. Case 1) Everything Chops The most obvious example of chopped boards is something like AKQJT rainbow, or AAAAK . The strongest hand either player can make is already on the board. So any strategy that doesn’t involve folding should be good. However, what happens if this is a cash game and rake is involved? 100bb SB vs BB single-raised pot. They arrive at the river with 12bb in the pot and 94bb effective behind. The board is A♠ K♥ Q♦ J♣ T♠. Every hand is a straight, and every hand chops. What is SB’s best strategy if this was a NL50 cash game? What is their best strategy if this was a NL500 cash game? NL50 Rake Structure: 5% rake, 4bb cap NL500 Rake Structure: 5% rake, 0.6bb cap In the NL50 example , any bet we make will be called, causing both players to pay more rake. Therefore, the best strategy is to check-range and try to showdown without donating more money to the house. However, in the NL500 example , we’ve already reached the rake cap (0.6bb cap / 5% = 12bb maximum raked pot) . Therefore, we don’t pay any additional penalty if we bet. Furthermore, betting allows BB to make a mistake (folding), so betting weakly dominates checking. For this reason, the SB shoves their entire range ! The Prisoner’s Dilemma Okay, but what happens if we pay a lot more rake or if the bet is much larger? Is it possible to leverage the rake against your opponent to force them to fold? Surprisingly, the answer is yes! Daily Dose #305 explores a peculiar variation of this toy game. What if the NL50 scenario above was a limped pot that checked to the river ? The optimal strategy, surprisingly, is to shove 99bb into a pot of 2bb, a 4950% pot-sized shove. This shove forces BB to fold everything. If BB calls, they win half the pot (1bb), but they pay 2bb in rake. Therefore the highest EV decision is to forfeit the pot! The first player to shove should win the pot. Hilariously, BB’s best strategy in a real game would be to shove out-of-turn order before SB has a chance to act! But let’s assume you’re playing online and can’t do that. Is folding the best strategy facing this shove? The BB can “spite call”, forcing both players to pay 2bb in rake. This is where the prisoner’s dilemma comes in. Is it correct for BB to spite-call sometimes in order to deter SB from bullying them? The following payoff table shows the expected
value for all strategy pairs . Note that any strategy which involves both players getting stacks in results in a negative payoff due to rake. Ideally, both players check down the pot. However, one can try to force the other to fold to gain an advantage. This is the definition of a prisoner’s dilemma , except in this scenario, the IP player knows the opposing player’s move. In 1981 Robert Axelrod hosted a tournament to find the best strategy in a game of Repeated Prisoner’s Dilemma. As it turns out, a simple strategy called “Tit For Tat” was the strongest. This strategy would start by cooperating, then retaliate if the opponent betrayed them. It was quick to retaliate, but also quick to forgive. However, this strategy is designed for the repeated game. In poker, this chopped spot occurs so rarely that the short human memory overshadows the point of “Spite Calling” or setting up retaliatory threats. Case 2) Only some hands chop Case 2 is the far more interesting version of this game. In this scenario, some hands chop, but others beat those chops. For example, an AKQJT board where flushes are possible. Let’s start with a simple toy game. There are three hand classes: Traps, Value Hands, and Chops. Villain’s checks a range of chops, and a few nutted traps. Hero has value hands that also beat chops, but lose to traps. Traps > Value > Chops In the original version of this toy game , hero needs to find the optimal bet size in order to extract maximum value from bluff-catchers, without donating too much to villain’s traps. However in this game, there are no bluffs or bluff-catchers. All chops split the pot with each other. This dynamic changes everything. Bluffing Frequency In a “typical” polarized vs. bluff-catcher toy game, the amount of bluffs you need to remain balanced is determined by the pot odds laid. If you over-bluff, then villain can gain EV by always calling you, whereas under-bluffing can be exploited by them folding all their bluff-catchers. Goal – Make villain’s chops indifferent between calling and folding. On a chopped board, your goal is the same, to make them indifferent between calling and folding. However, the reward of calling is much smaller in this case. When they call correctly, they only win half the pot (compared to the entire pot plus your bet in a typical bluff-catching scenario). This means the reward for calling is fixed, but the risk of calling still scales with the size of the bet. The following chart shows how often you should bluff on chopped boards compared to typical polarized scenarios. Note that the bluffing frequency skyrockets compared to traditional polarized spots. In a traditional polarized scenario, your bluffs per value bet are equal to the alpha equation, s / (s+1), where ‘s’ is the bet/pot.On a chopped board, your bluffs per value bet equals 2s, twice the size of the bet. The main takeaway here is that you should be bluffing far more often on chopped boards with value compared to polarized
spots. Calling Frequency How often should villain call the bet? This is a surprisingly complicated question. Well, we know that if we bet too big then villain will fold everything but their traps. But smaller sizes are harder to calculate. To solve this, we first need to ask what equations like MDF and Alpha are trying to calculate. The defending player’s goal is to make our chops indifferent between bluffing and checking behind . Goal – Make Hero’s chops indifferent between bluffing and checking. To do this, we set the expected value of each action equal to each other, then solve for the calling frequency. EV (Check Chop) = EV (Bluff Chop) The following explains how to derive defending frequencies on chopped boards: The EV of checking behind with a chop is a function of how many traps villain has. EV (Check Chop) = (1 – traps%) * pot / 2 The EV of bluffing a Chop is more complicated. The expected value is a function of how much equity we have when called and how often villain folds, both of which are dependent on our bet size. Let’s start by writing the formula with words. EV (Bluff Chop) = (Fold% × pot) + Call% {(How often we get called by chop × 0.5 pot) – (How often we get called by trap × bet size)} Defining variables: Call% = c Fold% = 1 – c Traps% in villain’s range = t Bet / Pot = s Traps% in calling range = t/c Non-traps% in calling range = 1-t/c Plug in variables and reduce: EV (Bluff Chop) = (1 – c) + c ( (1 – t/c) / 2 – st/c) Set EV (Check Chop) equal to EV (Bluff Chop) and solve for c: (1-t)/2 = 1-c + c((1-t/c)/2 – st/c) c = 1 – 2st Villain will never fold a trap no matter how large we bet, so the actual MDF formula becomes: Call% = Max (t, 1 – 2st) Unlike the curved MDF line we see in a “typical” polarized vs bluff-catcher toy game, on chopped boards, MDF is a linear line that slopes downwards relative to the number of traps in range. If you bet large enough, they don’t need to defend anything but traps, causing their defense frequency to flatten out and remain constant. EV Curves by Bet Size These expected value graphs show hero’s total expected value, as a percentage of the pot, according to their bet size. For simplicity, we’re assuming villain can only call or fold. In a typical polarized vs. bluff-catcher toy game, the highest EV bet size is a function of how many traps villain has . We’ve covered this in the How to solve toy games article . In a scenario with no traps, hero’s optimal river strategy is to shove (or bet geometrically on earlier streets, in order to shove on the river). If villain has traps, hero should bet smaller in order to avoid making the defending range too strong. The following charts assume hero starts with 50% value hands
and 50% bluffs (then bluffs or gives up optimally depending on sizing). In our chopped toy game scenario, things change. The expected value of betting hits an “ inflection point ” where hero runs out of bluffs. From that point on, betting larger only serves to decrease the EV of your value bets. Hero should have X% bluffs for every value bet , where X is equal to twice the size of the bet. For example, when putting in a 150% pot-sized bets, hero should bluff 3 chops for every 1 value bet, in order to make villain indifferent to calling their “chop-catchers. The following graph shows hero’s EV by bet size. Here we assume hero starts with 25% value hands, and 75% chops. At s = 150% we run out of bluffs, so that sets the theoretical maximum bet size. However, if villain has at least half as many traps as we have value bets, then the optimal bet size can become smaller, as is shown by the red line below where the villain has 20% traps in range. Conclusion The toy game above is relatively simple. The player with traps is pacified, and none of the hands block each other. In a real game there are far more variables involved. Players can raise and re-raise. Sometimes the only nutted hands you could have would block your opponent from having those hands. However, we can still learn several key takeaways from this chopped board toy game: Bluff more often on boards where a large portion of your range chops. You will often run out of bluffs and should therefore range-bet these boards. Typically that means you should also call wider on these boards. How wide you should defend overall is a function of how many traps you have. Pay attention to the rake structure. If you can’t make them fold, then it may not be worth unnecessarily increasing the pot and paying more rake. 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 Navigating Nasty Rivers Out of Position Playing out of position (OOP) is hard. It’s fundamentally disadvantageous to act on each street… Crack the Shell of Nut Draw Strategy Nut draws hold obvious appeal as betting and raising candidates. They benefit from fold equity,… 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
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C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to continuation bet most flops at a high frequency, usually for a small size, without fear of exploitation. There are exceptions, however. In some scenarios, the preflop raiser’s equilibrium strategy involves checking more than half their range on the flop. This is the case even on some flops where they have significantly more equity than the BB. Such scenarios occur more commonly when the preflop raiser is in late position and when stacks are shallow . These are spots where the BB can easily flop hands strong enough to check-raise and play for stacks. This enables them to have more check-raise bluffs and semi-bluffs resulting in an overall more aggressive check-raising strategy , which incentivizes the raiser to check many medium-strength hands that would face tough decisions when raised. This drives the raiser to construct their continuation betting range in a more polar fashion, which often results in the usage of larger sizes. But what if the BB does not take advantage of this opportunity? What if they do not raise as aggressively as a solver would? Is the raiser then incentivized to bet at a higher frequency? Or for a larger size? Or both? With the help of the nodelocking feature , we can investigate these scenarios in depth to better understand how to exploit opponents who do not check-raise aggressively , even on favorable boards. The Experiment For this experiment, we will investigate three flop textures on which the BB can often check-raise aggressively. Our example flops will be: 6 ♥ 3 ♦ 2 ♣ , a low card board where the BB is more likely to flop straights and two pairs. J ♥ 7 ♦ 5 ♣ , a medium, coordinated board where the BB’s range interacts more heavily via pairs and draws. K ♥ 4 ♥ 4 ♦ , a paired board where the BB has a trips advantage. These simulations use an MTT Chip EV model with 30bb stacks . They assume a single-raised pot between a BTN raiser and a BB caller . In addition to the board texture, the late position of the preflop raiser and the shallower stacks incentivize a lower continuation betting frequency at equilibrium. As always, with experiments like these , the goal is not to master these specific spots but rather to better understand the relationship between continuation betting and BB aggression . The principles derived from this experiment will apply in many other scenarios, regardless of stack depth or position. They will be relevant in cash games and even in other games besides hold ‘em! You can see from this Flop Report that, despite their late position and the shallow stacks, BTN continuation bets more than 75% of the time on average in this scenario, but when lower cards flop, they can end up doing a good bit of checking: In this experiment, the raiser will have three continuation betting options: 33%, 67%, or 100% of the pot. BB will
be allowed to respond with a fold, a call, or a 33% pot raise— regardless of the opponent’s c-bet size. After taking note of the raising frequency against each bet, we will nodelock BB to raise at roughly half those frequencies to see how that changes BTN’s continuation betting strategy. All other betting and raising options are determined by the Automatic bet sizing feature , with one important exception: we will force the BB to check to the raiser on the flop . Boards where the raiser has the least incentive to bet are the ones where BB has the most incentive to donk bet. But the forced check is important for our nodelocking experiment. It serves to prevent the BB from compensating for the reduced check-raising frequency by donk betting more often instead, which would confound our results. Forcing the check is also consistent with the assumption that BB is too passive . A real life human opponent who does not check-raise enough will probably also not make aggressive use of the donk betting option. We should expect that, when the BB is not allowed to donk bet, BTN will have an even lower continuation betting frequency than they otherwise would. To reiterate, these experiments may not be perfect examples of how you should play these spots. What they will demonstrate are some general principles about how to exploit overly passive blinds . The Low Connected Flop Here is BTN’s equilibrium continuation betting strategy on 6 ♥ 3 ♦ 2 ♣ when BB is forced to check: They bet infrequently and mostly for a large size in this spot. This is because much of their range consists of unpaired overcards , hands that have significant equity and could even be ahead but would struggle to continue to a raise. In the rare case that they have strong hands, they are generally overpairs, which are vulnerable to losing their value on later streets and therefore prefer to get in a lot of money immediately. The threat of a check-raise compels BTN to check behind with many medium-strength hands that would love to deny equity to BB but are in danger of having their own equity denied. How do you expect this to change when we force BB to cut their check-raising in half? Try to make a few predictions of your own before you read on to the results. When we nodelock the BB to raise half as often against all continuation bet sizes, BTN bets much more often . MUCH more: They also use a smaller bet size, on average . The pot-sized bets are gone entirely, with 67% pot now being by far their most frequent bet and also an increase in the use of the 33% pot bet. To get a better sense of what’s going on here, we can examine the Equity Distribution graph : There are three important things to recognize here: BTN has the overall equity advantage , roughly 52% to BB’s 48%. On balance, their hands are stronger than BB’s, which is why they can
bet so often. BB has the nuts advantage . Although their range is equal overall, BB is more likely to flop the very best hands like straights and two pairs. There are no worthless hands . Both players’ very worst hands retain around 25% equity. At worst, they will have either two overcards to the board or one overcard plus a gutshot. This last point is what makes continuation betting so valuable. BTN profits from betting so often because even if BB folds only their very worst hands, they are still giving up a quarter of the pot when they do so. And if BB calls, even BTN’s very worst hands have a fair chance of improving. Even if BB folds only their very worst hands to a continuation bet, they are still giving up a quarter of the pot. This is also what makes betting dangerous for BTN. They have many hands that benefit tremendously from folds and are in fine shape when called but will struggle to continue to a check-raise. If BB turns their aggression back on them , then they are the ones in danger of being denied equity . At equilibrium, BB can leverage their nuts advantage to check-raise at a higher frequency than their equity alone would permit. Even hands as strong as overpairs are in a rough spot if BB check-raises and then continues to barrel turns and rivers. So, the threat of a check-raise compels BTN to check behind with many medium-strength hands that would love to deny equity to BB but are in danger of having their own equity denied. Once BTN is assured they will not get check-raised too often, they can run wild. The Medium Coordinated Flop Now, let’s see how this experiment plays out on a different sort of flop. Here’s the Equity Distribution Equity Distribution A line graph or scatter plot of a player’s hand vs range equity, sorted from weakest to strongest, such that the equity of every individual combination in the range is represented. Commonly used in game theory analysis. graph for J ♥ 7 ♦ 5 ♣ . What do you notice? How does it differ from 632 r? What do you expect the implications of that will be for continuation betting and check-raising strategy? To begin with, BTN has a larger equity advantage on this flop, 54.6% to BB’s 45.4%. They also have the nuts advantage as the only player with JJ , the literal nuts, and overpairs, which are very close to the nuts on this board (though that could easily change on the turn). BB flops a lot of strong hands as well, but their only advantage lies in the middle, where they are a bit more likely than a BTN raiser to pair the 7 or the 5 . They are also more likely to whiff entirely , and when they do, their worst hands have less equity than they did on 632 r. BTN leverages their nuts advantage to use mostly the 100% pot bet, which makes even BB’s middle of
range like second and third pair hands uncomfortable. They also get some use out of the 33% pot bet by denying equity to those hands at the bottom of BB’s range . What they don’t do is bet the medium size, which would play to the one part of the distribution where BB has the advantage: Despite their nuts advantage, BTN can’t bet too often because BB still has plenty of nutty hands. Any Jack is good enough to check-raise and stack off with on this flop, and just like on 632 r, BTN’s worst hands still have at least 25% equity they do not want to be denied. Indeed, BB check-raises quite aggressively against the small continuation bet—more than 23% of the time. Against 67% pot, they check-raise 13% (the solver generates an unexploitable response to this bet even though it doesn’t recommend BTN make it), and against full pot, they check-raise nearly 9%. (Remember that this experiment forces BB to check to the raiser. A simulation without this restriction would result in more continuation betting and less check-raising, as some of BB’s check-raise candidates would go into a donk betting range instead. BTN avoids the middle of the equity distribution, where BB has the advantage. When we force BB to check-raise half as often , the 33% pot continuation bet becomes much more appealing: BTN still wants to avoid the middle of the equity distribution, where BB has the advantage. But they can now bet small with impunity, and a good 90% of their range will be happy to deny equity to the BB. Only their very best hands, AA and better, are invulnerable enough that they don’t gain much from denying equity with a small bet. Once they don’t have to worry about getting their own equity denied too often, they can take advantage of the opportunity to bluff and protection bet cheaply . They still want to mostly bet big with their strong-but-vulnerable hands like AJ , QQ , and KK . These hands would actually prefer BB to check-raise more often because their objective is to shovel money in as quickly as possible before the board turns ugly. High Card, Low Pair The K ♥ 4 ♥ 4 ♦ flop offers an even more pronounced example than 632 r of the dynamic where BTN enjoys an equity advantage (58.6% in this case), but BB has the nuts advantage. BB has a significant edge in the 4-x department but also has nearly as much King-x as BTN. Their kicker is less good, on average, but at this stack depth, that’s not terribly important. Any King-x is a strong hand. This results in BTN betting both rarely and for a small size: BTN’s dilemma is that they very often have the best hand, even when their hand is not great. They would like to bet for thin value and protection but are vulnerable to raises. When BTN does not have a King , the risk of betting into one is significant, both because BB has a lot of them
and because, when BB does have one, they are hard to outdraw Outdraw To hit a player’s outs and thus improve to a stronger hand than their opponent. . Even worse, betting opens up a significant risk of getting check-raised off their outs or even the best hand. When BTN does have a King , the value of betting is minimal unless the kicker is good ( AK is BTN’s only pure bet). Weaker King-x is not necessarily looking to play a big pot anyway, nor does it gain much from BB’s folds, most of which would have little or no chance of drawing out. Even with BTN showing so much restraint, BB check-raises quite aggressively, with more than 30% of their range. Against the larger bets, they would still check-raise 15-20% of hands. When we nodelock to reduce these raising frequencies by half , we see a familiar pattern. BTN now bets their entire range : They still prefer the small size since they don’t have the advantage at the top end. Even when getting favorable pot odds of 4:1, BB will struggle to continue because they have many hands without coordination with the board. Their ideal solution to this problem would be to raise, but since we disallowed that option, they must either call or fold, and that’s a win-win for BTN when they have hands like A8 o or 77 , hands that would fear a check-raise from a more aggressive player. Essentially, BTN’s dilemma is that they very often have the best hand, even when their hand is not great. They would like to bet those hands for thin value and protection , but betting anywhere near all of them would make them vulnerable to raises . Once they don’t have to worry so much about those raises, they can take the easy range-bet and deny significant equity to BB. Conclusion The preflop raiser enjoys an equity advantage relative to a BB caller on virtually all flops. They would like to leverage that advantage by betting aggressively and denying equity to the many weak hands in BB’s range. On flops where they also enjoy a nuts advantage, they can do just that. But when BB has enough strong hands to check-raise aggressively, the raiser must show more restraint. This risk is most pronounced when they open from late position and/or the stacks are shallow, both enable BB to include thinner hands in their value-raising range and thus to bluff more as well. That’s how it is against tough opponents, anyway. If you suspect the BB will not check-raise so aggressively , then you can proceed as you would on more favorable flops, betting at a high frequency. These bets should generally be small, but larger bets might be called for on boards where it’s easier for BB to flop modest equity. When we talk about the BB check-raising aggressively, we’re mostly concerned with check-raise bluffs or perhaps thin value raises, if that will lead to you folding significant live equity after betting. Getting check-raised by very strong hands
is not really a problem because you will simply fold and lose a pot you were going to lose anyway. Lighter check-raises are how the BB punishes you for continuation betting too often . If your opponent rarely makes such raises—a trait especially common to many live recreational players especially—then you can and should exploit them by betting more aggressively yourself. The first and most important exploit is simply to bet much more often . Getting the solver-approved sizing right is a very secondary concern. Betting small with your entire range is a good first approximation that will capture most of the value of this exploit for you, so don’t worry if you aren’t confident about when to bet larger. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny
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Navigating Nasty Rivers Out of Position Theory Playing out of position (OOP) is hard. It’s fundamentally disadvantageous to act on each street without knowing… 26/03/2024 14 min. / 20 sec.
Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which player has the stronger or nuttier range and the distribution of equity across each player’s range. Whether a player has mostly medium-strength hands or a more polarized mix of very strong and very weak hands has huge implications for their preferred betting frequency and size. These graphs display that information clearly and concisely. On these graphs, the x-axis plots each player’s range from their lowest-equity hand, on the far left, to their highest-equity hand, on the far right. The y-axis plots the equity of each hand. The lines on these graphs always slope from the bottom left to the upper right. The things to pay attention to are: which player’s line is above the other’s at various points on the x-axis and by how much . Check out this article to learn more about equity distribution graphs 📉 A Polarized Range vs a Condensed Range Take a look at the graph below, where the 🔵 blue line represents BB’s equity distribution and the 🟢 green line BTN’s equity distribution. Which of these players has the more polarized range? How can you tell? What do you expect each player’s betting strategy to look like on this street? (I am deliberately not giving you the action that led to this distribution so you can practice deriving optimal strategy from the graph rather than from familiar patterns of previous action.) BTN has the more polarized range here . Notice their green line is consistently well above or well below BB’s blue line, intersecting it only briefly in the middle, where the line slopes steeply upward. That means BTN’s hands are mostly very bad, with 0-15% equity, or very good, with 70%+ equity. That vertical stretch in the green line indicates BTN has no hands with 30-60% equity. The long, flat, horizontal section of the blue line represents medium-strength hands, with about 60% equity, predominating in BB’s range, with just a few very good or very bad hands at the extremes. Knowing this, we should expect BB mostly to check. Those medium-strength hands do not benefit from betting, because they will only cause worse hands to fold and better hands to call. Their preference is to keep the pot smaller, get to showdown, and maybe induce some bluffs from BTN’s weaker hands 🙌 BTN is the one who wants to bet. Their weaker hands can get folds from better, and their stronger hands benefit from making the pot larger. Given the magnitude of BTN’s advantage here, we should expect large bets, if the stack-to-pot ratio permits it. This graph is from a 100BB cash game simulation, BTN vs BB in a single-raised pot . After the BB checks and calls a 50% pot on an A ♠ T ♥ 8 ♠ flop and a 125% pot bet on a 2 ♣ turn, they see the 6 ♥ river with the ranges shown on this graph. As we predicted, the BB checks 97% of their range in this situation,
and the BTN makes large bets with a polarized range , using all in for more than 200% of the pot as their most frequent bet size. This is an extreme example of polarization. To arrive at such a distribution of equity, BTN had to take several polarizing actions (large bets on the flop and turn), BB had to take several condensing actions (checking and calling bets), and the board had to develop in such a way that very few of BB’s medium strength hands improved. Had a draw come in on the river or the board paired, the distribution would have not have been so dramatic. Quiz: Match the graphs to the flops Now that you’re familiar with these graphs let’s practice using them to evaluate flops. The following graphs depict the equity distributions for a single-raised pot, UTG vs BB, in a 100BB 6-max cash game on three very different flops: T55r, T86tt, and AK6r. See if you can determine which graph depicts which flop . A few hints follow, in case you have trouble. Hints In the first graph , the equity is quite evenly distributed. BB’s hands are a bit weaker on average, but neither player enjoys a significant range advantage. Both players have the strongest possible hands in their ranges. In the second graph , UTG’s range is noticeably stronger except at the top end. Around the 95th percentile of hands, the BB’s blue line actually surpasses UTG’s green line, suggesting BB is more likely to have the very strongest hands despite their overall equity disadvantage. In the third graph , UTG has a huge equity advantage that persists across all segments of hand strength 💪 Their weakest hands are much stronger than BB’s weakest hands, their medium hands are much stronger than BB’s medium hands, and their strongest hands are moderately stronger than BB’s strongest hands. Answers The first graph The first graph is the T86tt flop . Flops with three medium cards give BB the best opportunity to catch up to UTG’s stronger pre-flop range, especially when there are also straight and flush draws possible. Neither player has tremendous incentive to grow the pot, but BB still suffers a positional disadvantage along with a slight equity disadvantage. So they check their entire range on the flop, but UTG continuation bets just 44%, which is quite low for an UTG vs BB spot. These bets are mostly small, 33% or 50% of the pot, pressuring the weakest part of the range, where UTG’s advantage is greatest. The second graph The second is the T55r flop . Offering no straight or flush draws and only two cards to match, this flop makes it quite difficult for BB to flop equity. UTG enjoys a significant range advantage but must be careful, because while the BB has many weak hands in their range, they are also more likely to have trips. For this reason, UTG continuation bets only about 50%, which is low considering the magnitude of their equity advantage and the dynamism of the board. Again, UTG’s preference
is for small bets, because their weaker hands are ahead of BB’s weaker hands, an advantage they will not enjoy if the pot becomes too large and ranges too strong. BB also does some donk betting on this flop, with about 20% of their range. Their nuts advantage incentivizes them to start forcing some money into the pot and deny UTG the opportunity to pot control. The third graph The third graph is AK6r , one of the worst flops for BB. While they can flop middle or even top pair fairly easily (notice the two “shelves” on their blue line where their hands abruptly gain a lot of equity), even these hands pale in comparison to UTG’s best hands. BB never has AA or KK and only rarely AK, while all these are in UTG’s range at full frequency. To capitalize on this range advantage, UTG continuation bets their entire range, often for a large size: 124% pot is their most common bet size. Conclusion By studying these graphs, we can glean a lot about which player has more of which kind of hand and, consequently, how large of a pot that player will prefer to play. These preferences drive betting frequency and sizing . Considering these same factors in-game and visualizing what these graphs would look like in a given situation can help you make better decisions about whether and how much your range will prefer to bet. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Navigating Nasty Rivers Out of Position Playing out of position (OOP) is hard. It’s fundamentally disadvantageous to act on each street… Crack the Shell of Nut Draw Strategy Nut draws hold obvious appeal as betting and raising candidates. They benefit from fold equity,… Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who…
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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 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
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