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Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack , the postflop play against the BB should resemble that of a single-raised pot (SRP). That is, the BB, having taken no preflop risk, arrives at the flop with a weaker range and so should mostly check. Then the BTN, with the stronger range, should most commonly bet small, just as if they were continuation betting in an SRP. Not all players occupying the BB understand these concepts, however. Because the scenario is less familiar, even players who understand the concept of “checking to the raiser” will fail to appreciate its application in a limped pot. This is especially true on boards they believe are favorable to the BB and when holding the sorts of strong-but-vulnerable hands that benefit most obviously from aggression. As a result, you will often see players in the BB seat bet in limped pots, including on flops where a solver would advise checking their entire range. In this article, we will investigate how to exploit Big Blinds who are excessively concerned with protecting their flopped pairs in limped pots . Methodology The following custom simulations are based on 14bb ChipEV ranges, which are the deepest stacks at which BTN plays a mostly limp-or-shove strategy. On each street, players have the option to bet 20% (or 29%, which is a minimum bet in a limped pot), 50%, or 80% of the pot, or all-in. Raises of 33% or 66% of the pot or all-in are allowed. We will compare unlocked simulations to those where the BB is nodelocked to bet half pot with 75% of their top pair and second pair hands to see how the BTN can adapt their strategy to exploit this mistake. Anticipating that BB will make this mistake, BTN may have some incentive to limp more or different hands as a further exploit. However, we will use the same preflop ranges in both scenarios for the sake of consistency. Responding to BB’s Bet on a Low Flop 8 ♥ 6 ♥ 3 ♦ is a good example of a flop that could be wrongly perceived as favoring the BB, which, if true, would incentivize aggressive betting from flopped pairs because they are vulnerable to both draws and overcards. However, in actuality, BTN enjoys a significant equity and nuts advantage on this flop! That’s why the solver recommends 100% checking from BB. BB vs BTN on 8 ♥ 6 ♥ 3 ♦ To say that the solver recommends a pure checking strategy for the BB is not to say that it assumes BB will play that way. It provides a robust, unexploitable response to all BB’s bet sizes , even though none of them are actually used at equilibrium. Here is the solver’s response for BTN to a half-pot bet from BB on this 8 ♥ 6 ♥ 3 ♦ flop : BTN response vs BB 51% pot bet This response makes no assumption about what BB’s betting range will look like. Rather, it is optimized to ensure that whatever hand(s)

BB bets, they will make no more than they would checking. Some of them will make less because when we nodelock BB to bet 75% of the time with top or middle pair , BB’s EV drops by about 10bb/100 . Nodelock BB to bet top and second pair for half pot with a 75% frequency Nodelocking in this way does not force BB to bet only these hands. The solver can and does balance by betting other hands as well, mostly draws of various sorts: BB’s nodelocked betting strategy Let’s see how BTN ’s response to this bet changes from the equilibrium: BTN’s adjusted response vs BB 51% pot bet (given BB’s locked strategy) Our nodelocking forced BB to shift excessively many of their strongest hands into their betting range. BTN exploits this by calling less than at equilibrium but folding only slightly more . Most of those calls actually turn into raises, including many all-in shoves, a play barely used in the equilibrium response. This goes back to why BB shouldn’t be betting in the first place: they have many good hands but few great ones. BTN has the nuts advantage and, by shoving, puts BB to a tough decision with all their middle pairs and even their worst top pair: BB’s strategy facing BTN’s raise all-in (158% pot) Responding to BB’s Check on a Low Flop As we discussed earlier, the equilibrium strategy on the 8 ♥ 6 ♥ 3 ♦ flop (and most others) involves a lot of checking from BB and a lot of betting from BTN. Because this is a dynamic flop on which check-raises are likely, BTN has a checking range and a polarized Polarized Describes a range that is mainly very strong made hands or bluffs, with very few middle-strength hands. betting range that mostly prefers larger bet sizes: BTN strategy vs BB check As with BTN’s response to a bet, this strategy does not assume BB will check their entire range. It merely ensures no hand can be played more profitably as a bet. That means the solver’s response will change if we signal to it that BB will often bet their better pairs, an assumption we can build into the simulation with nodelocking. BB’s resulting checking range is weaker and less likely to check-raise, incentivizing BTN to convert checks into small bets : BTN’s adjusted response vs BB check (given BB’s locked strategy) This is also in line with how BTN can exploit BB in an SRP. Against a BB who does not check-raise aggressively enough , BTN c-bets aggressively, even on boards where they normally, at equilibrium, would check often. When BB Is Supposed To Bet Aggressive betting from the BB in limped pots (especially against IP opponents) is usually a mistake, but there are boards where it is correct. These are mostly low, connected boards where straights are already possible: Average BB strategy across all flops and subsets (highest ranked card) On these boards, the same exploits apply against a BB who bets too often or with the wrong range,

but their magnitude is much reduced. For example, on 542 r , BB’s equilibrium strategy entails a lot of betting, with a range that is heavy on top and middle pair: BB’s unlocked strategy on 542 r Even so, BTN plays cautiously against a check, betting less than half the time. When they do bet, it is with a polar range for a large size: BTN’s response vs BB check Nodelocking BB to bet 75% of their top and middle pair hands, as we did in the previous example, does force them to bet slightly more often and weakens their checking range accordingly. BTN exploits by betting into their checks a bit more often, with some of their equilibrium checks shifting to small bets, just as we saw on 8 ♥ 6 ♥ 3 ♦ : BTN’s adjusted response vs BB check (given BB’s locked strategy) Because BB’s deviation from the equilibrium is small, the resulting exploit is small as well. Any change to BB’s EV is within the margin of error, as the solver shows BB flopping 1.73bb in EV in both scenarios. Why Limp? The truth is that even though limping overtakes min-raising as a solver’s dominant BTN action when short stacked, the EV gain from limping is minimal at equilibrium . In the 14bb scenario we’ve been investigating, BTN almost never min-raises. Still, the EV Comparison tool reveals that none of the hands the solver limps lose a noticeable amount of EV by raising (the red and green cells are all hands that would either shove or fold, so although they don’t have a strong preference between limping and raising, there is a third option that surpasses both): EV comparison of min-raise vs limp for BTN at 14bb effective Why add the extra complexity to your game at all? If you are more familiar with strategies for min-raising and playing single-raised pots, why experiment with limping? It’s possible you shouldn’t. Recall that the above chart is from a ChipEV simulation. But ICM considerations tend to incentivize more aggressive play , steering us away from more passive play like limping. The best reason to explore limping stems from the high likelihood that your opponents in the blinds may also be more familiar with responding to min-raises and contesting SRPs after the flop. Familiarizing yourself with common errors and exploits in limped pots gives you another tool you can reach for when the time is right. Conclusion Limped pots are really not so tricky, especially not for the limper. The range dynamics are similar to those of BTN vs BB in single-raised pots (SRP) , so the general contours of the strategy should be similar as well. If your opponents do not understand this , however, they may make easily exploitable mistakes. This could result in them donating more EV to you than they would on the more familiar terrain of an SRP. Because the BB is generally at a range disadvantage, they are supposed to mainly check the flop. Opponents who misunderstand this concept and develop betting ranges often do

so in unbalanced ways, favoring “obvious” betting candidates such as vulnerable pairs. You can exploit these bets either by respecting their strength and folding your own weaker hands and/or by putting them to the test with shoves. More importantly, you can exploit their overly weak checks with frequent, small bets just as you would with small c-bets in an SRP. 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… 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

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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…

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

flops. However, we’ve added subsets by popular demand. We offer four subsets: 25, 49, 85, and 184 flops. There are two main ways to utilize subsets: ☝ Use subsets to make training against the solution easier In the GTO Wizard Trainer, we offer the option to apply board filters (Settings>Board). Users may select a subset of flops meaning they will only be dealt flops within that subset. Fewer situations make it easier to study and memorize patterns. ✌ Use subsets to make visualizing reports easier GTO Wizard has aggregate flop reports that show data for all possible flops. These reports are fantastic tools for finding heuristics and bet sizing trends. However, some users wanted a way to simplify things. So now you can apply subsets as a filter to view fewer flops. This is useful for a quick overview of varying spots. Just keep in mind that bet sizing trends by texture will be less accurate when applying subsets. Subsets were designed to make solving preflop EVs more efficient. They weren’t designed to provide an optimal mixture of flops to study. Despite that, they can be used to simplify things and do tend to offer a good mix of flops. ☝ Use subsets to make training against the solution easier In the GTO Wizard Trainer, we offer the option to apply board filters (Settings>Board). Users may select a subset of flops meaning they will only be dealt flops within that subset. Fewer situations make it easier to study and memorize patterns. ✌ Use subsets to make visualizing reports easier GTO Wizard has aggregate flop reports that show data for all possible flops. These reports are fantastic tools for finding heuristics and bet sizing trends. However, some users wanted a way to simplify things. So now you can apply subsets as a filter to view fewer flops. This is useful for a quick overview of varying spots. Just keep in mind that bet sizing trends by texture will be less accurate when applying subsets. Subsets were designed to make solving preflop EVs more efficient. They weren’t designed to provide an optimal mixture of flops to study. Despite that, they can be used to simplify things and do tend to offer a good mix of flops. Limiting bet sizes The property that brings so much complexity to No Limit Hold’Em is the ability to use any bet size at any point. Heads Up Limit Hold’Em has been solved. That is to say that a “perfect” (unbeatable) strategy has been calculated. Unfortunately, it is impossible to solve No Limit Hold’Em with today’s technology due to the immense number of additional nodes created by removing this betting restriction. Solvers function by artificially re-implementing this betting restriction . Humans input a list of bet size choices meant to model the game, and an algorithm calculates a reasonably accurate solution to this model. In GTO Wizard’s model of a heads-up cash game 100BB deep, SB can c-bet 33%, 67%, 100%, 150% or move all-in. In a real heads-up cash game 100BB deep, SB can c-bet for 25%, 40%,

41%, 41.1% or any other bet size greater than 1BB. Betting Caps Players are limited to a maximum number of bets or raises per street to further simplify betting trees. For example, GTO Wizard simulations use a cap of 5 bets or raises, with the last one being converted to an all-in. This is demonstrated in this SB vs BB single raised pot 200BB deep. Facing a 50% 4-bet on the flop SB is limited to folding, calling or shoving. They cannot 5-bet to a non-all-in size 🤔 This may seem small, but it significantly reduces the size of the game tree. Bucketing Bucketing is the process of clumping similar hand classes together. For example, A ♠ K ♥ on A ♦ 3 ♣ 9 ♣ might become “top pair good kicker with no BDFD draw”. All hands lumped into this category would then be considered a single hand and played the same way. This drastically reduces the gamespace! Tests have shown that efficient buckets produce almost perfect preflop results. Bucketing Bucketing is the process of clumping similar hand classes together. For example, A ♠ K ♥ on A ♦ 3 ♣ 9 ♣ might become “top pair good kicker with no BDFD draw”. All hands lumped into this category would then be considered a single hand and played the same way. This drastically reduces the gamespace! Tests have shown that efficient buckets produce almost perfect preflop results. All multiway preflop solvers use bucketing to reduce the gamespace (postflop solvers do not use bucketing). The number of buckets can range from a few dozen to tens of thousands. Clustering algorithms were developed to make bucketing more efficient. Read more about bucketing in this article by HRC , who based their bucketing on this paper by the University of Alberta. Subgame A subgame is a smaller representation of the true game of poker. That subgame includes several abstractions used to shrink the gamespace complexity. Solvers do not solve poker – they solve a subgame, a miniature version of poker. When people use the term “subgame” in poker, they are distinguishing between the full gamespace and the abstracted gamespace we use in solvers. Conclusion The most important takeaway from this article is that No Limit Hold’Em is far from solved. We have succeeded in calculating very accurate solutions to our models of this game, and that is what GTO Wizard’s Study mode presents you with. Solutions are excellent tools to study trends and learn concepts but will never be a perfect strategy you should attempt to replicate in game. Next time you face an unexpected line or bet size in game, you understand that they may simply be playing a different model of this beautiful game than you are. 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…

Mastering Three-Bet Pots In Position in MTTs Playing in position against a three-bettor is a lesson in playing to your advantages. As the defending player, you will not have the equity advantage or the nuts advantage. What you will have is the position al advantage. This incentivizes you to play even more passively than you usually would as the defending player facing aggression, forcing your opponent to make tradeoffs and reveal information by acting first on future streets while you bluff, pot control, and squeeze extra value from marginal hands. Deeper stack depths magnify your positional advantage, as do more dynamic boards , so you’ll need to assess these factors to determine the incentives of your specific hand in any given situation. Playing Before the Flop The following chart shows the CO’s response to a three-bet from the blinds at various stages of the tournament, always with 50bb stacks. The numbers are slightly different when the open comes from other positions, but the patterns are the same. The patterns are different if someone has called the open raise and then one of the blinds has squeezed. More tight and aggressive play is generally correct in that scenario, as described in this article . Calling is an important part of your strategy even under ICM pressure, which incentivizes more tight and aggressive play. A higher risk premium Risk premium Risk Premium measures the extra risk you take stacking off in an MTT. It’s a measure of survival pressure and a valuable tool for understanding ICM spots. Risk premium is defined as the extra equity you’d need to call someone’s shove, compared to a (chip EV) pot odds calculation. RP = Required Equity (ICM) – Required Equity (cEV) when stacks are fully invested. Each player has a unique risk premium against every other player in a tournament. results in less calling, more folding, and more raising, as is to be expected. But the magnitude of these differences varies dramatically depending on whether the three-bet comes from the SB or the BB, which is perhaps more surprising. Your response to a three-bet heavily depends on whether the three-bet comes from the SB or the BB. Indeed, there are several notable differences in how CO responds to a SB three-bet versus a BB three-bet. Across the board, they fold more and four-bet less against the BB . Their response to a BB three-bet does not change that much at various stages of the tournament, especially not compared to how much their response to a SB three-bet changes. Responses versus BB three-bets stay relatively stable compared to responses versus SB three-bets. This reflects differences in the ranges, raise sizing, and incentives of the three-bettor . For the SB , calling is a less appealing option. They are getting only a small discount from their small blind, and they are not closing the action. Thus, they three-bet a more 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. range, including

many hands that would otherwise play well as calls preferring to deny equity to the BB. This is especially true as ICM pressure increases. For the BB , calling is very appealing. They are getting amazing odds, thanks to their big blind and the ante, and they do not have to worry about anyone calling or raising behind them. When they do three-bet, they prefer to do so with a more polar Polarized Describes a range that is mainly very strong made hands or bluffs, with very few middle strength hands. range consisting of very strong hands that will be happy to get all-in preflop and hands so weak they are not especially appealing calls. Thus, they are less likely to have a tough decision when faced with a four-bet. This more polar range incentivizes BB to use a larger size when they three-bet as well, so it is correct for the opener to fold hands they would not fold to the SB. The other interesting trend here is that CO’s calling frequency goes up as the stacks get deeper. This is the opposite of what happens when the opener faces a three-bet from an in position player, which provides a clue as to what is going on here. Playing after the flop is good for the player in position. The more money remaining to be wagered, the more their position is worth. Thus, the out of position player—at deeper stack depths—has more incentive to avoid playing postflop by either folding or four-betting. As stacks get shallower, it matters less and less that they are out of position, which makes it increasingly appealing for them to take advantage of the pot odds by calling and seeing a flop with hands that would have folded if stacks were deeper. Playing after the flop is good for the player in position. Conversely, CO prefers not to end the hand preflop when stacks are deep because they expect to over-realize their equity postflop. They call with some weaker hands that they would fold with shallower stacks but also with some surprisingly strong hands that would four-bet if stacks were shallower. Here’s their full strategy when facing a three-bet from the BB with 50bb stacks and no ICM considerations : Suited and connected hands are best equipped to profit from the additional stack depth. Not only is the reward for making a straight or flush higher, but deeper stacks also enable these hands to apply more pressure when floating and semi-bluffing Semi-bluff A bet made with an unmade hand (such as a draw) that has the chance to improve on future cards. their draws. Even some more offsuit broadway hands can call against the blinds which would not call against the BTN, hands like AT o, which often turn into top pair with a modest kicker or middle pair. Position makes it easier to keep the pot small and/or get away when dominated, and to get to showdown and maybe even squeeze out some additional value when ahead. A lower SPR incentivizes the opener to protect

their equity when ahead rather than call to potentially win even more after the flop. With shallower stacks, these big offsuit hands go up in value, while the smaller suited cards go down. If we shrink the stacks from 50bb to 30bb , CO’s folding frequency doesn’t change much, but the composition of the continuing range changes a bit. Smaller pairs and suited connectors now fold while offsuit hands like A9 o and KT o call more often: The biggest change we see is more shoving from hands like AQ s, AJ o, and QQ . CO’s shoving frequency increases by about 50%, as the lower SPR incentivizes them to protect their equity when ahead rather than call to potentially win even more after the flop from dominated hands. Facing a Continuation Bet After calling a three-bet, you will likely face a small continuation bet on the flop. This is by far the most likely action for both a SB and BB three-bettor. With shallower stacks, they show a strong preference for betting 25% pot. With deeper stacks, they make many 50% pot bets as well, but your response to both is similar. CO Response to 25% C-Bet From SB in Three-Bet Pot with 50bb Stacks You should mostly call . Raising is a bigger part of your strategy on low card boards, which are more dynamic , but calling is always your most frequent action. Just like before the flop, playing poker on later streets favors the in position player, so you generally prefer that to ending the action on the flop. More cards coming down also tend to be worse for the preflop raiser because the big advantage they have over the caller is a prevalence of big pairs in their range. The more cards on the board, the weaker these big pairs tend to be . This is less true on low card boards because the three-bettor also has many unpaired overcards, which could easily become stronger as a result of the turn or river card. This is part of why the CO plays more aggressively on these boards. The pattern is similar when playing against BB : And with shallower stacks: Playing a Static Flop A62 r is a good example of a board where, even at 50bb, the three-bettor prefers a small continuation bet, and the caller virtually never raises. CO actually does not hit MDF on this flop, despite some ambitious floats with hands like KJ o and T8 with a backdoor flush draw. Ace-high boards are very good for the three-bettor, especially when they don’t offer many draws, so CO just has to take the ‘L’ with their worst hands. Facing a second 50% barrel on the turn , CO’s strategy is fairly intuitive: they call with any draw and most pairs but fold their whiffed floats and worst pairs , which are the low pocket pairs that now have just two outs to improve on the river. More commonly, however, they will face a check on the turn, and that’s where things get interesting.

On this board, CO starts betting geometrically with a polarized range . A strong top pair or better is the threshold for value, while their bluffs come not only from flush draws (many of those prefer to check back so as not to open themselves up to a raise) but from whiffed floats Floats To call a bet postflop with a weak hand with the intention of bluffing on a later street to win the pot. : You can see in the example above that K ♦ 5 ♦ , which turned a flush draw, is indifferent between betting and checking, but K5 in the other backdoor flush suits are pure bets. Playing a Dynamic Board Changing the Ace to a Ten makes the situation much more dynamic. Especially in a three-bet pot, ranges are concentrated around big cards, so when there is a big card—especially an Ace—on the flop, both players will flop a good number of strong hands that are relatively hard to draw out on. When there is no such card, then both will flop many hands with the potential to improve on future streets, which makes protection and equity denial bigger considerations. In a three-bet pot, ranges are concentrated around big cards. Facing a 25% continuation bet on this board, CO raises aggressively , with a strong preference for protecting their weaker top pair hands. These hands are strong enough to get all-in now but will lose value on many turns. They also fold quite rarely . Even with this robust continuing frequency, SB can profitably bet any two cards. This is because, with the more dynamic board, SB has no pure bluffs, hands with effectively 0 showdown value or potential to improve. Nor does CO have many hopeless hands. Getting five-to-one odds, most hands can justify taking one off in position. On the 8 ♦ turn , CO’s continuing strategy mostly follows the same logic as on the A62 r board, though as on the flop, they have a more robust raising range consisting mostly of strong but vulnerable pairs ( A8 is good enough to fit this bill): The trickiest bit here is probably the call with AQ , even when it does not have a diamond. Calling with smaller pairs can feel dicey as well, given the risk of a scary river card and/or bet. These plays are easier to conceptualize and execute if you keep in mind the following three factors: Your gut is right; you’re probably going to lose . These are your weakest calls, and against an equilibrium strategy, they are barely profitable. That means, getting 3:1, you’re going to claim about a quarter of the pot with them, whether that be by showing down the best hand or bluffing or value betting. These calls are nevertheless correct because of the price. (Things become more precarious when ICM is a factor, which is why you don’t call as much preflop in the first place.) These hands work together, along with your position and traps (note that there are lots of AA and

KK in your calling range as well), to give your opponents tough decisions on the river. Did the Ace just give you top pair, or did it crush the hopes of your 55 ? Should they bluff a blank river to get you off your AQ ? If they do, they risk running into your slowplays or the small pairs, which are a bit stronger now that they know no big cards have come. Your opponent will also have many medium-strength hands of their own that want to check or block-bet Block bet A small bet made by the out of position player designed to prevent or “block” the opponent from betting themselves. Sometimes used to induce raises. the river. Your lighter calls give you surprising value bets on some rivers and weak hands to bluff with on others, making your out of position opponent’s life difficult. Conclusion Playing against the strong range of a three-bettor is always intimidating, but having position is a big help. It also helps to remember that your objective is not to maximize your chances of winning the pot. Instead, it’s to make the most money. You have the weaker range and should expect to lose more pots than you win, which is fine because you were getting a good price to call before the flop. Rather, your goal is to give your opponent difficult decisions . When you call, as you often should both before and after the flop, they don’t know whether you are slowplaying or floating or desperately hoping for a cheap showdown with a marginal pair. Nor will they know whether that flush card or overcard on the turn just made your hand or wrecked it. This, in turn, makes it difficult for them to determine whether they should bet again, check and call, or check and fold. Sometimes they’ll guess right, but they’ll rarely be sure of the right play, and that’s the best you can hope for. Practice These drills have you facing a three-bet from the blinds from various seats and stack sizes. They are all based on ChipEV simulations so that you can practice both preflop and postflop decisions. If you want to practice incorporating ICM into your decisions, these ICM drills put you in similar preflop spots (postflop simulations based on ICM models are not yet available) with 50% of the field remaining. Once you’ve got the hang of that, you can tweak the parameters to practice other stages of the tournament, but you’ll likely get more out of focusing on one stage at a time rather than training on a set of drills that randomly draws from many different ICM models. These drills have you facing a three-bet from the blinds from various seats and stack sizes. They are all based on ChipEV simulations so that you can practice both preflop and postflop decisions. If you want to practice incorporating ICM into your decisions, these ICM drills put you in similar preflop spots (postflop simulations based on ICM models are not yet available) with 50% of the

field remaining. Once you’ve got the hang of that, you can tweak the parameters to practice other stages of the tournament, but you’ll likely get more out of focusing on one stage at a time rather than training on a set of drills that randomly draws from many different ICM models. 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… 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

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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…

ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but what does this actually mean? The Independent Chip Model (ICM) is a mathematical formula that converts your tournament stack into a monetary value. This formula was first applied to poker by Mason Malmuth in 1987. The model uses stack sizes alone to determine how often a player will finish in each position (1st, 2nd, etc.), then assigns tournament equity based on the payouts of those positions. Tournament equity is your expected share of the prize pool, given the payout structure, your position in the event, and stack sizes. Table of contents Why is ICM a thing? How do you calculate ICM? How to leverage this information Risk Premium General heuristics and effects Limitations of ICM Alternative models Conclusion Why is ICM a thing? In a cash game, every chip has a monetary value, and the value of chips scales linearly; doubling your stack means doubling your stack’s value. In tournaments, however, the value of chips doesn’t scale linearly; doubling your stack doesn’t double the value of your stack. If the value of chips doesn’t scale linearly, we need a method to transform the value of chips into a monetary value. We need to find the real expected value of gaining or losing chips to make strategic decisions. We need a utility function to transform chipEV into $EV. That’s where the independent chip model comes into play. How do you calculate ICM? The Independent Chip Model assumes all players are equally skilled, and therefore the probability of winning is purely a function of stack sizes. ICM calculates the probability of each player finishing 1st, 2nd, 3rd and so on, then multiplies those probabilities by the payouts of each position. To calculate the probability of a particular player finishing in 1st, divide their chips by the total amount of chips in play. Calculating 2nd and 3rd positions take more complex math. Example: Tom, Amy, and Bill are playing a 3-handed SnG. The stacks and payouts are as follows: What are the players’ tournament equity? Let’s start by calculating their 1st place equity. This is the easiest step, as the probability of any player winning is simply their stack divided by the total amount of chips in play. Multiply the probability of winning 1st place by the 1st place prize to get their 1st place equity. There are 1000 chips in play: Now we need to calculate their equity in 2nd place. This step is more complex, but still doable by hand. To calculate the probability of coming in 2nd, we take the following steps: Assume one of the other players wins, remove their chips from play, and divide our chips by the remaining chips in play Repeat 1. for every possible 1st place victory Multiply each outcome by the probability of the other player’s first place win. Ok, that sounds complicated, but it’s not so bad. Let’s get started: 2nd place equity: Assuming Tom wins (50% chance) 2nd place equity: Assuming Amy wins (30% chance) 2nd place equity:

Assuming Bill wins: (20% chance) Now we multiply the 2nd place equity by the probability of each scenario: Total 2nd place equity: Now we can simply add the first and 2nd place equity together to figure out the total equity: As you can imagine, this process gets exponentially more complex as we add more players and payouts. Luckily there are plenty of quick and easy ICM calculators online. It is nearly impossible to calculate ICM during play. The process is far too complex. Tournament professionals build their ICM intuition by studying thousands of ICM spots and playing with variables. Here’s the same calculation done with a free online ICM calculator ( Holdem Resources Calculator ): Tournament Equity Prizes How to leverage this information Let’s ask ourselves how this information can affect the strategy. Amy folds BTN, Tom shoves in the SB, Bill calls in the BB. What will their tournament equity be if Tom or Bill wins? You can calculate this by plugging the resulting stacks into any ICM calculator: Tom wins: Tom’s equity is $58 (+$12.82) Bill’s equity is $0 (-$22.57) Bill wins: Tom’s equity is $30.85 (-$14.33) Bill’s equity is $38.29 (+$15.72) In other words, Bill is risking $22.57 to win $15.72. Tom is risking $14.33 to win $12.82. ICM has the effect of creating an uneven downside relative to the shortstack. Bill is risking more tournament equity in this situation, so they need a stronger range to defend. This gives the big stack an advantage. Risk Premium To put it simply, chips won are worth less than chips lost . This uneven risk/reward ratio creates the effect of “risk premium”. You are risking more than a straight chip-EV calculation would suggest. Total required equity Let’s use the example above to figure out Bill’s risk premium facing Tom’s shove. We can imagine the blinds are 25/50, with Bill in the BB facing a shove from Tom in the SB. A simple pot odds calculation tells us how much equity Bill needs to call, in a cash game. We can call this amount the “Chip Equity”. Tom: 500 chips Bill: 200 chips Bill needs to call 150 more chips, and their stack will be 400 if they win. 150 / 400 = 37.5%. In a cash game, Bill should call any hand that had at least 37.5% equity against Tom’s range. But as we know, chips gained do not equal chips lost. Bill needs to weight the cost of a fold against the risk of calling. There are 3 situations, Bill folds, calls and wins, or calls and loses. Here is the tournament equity in each case: Bill can fold and retain $17.93 of tournament equity. So Bill is risking $17.93 by calling, and will have a stack worth $38.29 if they win. Let’s do a new pot odds calculation: $17.93 / $38.29. In other words, Bill actually needs about 47% equity to call! Because of ICM pressure, Bill needed an additional 12% equity. That additional 12% represents his risk premium. This extra risk premium allows Tom in the SB to

open much wider, since Bill will always have to overfold relative to his pot odds. That’s the advantage of the big stack. Risk premium is a variable that’s different for every stack vs every other stack at the table. In general, we can derive the following heuristic: Your risk premium is higher against stacks that cover you and lower against smaller stacks that you have covered. General heuristics and effects It’s not possible to run ICM calculations in game. However, studying these effects off table can greatly help develop your instincts at the table. Here are some of the most valuable heuristics to remember: Stack off with a tighter range in tournaments than in cash games. Avoid marginal spots. A marginal +cEV spot is usually a -$EV spot in a tournament. Medium stacks need to play tighter near the bubble. Big stacks can threaten smaller stacks as they take on less risk when stacking off. This is especially true near the money bubble. The value of gaining chips is smaller than the value lost when losing the same amount of chips Pay attention to the payout structure. Big pay jumps are associated with a higher risk premium. When a shortstack is about to bust, resulting in a pay jump, all players except the biggest stacks should generally tighten up significantly. Limitations of ICM ICM has some general limitations. It’s a pure math based system that ignores many of the intangible factors of actual play: ICM assumes all players are equally skilled. In reality, we’d expect the more skilled players to win a larger percentage of the time, relative to their stack. ICM calculations for big fields are computationally difficult. Recent algorithms have made progress in this area, but it’s still very difficult to correctly calculate ICM for large field MTT’s. ICM doesn’t consider players’ positions. A 3BB stack is much more valuable on the BTN than in the blinds. ICM ignores blinds increasing. If you know the blinds are about to increase, that can affect the optimal strategy, especially with shortstacks involved. ICM underestimates the chip leaders’ advantage. Bigger stacks can often bully smaller stacks due to ICM pressure, which leads to a higher win% for big stacks than ICM would otherwise indicate. Alternative models Some alternative models exist to address these limitations. One of the most popular is Future Game Simulation, which essentially is a recursion of ICM. It calculates several rounds in advance to take into account position, blinds increasing, and future play. This model is used in conjunction with regular ICM calculations to better approximate tournament equity, and is considered a staple in most tournament software. There is also the Dependent Chip Model, which seeks to address ICM underestimating the big stack advantage. Although this model tends to be more complex and overestimate shortstack advantage. Conclusion ICM is a complex tool that’s used to transform stacks and payouts into actual tournament equity. Although these calculations are not possible in-game, studying ICM off the table will greatly improve your chances on the felt! ICM encapsulates one of the most important

aspects of tournament play: The value of survival. Tournaments are not about maximizing BB/100, they are about maximizing your tournament equity. As you explore these concepts, you’ll run into spots where you need to play far tighter than your instincts might otherwise tell you, and other spots where you should play far looser than you anticipate. Learn how to use survival pressure to your advantage, and avoid committing ICM suicide! 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

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Flop Heuristics: OOP C-Betting in MTTs illustration Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller from the blinds . You should not expect to enjoy the sort of range advantage you would against a caller from the blinds. Depending on your position and that of the caller, you may not have an equity advantage at all, and being out of position puts you at a significant disadvantage . When someone cold calls your raise, an unfortunate event has occurred. When opening, most hands derive the majority of their value from stealing the blinds/antes, or from playing a heads up pot against the BB caller . When someone cold calls your raise, an unfortunate event has occurred. The caller has dragged you down one of your least profitable branches of the game tree, and you should adjust your expectations and your strategy accordingly. You are no longer favored to win the pot, and if you flop badly, you will often have to give it up. There is nothing “weak” or exploitable about this. The cold caller took on significant risk when they called you . They risked other players calling or re-raising behind them, they risked you having a strong hand, and they risked you flopping well. Should they manage to fade all those risks, their reward is occasionally winning a pot with a not-great hand of their own. Your preflop raises do not need to derive large amounts of EV from these scenarios, and you should not expect them to. The extent of your disadvantage depends on the position of the caller . The earlier their position, the stronger their range should be to compensate for the risk of so many players remaining behind them. The following chart shows UTG’s continuation betting strategy against a cold caller from each position with 40bb effective stacks. Notice that as the caller’s position gets later, UTG’s equity improves and they bet more often. But even in the best case scenario where they are heads up with the relatively wide range of a BTN caller and enjoy more than 53% equity, they bet barely half their range on average and favor small sizes. UTG C-Bet vs. Cold-Caller Another interesting pattern is that, while UTG bets less often into early position callers, they use bigger bets proportionately more often . This is because their betting range is more polar, with more of their middling hands incentivized to check. Adjusting to Shallower Stacks Not many changes when we compare UTG’s continuation betting strategy at 25bb to their strategy at 40bb, but we do see slightly less checking and slightly more use of the larger bet sizes. Being out of position is less disadvantageous with shallower stacks, and the lower SPR increases the importance of protecting equity relative to pot control . Note: GTO Wizard has no calling range as UTG1 facing an UTG open at 25bb stacks; it plays a strictly raise-or-fold strategy. UTG C-Bet vs. Cold-Caller Adjusting to Deeper Stacks These patterns continue when we look at UTG’s continuation betting

strategy with 100bb stacks: they check more often, and when they do bet, they use a smaller size more consistently (note that the bet sizes GTO Wizard considers at this stack depth are slightly different than those it uses with shallower stacks). This may seem counterintuitive, as UTG’s nutty hands would presumably benefit from growing the pot more aggressively when there is more to be wagered. However: Few hands are strong enough to be excited about playing for stacks at such a high SPR . These hands are such a small part of UTG’s range that they can profit from starting off the same way UTG’s many marginal hands, by checking. They may then check-raise or wait until a later street to start growing the pot. It’s hard to know from the flop what the nuts will be on the river . Being out of position with such deep stacks, UTG wishes to avoid a scenario where they grow the pot with a set just to see a flush come in on the river, or they grow the pot with the nut flush draw just to see the board pair on the river. UTG’s nuts advantage falls off at deeper stacks . The main advantage a preflop raiser has over a cold caller is the big pocket pairs the in-position player was not incentivized to call preflop. As stacks get deeper, even the best one pair hands drop off in value, so that the preflop raiser enjoys less of a nuts advantage even on more favorable flops. Lacking both a nuts and a positional advantage, they have little incentive to use large bets, even when they do have strong hands. What Makes a Hand Good For Betting? Once you understand which situations you should bet more or less often, it’s worth thinking about what properties make a hand especially good for betting or checking . As an out of position raiser, checking is a more important part of your strategy, so it’s more important to recognize good checking candidates. The best hands for betting Hands strong enough to play a big pot unimproved . These are especially incentivized to bet if they are in danger of losing their value to a change in board texture on future streets. However, in deepstacked high SPR scenarios, these hands might shift their strategy to pot control. Draws to nutty hands . Nutty here does not mean the literal nuts but rather any hand that will be strong enough to play for stacks. These hands prefer to get folds, but they don’t mind growing the pot because, with a little luck, they could be strong enough to value bet on later streets. The best hands for checking Marginal or medium-strength hands . These are hands, often low pairs and the best unpaired hands, that have decent equity in a small pot but perform poorly when called. Betting these causes your opponent to fold mostly hands you were ahead of anyway while growing a pot you will not be favored to win. Draws to marginal hands .

Depending on the board texture, this may mean draws to low straight or flushes or two big, unpaired cards. You want to avoid growing a pot while drawing to a hand you will have to play conservatively should you make it. Such hands under-realize their equity and thus benefit less from growing the pot. Airballs . These are weak hands with little prospect for improving. While it’s great to get folds with them, their lack of equity when called makes them a liability. These same heuristics apply to continuation betting against the blinds . The difference is that, as an out of position raiser, checking is a more important part of your strategy , so it’s more important to recognize good checking candidates. An in-position raiser often enjoys a large enough range advantage to bet even the less good candidates. But as an out of position raiser, you won’t generally have the range advantage that enables you to bet your worst hands profitably, and growing the pot with marginal hands and draws is more dangerous as you won’t be able to use your position to control the pot size later. Static Flop Example Static flops are better for playing against a cold caller because they reduce the liability of being out of position. The flop we’ll take as our example, A ♠ J ♥ 6 ♦ , is a particularly good one, as the raiser enjoys a significant equity advantage and is slightly more likely to have the strongest hands. Static flops are better for playing against a cold caller because they reduce the liability of being out of position This incentivizes the raiser to continuation bet at a high frequency, so even some hands that would be good checking candidates, according to our criteria, make their way into the betting range. Even so, the raiser checks 28% of their range, and those checks come primarily from two places: medium-strength hands, and hands that missed the flop entirely . This chart of the raiser’s strategy shows two significant green patches, one among their lowest equity hands and one in the middle of their range, clustered around the 50% equity mark. UTG’s most checked hands are 99 , 88 , and K ♣ 9 ♣ . The medium pocket pairs are good examples of hands that can win a checked down pot but fare poorly if they bet and get called, while K ♣ 9 ♣ is the best unpaired hand that lacks both a straight draw and a backdoor flush draw (all the K9 combos check frequently, but K ♣ 9 ♣ is the only pure check in UTG’s range). Dynamic Flop Example By the numbers alone, 9 ♥ 8 ♦ 6 ♦ doesn’t appear to be such a bad flop for UTG. Ranges are basically symmetric on this board, with the equities split almost exactly evenly. Yet the dynamic nature of the board makes it a tough one to play from out of position, causing UTG to realize just 93.67% of their equity. By comparison, they realized more than 99% of

their equity on AJ6 r and enjoyed a significant equity advantage. Growing the pot on the flop is dangerous for UTG , because no matter how good their hand is now, the turn and river could tank its value and leave them in a tough spot out of position. Thus, UTG checks 65% of their range, including many of their weakest hands. Checking is not exactly giving up , because BTN is not guaranteed to bet, but these hands are mostly resigned to losing the pot . It can feel like you are being “too weak” or that you are giving up too easily when you simply check and fold the flop as the preflop raiser. Yet this is often correct. Playing from out of position is difficult, and you’ve lost a lot of EV the moment an in-position player cold called you . Refusing to confront that fact isn’t going to make it go away; it’s only going to lead to you throwing good money after bad. When UTG does bet, it is mostly with strong but vulnerable overpairs and various draws and backdoor draws . For example, they only bet KJ o when they hold a diamond to give them a backdoor draw (and a blocker to BTN’s draws). UTG’s strategy is similar for their many combos of two overcards, only betting when they have a backdoor draw. The exceptions are AT and KT , which also have a gutshot. All combos of these are candidates for betting. Conclusion Playing out of position is hard. When you see a solver strategy like the one for 986 tt, where every hand seems to be mixing, what you’re seeing is that even the solver can’t find great options. Every mixed strategy represents a tradeoff , a dilemma, a hand torn between two competing objectives. There isn’t going to be a cost-free option. All those things we hate to do–giving free cards, folding to bluffs, paying off value bets–we have no choice but to risk doing them. Under-realizing your equity and losing more than your share of pots is to be expected. Once you accept that the IP cold-call has put you in a bad spot and some “mistakes” are inevitable, you can focus on how to make the best of a bad situation. 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,…

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River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing in versus out of position involves betting frequency and sizing on the river . Solver strategies for the OOP player, when they involve betting at all, often bet tiny —as small as 10% of the pot—with a wide range. For the IP player, seeing a mix of large bets and checks is much more common, with solvers showing little interest in small bets. This is because betting in position reopens the action , giving opponents the opportunity to check-raise. The hands that lose the most when raised are the ones in the middle of your range , the kind you might like to bet for thin value . With your strongest and weakest hands, you don’t mind getting raised so much. With the strongest, you’re obviously happy to see more money going into the pot. With the weakest, you aren’t in danger of folding the winner—an expensive mistake that would cost you not just your bet but also the entire pot you would have won by checking. The strongest and weakest hands are the ones that benefit from large bets, which is why betting strategies in position tend to consist of larger and less frequent bets from a polar range . When out of position, there is very little difference between checking and betting small , so it’s easy to prefer the latter. If BB has a hand to raise the small bet, they can still bet it after you check. If you expect to be only a slight favorite when called, it’s typically not worth risking a check-raise. This is why it’s rare to see the IP player bet less than half pot on the river (unless that’s all that remains in the effective stacks). Usually, if you’re betting small, it’s because you’re betting for thin value. But if you expect to be only a slight favorite when called, then it’s typically not worth the risk of opening yourself up to a check-raise. Your medium-strength hands will, in theory, be roughly indifferent between calling or folding a raise from a polarized range. No matter how you respond, your hand loses its value as soon as you get raised . Once you factor in even a small risk of such a raise, that’s usually enough to negate the value of a thin bet . But what if your opponent is bad at check-raising rivers ? What if they don’t have the courage to do it as a bluff, nor the wherewithal to check a nutty hand in the first place? Does this mean you can get away with more thin value bets when in position? Let’s experiment and find out! After the Turn Checks Through The aggressor usually has the nuts advantage, so check-raising is not necessarily important for a player who’s been checking and calling all the way to the river. If the flop aggressor checks behind on the turn, however, many nutty hands get removed from their range. Which then makes check-raising the river a

more important consideration for their opponent. Many players can’t bring themselves to check strong hands on the river. Yet, when first to act in this scenario, many players can’t bring themselves to check strong hands. One of my coaching clients named this tendency: “ value panic ”—the fear of winning only a small pot with a big hand if your opponent checks back the river. To be fair, this is not necessarily an irrational concern. As we will see, river check-raises from the OOP player and thin value bets from the IP player exist in a delicate balance. Against a passive opponent who will not value bet thinly, it is correct to bet strong hands instead of going for a check-raise. But many people who learn the game playing in passive environments fail to understand the exploits at work here and simply learn from experience not to check strong hands on the river. This opens up an exploitative opportunity for their opponents. After range-betting the flop and checking back the turn, BTN arrives at the river with both a nuts and equity disadvantage. This first experiment is based on a 40bb, single-raised pot, BTN versus BB MTT scenario on an A ♥ 9 ♠ 4 ♦ 7 ♣ 5 ♥ board . I used the Automatic bet sizing feature to determine the most common bet/raise sizes before the river. Only the most common size was allowed at each node except for BTN’s river bet, where they were allowed to bet 25%, 50%, 100%, or 400% (all-in). Here’s the resulting river strategy for BTN when BB is allowed to check-raise optimally : After range-betting the flop and checking back the turn, BTN arrives at the river with both a nuts and equity disadvantage . If they were first to act, they would have to check frequently for fear of betting into a stronger range. This means BB cannot count on them doing a lot of betting, and therefore, they legitimately have the incentive to bet many of their own strong hands; bet 43% of the time for a size of 66% pot. However, BB’s incentive to bet their strong hands also gives BTN more incentive to bet when checked to. Look how much BB’s check shifts the equity distribution ! Note that BB is still supposed to retain the nuts advantage , however, by checking many of their strongest hands. This is why BTN prefers the 50% pot bet size. The middle of the distribution is where they have the advantage. If the pot gets very large, either because they bet big or get check-raised, they no longer enjoy an advantage. Even BTN’s few nutty hands mostly bet 50% pot. They very occasionally bet full pot but never all-in. It’s not that they aren’t strong enough. Rather, it’s that hands strong enough to call a big bet will mostly check-raise anyway , so BTN isn’t giving up anything by betting small. In fact, they make more because they also induce raises from bluffs that would have folded to a big bet. Check and

Raise Prohibited Take a look back at BTN’s strategy when checked to. How do you expect it to change in a simulation where BB is not allowed to check-raise the river ? Will BTN’s overall betting frequency increase or decrease? Which bet sizes do you expect them to use more and less often? Answer these questions for yourself, then click the dropdown below to see the results! See Answer BTN bets slightly more often, but that’s not the primary change in their strategy. The biggest difference is the increased use of both smaller and larger bet sizes . A few things are happening here: BB has less incentive to check strong hands when they can’t raise them on the river. This makes it safer for BTN to shove hands as weak as two pair A5 , and to make pot-sized value bets with top pair and even second pair top kicker K9 ! BTN can also bet more hands for a larger size when they don’t have to worry about getting raised off a winning hand by a bluff. Hands that were not strong enough to bet for value at all when the risk of a check-raise loomed can now eke out a 25% pot bet. This includes hands as weak as third pair J7 . Bluffing is also more appealing when BTN is betting into a weaker range and does not have to worry about getting rebluffed by a raise. Once raising is off the table, BTN has more options, but half pot remains their most commonly used size, as the middle of the equity distribution is still where they retain the largest advantage. BTN’s EV, when checked to, is 5.03bb in the simulation where BB cannot raise—up from 4.73bb in the unrestricted simulation. That amounts to 30bb/100 or a little over 6% of the pot, so it’s worth looking for these bigger, thinner bets when the opportunity arises. Triple Barreling Check-raises function a bit differently when the preflop aggressor continues betting the flop and turn. Unlike in our previous example, they have many nutty hands in their range and a lot of incentive to make big bets. Indeed, in a simulation where BTN double barrels this same board, BB rarely gets the opportunity to raise the river because BTN mostly plays a shove or check strategy: With only a pot-sized bet remaining, betting less is not terribly appealing. After betting 50% pot, BTN would be getting 5:1 to call a raise all-in, so a solver is mostly paying off BB’s strong hands with BTN’s value range anyway. Occasionally, BTN loses half pot instead of full pot with a bluff, but that means they also sometimes get rebluffed by a hand that would have folded. The major downside of betting smaller is winning less from hands that would have called a shove while still losing the maximum to the top of BB’s checking range. The major downside of betting smaller is winning less from hands that would have called a shove while still losing the maximum to the top of BB’s

checking range. When BB is not allowed to raise , BTN makes substantial use of the half-pot size, so much so that they use it more than the shove: This gains them an extra 0.5bb in EV, about 2% of what is already a fairly large pot. The breakdown of which hands belong in which range is as intuitive as it gets. BTN shoves all their strongest hands and bets 50% pot with a slightly weaker range . If BB won’t raise, there’s no need to get deceptive by betting small with strong hands or shoving second-tier hands because they’ll be priced in to call a raise all-in anyway. Most bluffs are indifferent between the two sizes: With the risk of a raise off the table, the strategy is straightforward. Your best hands make more money shoving and winning the maximum from the top of BB’s range . Your second-tier hands make more by cutting their losses against the top of BB’s range while incentivizing calls from more hands they are ahead of because of the better price. They Always Have It Realistically, even the nittiest nit will raise when they have the nuts. What they won’t do is raise with anything less. They won’t raise for thin value, and they won’t raise as a bluff. For their opponent, this changes nothing from the simulation above. If they are only check-raising the nuts, they might as well not be raising at all… as long as you don’t pay them off . Against such a player, your strategy should be just what we see above: shove your strongest hands and bet somewhat smaller with the next tier of hands. Then, you fold if they raise. An opponent who won’t raise without the nuts might as well not be raising at all. That last part is the key. The whole thing falls apart if you start making excuses about “pot odds” and “being priced in.” If they always have a hand better than yours, there is no price at which it is correct to call. You made an exploitative assumption, built your betting strategy around it, and you should follow through on it by folding when they raise, no matter how good your hand is. Any hand good enough to call the shove is a hand you should have shoved yourself . If they always have a hand better than yours, there is no price at which it is correct to call. Conclusion Solvers rarely recommend small bets in position because the hands that benefit most from small bets are medium, thin value hands, and those are the ones that risk the most by reopening the betting . But if that risk is mostly mitigated because your opponent will rarely/never check-raise the river or only check-raise their strongest hands. In that case, you can exploit them with more thin value bets and an overall less deceptive strategy. You just bet your hand strength—bigger with your best hands, smaller with your thin value—and fold if they raise. 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 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

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Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs. Apart from the benefit of always having position postflop, in Progressive Knockout Tournaments , we potentially have the opportunity to play our widest range for bounties against the Blinds. In this article, we’ll look at how covering others and being covered ourselves affects our preflop BTN ranges in a PKO. RFI Range Comparisons As a starting point, it’s essential to understand the impacts of tournament stage and relative stack sizes on our opening ranges . Both the risk premium of playing a hand, as well as the value of bounties, will impact how wide the optimal BTN opening range is. Let’s start our examination by taking a sample of a few Button ranges at various average stack depths and tournament stages. Note that these examples are from 8-max solutions, so the full table averages 40bb rather than just these three positions. For our purposes, we have excluded these previous positions as we are discussing Button RFI ranges. 40bb Average, 50% Field Remaining Check out these linked articles to learn more about Bubble Factor (BF) and Risk Premium (RP). The following chart compares BTN’s risk premium (averaged against SB and BB) to their opening frequency: We can immediately see some interesting trends for Button based on these examples: Play least amount of hands when covered by both Blinds relative to symmetric stacks. (Decrease in VPIP VPIP An online poker acronym which stands for ‘voluntary put in pot’, a statistic that measures the frequency with which a player voluntarily put money into the pot pre-flop. of 11.6%) Also play less hands when only covered by one of the Blinds compared to symmetric stacks. (Decrease in VPIP of 3.5–6%.) BTN’s range increases only slightly increases by 0.6% when covering both Blinds without being covered themselves (like in the symmetric scenario). Based on these observations, we can see that: In the early to middle stages of a tournament, being covered by opponents has a significantly greater impact on ranges than covering opponents, relative to symmetric stacks. For comparison purposes, let’s look at how average stack depth and overall tournament stage impact our range. Below is a similar table to the one above, but with a 30bb average stack near the bubble when ICM ICM A commonly used acronym for the term independent chip model. ICM is a model that translates the value of a tournament chip to actual cash value, better known as tournament equity. ICM calculations are based on the stacks and payouts of all players remaining in the tournament. pressure is high. 30bb Average, Near Bubble When we compare these spots to the previous examples, we can see that: The overall symmetric opening range when we’re shorter stacked and closer to the bubble decreases by 7.1% . While it’s intuitive that we play fewer hands close to the bubble, it’s worth noting how significant this impact is in a PKO. Because of this, we see less of a change when the Button goes from

equal stacks to covered as we’re playing fewer hands to begin with. The Button now plays significantly more hands when covering both the Blinds , with their range expanding as their chip lead increases. The Button still plays significantly more hands even when only covering the Big Blind and not the Small Blind, as opposed to the inverted scenario (covering SB but not BB). The key takeaway from these two datasets is that: In PKO tournaments, the BTN’s opening range is mainly influenced by your risk advantage . Covering both blinds lets you target bounties and apply ICM pressure. For reference, this is what a 76% RFI range looks like: Adding All-ins Into RFI Ranges Now that we’ve seen some examples of our opening ranges throughout a PKO tournament from the Button, let’s find out when we can consider shoving. Again, we’ll compare similar tournament stages and stack sizes. All-in Frequencies The following interactive chart shows how your strategy changes with stack depth. You can filter the tournament phase: Looking at these solutions, we can see: Except for the first “50% field remaining” example, the Button only uses an all-in open size when they or one of the Blinds has a stack at or below 20bb. When the Button has over 20bb and is covered by one or more players, they have little to no shoving unless they have a significantly below-average chip stack. When all three positions are close in chips, the Button shoves the most when the Blinds face a high risk premium and are both covered. All-in Ranges Now that we’ve seen the frequencies for all-ins, let’s look at how to build our all-in ranges. Below are three examples of the specific portion of our range that expands as we increase our all-in frequency: 1-10% All-in Ranges 1.4% 4.2% 9.2% We can see that our all-in range begins with A9 o and 55 , and expands to include suited wheel aces, 33 – 77 , some suited Ten-x, and additional middling Ace-x. 10%+ All-in Ranges 12.5% 15.2% 23.7% As we expand our range further, we see more of our offsuit Ace-x added in, as well as our lowest pairs and wheel aces Wheel ace Any hole cards that can make a wheel straight. A2 , A3 , A4 , or A5 . . At our widest (covering both Blinds near the bubble), we see a number of suited hands added in, as well as some offsuit connectors. It’s important to note most of our strongest hands prefer to open non-all-in because we want to keep our opponents in with a relatively wide range when we’re ahead. Hands that are not quite as strong are served by going all-in because they want to maximize their equity realization (enticed additionally by the potential of unlocking a bounty). Summary Playing from the Button presents the most opportunity in a PKO but requires some finesse in determining when to expand our range versus when to tighten it up. And when to use all-ins and how to construct that range. We have seen that

due to the impact of stack sizes in a PKO: In the early to middle stages of a tournament, being covered by your opponents has a significantly greater impact on ranges than covering your opponents. Chip advantages have more leverage in high RP spots, particularly when the Button has a significant chip lead. The Button only uses an all-in open size when they or one of the Blinds has a stack at or below 20bb. All-in ranges expand as risk premiums increase when we have both Blinds covered. 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 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… 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

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Delayed C-Betting This is a companion piece to Probe Betting . It stands on its own, but understanding how to play these scenarios from both sides will enhance your overall understanding of the underlying concepts. A “delayed c-bet” means checking the flop as the preflop aggressor, then betting the turn. Many players believe that if they check the flop after raising pre-flop, they have “shown weakness” and must therefore respond stubbornly to any aggression on future streets. This belief is not baseless: by declining to bet, you have not allowed your opponent to fold their weak hands, so they will have plenty of bluffing candidates on later streets. An opponent who chose to bet all of them would in fact be bluffing too often, and stubbornly calling down would be the correct exploitative adjustment. By declining to bet, you have not allowed your opponent to fold their weak hands, so they will have plenty of bluffing candidates on later streets. They are not required to overbluff , however, and it is not correct for them to do so. On most turns, you should expect them to check fairly often, at which point you will be able to value bet more thinly than on the flop. If they do bet, you should rarely raise , as your flop check makes it unlikely you will hold a nutty hand. The opportunity to act with the benefit of this additional information is a big part of what incentivizes checking in the first place. We will examine two examples in greater detail: one where the pre-flop raiser enjoys a large equity advantage on the flop and one where the equity is evenly distributed . Both examples assume a single raised pot, LJ vs BB, in a 100bb cash game, but the general principles discussed here will apply in any situation where a player who had been the aggressor stops betting. A Favorable Flop On an A ♦ K ♥ 8 ♥ flop, LJ has 65% equity and many more of the nuttiest hands in their range. Consequently, they bet 90% of their range, but some hands do not gain terribly much from betting. LJ’s checking range consists of three types of hands: Robust , medium-strength hands like A2 , K6 , and JJ , which gain little from folds and do not perform well in large pots. Extremely weak hands with little hope of improving . LJ sometimes checks 7♠ 6 ♠ but never 7♥ 6♥ and rarely 7♦ 6♦ . This check is not “giving up” – LJ will bluff eventually. These hopeless airballs make just as much bluffing later, to represent a delayed value bet, as they would betting immediately. Monster hands with heavy blocking effects . On this board, that just means AA . Mostly, LJ wants to start betting their strong hands immediately to give themselves a chance to get three bets paid off. Because so much of BB’s range for calling three streets is A x, however, AA doesn’t give up anything by checking because it’s not likely to get three

streets anyway. You can see this effect in the image below, which shows LJ’s checking range concentrated around medium pairs and “ No Made Hand ”. On this board, LJ retains a range advantage on all turns, even after checking. Consequently, the BB ought to check to them quite often, at which point they can bet many of the hands they declined to bet on the flop. Thin Value Bets All this checking serves to promote hands. Essentially, all this checking serves to “promote” hands, making them more valuable than they were on the previous street, even when they have not improved in rank. When LJ checks the flop, BB can reasonably conclude they are unlikely to hold AK , AQ , KK , 88 , and other very strong hands. This incentivizes them to call bets lighter on later streets, which in turn incentivizes LJ to value bet more thinly than they did on the flop. LJ can also bet more thinly after seeing BB check a second time , as this similarly makes strong hands less likely for BB. On the flop, LJ mixed between betting and checking A9 and AJ . If BB checks again on a 4♦ turn, LJ purely bets these hands. However, BB’s second check is not a license for LJ to bet with abandon. In fact, they now have even more incentive to check their most medium hands: QQ , JJ , and TT . This is a common turn dynamic, where players are incentivized to play more honestly than on the flop. Responding to Bets Turn bets from the BB should be rare but large . LJ, having mostly capped their range by checking the flop, rarely raises. The bigger the bet, the more rarely LJ raises. Mostly they are playing a bluff-catching game where the objective is to avoid folding at greater than Minimum Defense Frequency . Facing a 130% pot bet, for instance, they can call profitably with any Ace because it blocks many of BB’s value hands. With lower pairs, they are indifferent or pure folding. Their few raises are almost exclusively slowplayed monsters ( AA ) or turned monsters ( 44 , A4 ). This range includes some counterintuitive calls , specifically the gutshots like 7 ♠ 6♠ which have just four outs, two of which are not even to the nuts. These calls rely on river bluffs for much of their EV. The obvious hands with which LJ would check the flop and then call an overbet on the turn all have too much showdown value to bluff when checked to on the river. Thus, BB should mostly not pay off bets after checking the river, and bluffing with the rare weak hand ought to be profitable enough for LJ to make calling turn with a gutshot no worse than folding. That’s the theory, anyway. It relies on your opponent doing some sophisticated hand reading and disciplined folding to work, and even when it works, it still makes peeling the turn with 7 ♠ 6♠ no better than folding.

As a mixed strategy, this particular decision offers a low-risk opportunity for exploitative adjustment , and you would do well to fold against opponents you do not consider particularly sophisticated or disciplined. The fact that this board is especially good for the pre-flop raiser is not a reason to fight back extra hard against the BB’s turn bet. In fact, it is reason to be wary: this situation ought to be scary for the BB, yet they are shoveling money in anyway. An Unfavorable Flop Medium connected flops help the BB catch up to the pre-flop raiser’s range advantage better than most. The LJ’s strategy here must begin with the acceptance that this was an unlucky flop and they are not going to win the disproportionate share of equity they would on many other flops. Trying to force it by continuation betting at a high frequency anyway exposes them to check-raises from the BB which will deny their equity. For the most part, the best the LJ can do is check behind and hope the turn card is better for them than the flop was. The LJ must accept that this was an unlucky flop and they are not going to win a disproportionate share of equity. Because the turn can so easily improve LJ’s range, they have less incentive to slowplay monsters. What little continuation betting they do comes primarily from sets and straights. Responding to Bets LJ has a relatively capped range after checking, so they rarely raise turn bets. LJ has a relatively capped range after checking, so they rarely raise turn bets. Even facing a small 33% pot bet, raise is LJ’s least used option on all turns. On the worst turn cards, which put four-card straights on the board, LJ folds often enough to give BB profitable bluffs with any two cards, but mostly LJ continues at the Minimum Defense Frequency . LJ’s response to a bet is not significantly more aggressive on the turn cards that are best for them, such as A or K . A s on the AK8 board, the fact that the turn favors the LJ ought to be built into BB’s betting range . BB checks more often on these cards, but when they do bet, their range is strong and LJ has little incentive to raise . When LJ does raise, they do so mostly with slowplayed monsters and hands improved by the turn card. For example, on a 9s turn, they raise not only sets and straights but also A9 , K9 , 98 , and 97 . LJ raises mostly slowplayed monsters and hands improved by the turn. Thin Value Bets Whether LJ value bets more thinly after BB checks a second time depends on how much the turn card helps them. On the 9 s, which does not improve many of the unpaired hands with which they checked the flop, LJ consistently bets strong but vulnerable pairs such as A6 , A5 , and smaller overpairs. They continue to check AA and KK heavily, however, as a

check-raise from a polarized range remains a threat. LJ’s weaker pairs benefit from multiple promotion effects after this action. The combination of the flop check and the blank turn leaves A5 fairly high up in LJ’s range, even though it’s just third pair. Compare this to a K s turn, which improves many of the weaker hands in LJ’s flop checking range. Now A5 is no longer so high in LJ’s range and so never bets. The medium pocket pairs bet less often as well. Conclusion Taking the pot immediately is always nice, but an in-position player can sometimes do better than stabbing into the dark by gathering more information before investing. By checking behind, they get to see the next card and their opponent’s next action, both of which help them value their hand more accurately. Medium-strength hands benefit most from this additional information, so checking weights the aggressor’s range toward such holdings. As a result, they are not terribly aggressive after checking. If the opponent bets, they mostly play a bluff-catching game, aiming to call down at a frequency that makes the opponent indifferent to bluffing and rarely raising. This is not the primary branch of the game tree where the check pays off . Some of your hands will face some tough decisions if your opponent bets into you, and it’s ok to have no good options when that happens. You got unlucky that they bet and unlucky to hold the kind of hand that would face a difficult decision. Sometimes you just have to make the best of a bad situation. It is better to think of these scenarios as the price of doing business, a cost you occasionally pay in exchange for the benefit of getting a lot of profitable opportunities when your opponent checks a second time. If the opponent checks again, as they should do relatively often on all but the most favorable boards, the in-position player now has a lot more leeway to make thin value bets , to bluff into a twice-weakened range , and to keep the pot small depending on what their hand prefers. This opportunity to make better decisions when armed with more information is a big part of what the aggressor buys themselves by checking on the previous street. 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

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Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend to consider how well various candidates will perform when called: Will they be ahead? Will they have good prospects for improving? Will they be good candidates for betting later streets, whether for value or as a bluff? Or alternatively, will they gain so much from fold equity that the hand doesn’t need (m)any of the above points to be positive? But all this taken together is still only half the equation. To be a good betting candidate, a hand must not only be profitable as a bet, it must be the most profitable option. No matter how much a hand gains from betting, that amount must be at least as much as it gains from checking, or else it will play better as a check . That means we can and should ask the same questions about how each hand will perform on the checking node. Will it be ahead? Will it have good prospects for improving? Will it be able to bet later streets, either for value or as a bluff? Will it be in danger of getting bet off its equity on later streets? When the hands you are likely to improve to are modest, the sort that could win at showdown in a small pot but not in a large one, you have more incentive to keep the pot small. This is the essence of equity preservation. It’s not just about taking a free card; it’s about retaining and maximizing the equity of your cards . What Happens When You Check? A check is a choice to keep the pot smaller. Depending on the situation, that choice may be more or less meaningful and so convey more or less new information to your opponents. For example, as the preflop caller in the BB, you will often check your entire range on the flop. This does not convey any information your opponent does not already have, but it is in line with the principles mentioned above: the reason you are checking your entire range is that it is much weaker than your opponent’s and consists mostly of hands that do not want to grow the pot. A check is a choice to keep the pot smaller. If, instead, you were the preflop raiser playing against a BB caller, your check would be more meaningful. As the player with the stronger range, you would see the flop with many hands strongly incentivized to bet. This could be because they are already very strong or are drawing to something very strong. It could also be because they are so weak they have little equity to preserve and just want to bet once to cash in on the fold equity your range advantage buys them. Check When you check, you are telling your opponent you do not have such a hand . More precisely, you are telling them you probably do not have such a hand. Solver strategies usually incorporate occasional deceptive checks, but

not so many as to disrupt the overall pattern. Hero’s checking range should have less equity and be more capped than their betting range. And your opponent should be able to predict that. What can they do with that information? They should be more inclined to bet into your weakened range on the turn than they were to bet into your uncapped Uncapped A range that includes the strongest hands. See: Capped . range on the flop. If they don’t bet, they should call and even raise your bets with weaker hands than they would have called or raised on the flop. In addition to capping and weakening your own range, a check keeps your opponent’s range wider and weaker than their range for calling a bet would be and incentivizes them to put chips in on later streets with a weaker range than they otherwise would. Bet Conversely, when you bet, you make the pot larger against the strongest parts of your opponent’s range while causing the weakest parts to fold. You also give your opponent the opportunity to raise you, which is the typically well understood component of equity preservation. One reason to check is to avoid the risk of getting raised off your equity. The typically well understood reason to check is to avoid the risk of getting raised off your equity. Another but less understood reason is to avoid growing the pot when your hand performs well against the weaker part of the opponent’s range but poorly against the stronger part. A less understood reason to check is when your hand performs well against the weaker part of the opponent’s range but poorly against the stronger part. Flop Examples For these examples, we will consider a single-raised 100bb cash game pot between BTN and BB . Despite a 54% equity advantage, BTN’s equilibrium strategy checks the flop more than half the time: BTN’s flop strategy vs BB on K94 tt (100bb effective SRP) One surprising hand which strictly prefers checking is A ♠ J ♠ . This hand has many properties that make betting appealing: Equity when called . A ♠ J ♠ retains 30–35% equity when called, depending on the size of the bet. Fold equity . Some better hands will fold to larger bets, but even a small bet can push BB off many hands with 15–25% equity. Barreling potential . If BB calls a flop bet, A ♠ J ♠ can easily turn a draw and keep barreling. Nut potential . The outside chance of rivering the nut straight or flush provides a nice consolation prize if BB does not fold to earlier street bets. Despite all this, A ♠ J ♠ never bets. Why? Because most of these arguments apply at least as well to the checking node as to the betting nodes. Equity . A ♠ J ♠ has 49% equity in the checking node, meaning it loses roughly ⅓ of its equity by betting. This is the strongest argument for checking, and we will return to it later. Fold equity . There

is no fold equity on the checking node, of course. But many of BB’s folds are not especially profitable when BTN holds AJ , as they are often dominated Ace-x and Jack-x. Folding out A6 sometimes results in winning a pot that would have been lost to a turned 6 , but it also sometimes results in missing out on bets that would have been won on a turned Ace. Barreling potential . AJ has enough showdown value that it may not need to bluff after checking back the flop. Nut potential . Turning a nut draw doesn’t just make barreling more profitable; it also makes bluff catching more profitable. If BB does bet the turn after the flop checks through, A ♠ J ♠ will have an easier time defending its equity when it turns draws. BB response vs BTN’s 33% pot c-bet Equity Analysis Let’s look at how A ♠ J ♠ compares to some other bluffing candidates in this scenario. The following chart shows how much equity these hands flop and how much they retain after bets of various sizes are called. Unlike A ♠ J ♠, these other hands are all candidates for betting the flop. None purely bet—BTN has very few pure bets in this spot—but they all mix across all the bet sizes. Yet some of them, A ♠ 5 ♥ and 8 ♦ 6 ♦ , lose even more equity than A ♠ J ♠ when they bet. So why are they better candidates for betting? Equity is only a weak proxy for how likely a hand is to win at showdown. In order to realize that equity, a player must navigate later streets to get to showdown without paying too high a price when behind. Some equity is easier to realize than others. Both AJ and A5 lose a big chunk of equity, roughly 15% of the pot, as soon as they bet even a small amount. This is because, in a BTN vs BB confrontation, unimproved Ace-high could easily be ahead. Some equity is easier to realize than others. These hands have a lot of equity locked up in scenarios where neither player makes a pair, but that equity is tough to realize. A tough opponent will often bluff the turn and/or river if they can’t beat Ace-high, presenting BTN with some no-win decisions to either call and risk paying off value bets or fold and forfeit their equity (including the potential to improve on the river). No matter which they choose, they lose most of their value as soon as they face a bet from a well-constructed range . This is less of an issue for AJ , which will have an easier time calling turn bets without a pair after checking back the flop. Sometimes, it will turn a draw, but even when it doesn’t, it has more outs when behind some of BB’s thinner value bets. A5 may struggle to realize equity even when it turns a 5 . Betting is less of a trade-off for A5, which is going

to lose most of its equity no matter what it does . Q ♥ 5 ♥ and Q ♦ J ♥ lose much less equity when they bet because more of their equity comes from strong hands like straights and flushes. Q ♦ J ♥ makes such a hand somewhat less often, but it has more potential for making a decent pair. 8 ♦ 6 ♦ loses nearly as large a percent of its equity as A ♠ J ♠ when it bets. But it has poor equity to begin with, however, so that doesn’t amount to much in absolute terms. Backdooring a straight is a remote possibility. Most of this hand’s equity comes from making a pair on the turn or river, but such weak pairs will struggle to realize equity even after checking the flop . Barreling a Wet Turn Protecting the equity of marginal hands is an even bigger consideration on the turn , when the hand is closer to showdown, so equity is easier to realize on the checking node. Let’s look at how each of these hands play on a few turns after having bet 75% pot on the K ♥ 9 ♥ 4 ♠ flop (we’ll substitute in A ♦ J ♥ for A ♠ J ♠ since the latter would not have bet the flop). Here is how each hand performs on a J ♠ turn , which improves many hands in both players’ ranges (action frequencies may not add to 100% because there are a few low-frequency bet sizes not included in this chart): The best candidate for barreling this turn is Q ♥ 5 ♥ . It has decent equity, and because most of that equity comes from rivering a straight or flush, it sacrifices very little by betting . With this hand, BTN does not mind strengthening BB’s range with a bet because if they miss on the river, they aren’t going to win anyway , and if they improve to a straight or flush, they will win often even against that strengthened range . We gain extra confidence in this hypothesis because of the fact that this hand is even a candidate for overbetting, which will strengthen BB’s range even more dramatically than a 75% pot bet. AJ and QJ , on the other hand, have much more fragile equity . A pair of Jacks holds up better in a smaller pot than in a large one. They lose a lot of equity when they bet 75% pot, but they will generally pay off such a bet on the river after checking behind anyway, so betting the turn and checking behind when unimproved on the river is also an option. They are terrible candidates for overbetting, however, which all but destroys the value of their pair. As for A5 and 86 , they are poor candidates for bluffing because they have terrible equity when called but do actually have a slim chance of winning when they check. A tough opponent will not allow Ace-high to win at showdown, but checking behind

and rivering a pair is a path to victory for both these hands. Overbetting destroys the value of second pair. Barreling a Blank Turn After betting 75% pot on the flop and getting 2 ♣ turn , all these unpaired hands have modest equity at best. Some of them lose more than others by betting again, however: AJ has slightly less equity than the straight and flush draws, but it loses the most by betting, so it bets least often. Its only hope for improving is to make a pair on the river, and that will be worth more in a small pot than in a large one. A5, Q5, and QJ find themselves in a similar situation in terms of pair outs, but because they also have stronger draws , they are better candidates for bluffing. 86 has such poor equity to begin with that it’s not giving up much by bluffing on a turn card where BTN gets to do a lot of bluffing. One pair on the river will be worth more in a small pot than in a large one. 175% pot is by far BTN’s most used size in this spot, and the chart provides some clues as to why. In addition to having many strong hands that want to shovel money into the pot, BTN also has many weak hands like these whose equity when called does not depend terribly much on the size of the bet . Our example hands all do about as badly when an overbet is called as they do when 75% pot is called, so they aren’t giving up much by using the larger size. Conclusion Equity when called is a good metric for determining how good a hand is for betting, but it is only a first approximation. No matter how +EV a bet may be, checking could still be better. You can compare the values of betting and checking with a few simple questions, which will help you determine not only whether to bet but also how much to bet: Where does this hand’s equity come from? If the hand improves, will it perform better in a smaller or larger pot? How well will the hand realize its equity after checking? How much does the hand benefit from fold equity? Keep in mind that the answers could change from street to street! A hand that was not strong enough to bet the flop could still be a good bet on the turn, even if it did not improve. Protecting your equity in this way will help you prosper by squeezing maximum value from your marginal hands. 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

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Attacking Paired Flops From the BB Paired flops present unique challenges to both a preflop raiser and a BB caller. The difficulty of flopping pairs or draws forces both players to bet, raise, and call with hands that have no obvious coordination with the board , plays that do not feature prominently in continuation betting and check-raising strategies on other board types. As we will see, however, “paired flop” is a broad classification that conceals a lot of nuance. The stack depth , the position of the preflop raiser , the size of the pair , and even the size of the third card on the flop all influence optimal strategy in important ways. The Big Picture The following chart shows the BB’s response to a 33% pot continuation bet on paired flops, depending on the size of the pair. The bottom two rows show, respectively, the average response across all paired flops and, for a baseline comparison, across all flops. We can immediately observe a few trends: Relative to a random flop, paired flops entail less calling , more raising , and more folding for the BB. This is true regardless of the preflop raiser’s position and, as we will see, regardless of stack depth. Because defending with no pair, no draw is so difficult, BB folds more often, but also raises more often in order to present their opponent with the same dilemma. Boards with medium pairs are best for raising . Larger pairs – especially Aces–are worse for raising. This is because BB has more 7 s, 6 s, and 5 s in their range, while broadway cards make up a larger percentage of the raiser’s range. Neither player has many of the smallest cards, so while these board pairs are not as bad for the BB as the big pairs, they are not as good as the medium ones, either. BB raises slightly more often against a late position raiser and calls much more often . This reflects the late position raiser’s wider range, against which BB’s many unpaired hands are more likely to be live. Shallower Stacks Comparison to 40bb scenarios, depicted in the chart below, reveals similar trends and some important differences: At 40bb, BB check-raises paired flops somewhat more aggressively in general, especially the lower card flops that were not so good for check-raising at 100bb, but check-raises dramatically less against the BTN on AA x flops. This reflects differences in BB’s preflop calling range. Shallower stacks make for better equity realization when out of position , enabling BB to call preflop with somewhat weaker hands and thus to flop trips more often on low card boards. However, they are more likely to three-bet their A x against a BTN open, making it harder to flop (or represent) trips on AA x flops. With a low SPR, the question of who has more trips becomes less relevant, as any pair and even some unpaired hands can be strong enough to stack off with. These differences are even more dramatic at 20bb, where the BB’s strategy

involves considerably more raising. With a low SPR, the question of who has more trips becomes less relevant, as any pair and even some unpaired hands can be strong enough to stack off with. BB also folds more often with shallow stacks, but this mostly represents an important difference in the preflop action. Unlike at 40bb and 100bb, BTN’s preflop raise at 20bb is to just 2bb, incentivizing BB to call with more weak hands. Thus, they have more weak hands to fold on the flop . Which Hands Check-Raise? The charts above lump together raises of all sizes. When we break down the strategy by raise size, some new patterns emerge, providing insight into which kinds of hands raise and why. Here is the BB’s strategy vs an UTG 33% pot continuation bet on X22 flops, 100bb deep . The numbers on the x-axis represent the third card, so the column on the far left is 222 flops, the next one is 322 , etc., all the way up to A22 on the far right. When the third card is a 5 through T , BB prefers smaller raises. For the lowest and highest third cards, they use more large raises. This reflects the desirability of check-raising when they pair that third card. On a T22 flop, BB can check-raise even a modest kicker like T9 to simultaneously deny equity to overcards and get value from lower pocket pairs . Check-raising 93 on a 322 flop, however, would result in value cutting themselves against those same pocket pairs. And on a K22 flop, denying equity is less of a factor, as there is no opportunity to push UTG off two overcards. Here’s the full strategy for responding to a 33% pot continuation bet on T22 r . Notice how BB check-raises a pair of T s more often than they call them: Hands like T9 benefit from folds and have reasonable equity when called , because of the lower pocket pairs in UTG’s range. The only thing they fear is a three-bet. Fortunately, the risk of running into trips, which BB almost always check-raises, discourages UTG from three-betting . The larger BB raises, the more UTG’s calling range will be concentrated around hands that dominate these weaker broadway cards, which reduces the value of turning top pair after raising. BB rounds out their check-raising range with overcards and backdoor flush draws . On a disconnected rainbow flop, these are the highest equity draws available, the hands with the best chance of drawing out when called by a T or a pocket pair. Note that the lower broadway cards are pure check-raises, while the higher ones mostly call. AK and AQ , which could easily be ahead already, value fold equity much less than QJ , which can make not just better hands but dominating hands fold, cleaning up their equity for turning pairs. A smaller size suits this range well. The protection raises get most of the folds they want even with a small raise, and they welcome the lighter calls

the small raise entices. Hands like QJ and KJ would prefer folds, but they don’t mind inducing calls since they have a fair chance of drawing out. And they do benefit from keeping their risk low when they run into the strongest part of UTG’s range. The larger BB raises, the more UTG’s calling range will be concentrated around hands that dominate these weaker broadway cards, which reduces the value of turning top pair after raising. BB’s strategy looks quite different on 322 r : They mostly call their 3 x, making exceptions only for backdoor straight draws and the strongest kickers. When they do raise, it’s a more polar range consisting mainly of trips for value and many weaker bluff candidates such as a single big card with multiple backdoor draws . Trips, of course, are happy to make the pot as large as they can, and the weaker bluffs are happy to get as many folds as possible, since their equity against the top of UTG’s range is not that much worse than their equity against the middling hands that would be more price-sensitive. The most extreme example of this is A22 r , where those smaller check-raises drop out entirely, and BB’s raising range is almost exclusively trips and low-equity bluffs such as gutshots and backdoor draws: BB’s raises on the same flop are similar against BTN but the sizes are a bit smaller. This is because BTN has more trips in their range than UTG, so BB must raise a bit smaller to target UTG’s one pair hands . The biggest difference between BB’s response to BTN as opposed to UTG is more calling . Against a BTN opener, calling with King-high and even Queen-high is viable. These patterns reveal themselves most clearly when the board pair is low, as neither player is especially likely to have trips (though the BB is more likely). We have already seen that BB raises less in general when the board pair is higher. They also use smaller sizes, on average, as the risk of running into trips from the preflop raiser is higher. But the same principles hold even on higher paired boards. Here’s BB’s response ton a 33% pot bet from UTG when 100bb deep on QQ7 r . They raise a bit less often than on T22 r, but they raise the same kinds of hands: trips, 7 x, occasional lower pairs, and two big cards with backdoor draws: Medium Stacks With 40bb stacks stacks, BB’s strategy vs UTG on 322 r starts to resemble T22 r, with more small , thin value raises . A small raise with trips is less of a sacrifice, as they can get stacks in by the river regardless. Top pair still mostly calls, but there is more room to check-raise medium pocket pairs : Going from 100bb to 40bb does not change BB’s A22 r strategy so dramatically. Their raise size comes down, but that’s mostly because they no longer need to raise so large to get stacks in with trips. There’s

a little more raising from top pair, but their range is still polarized to mostly trips and low-equity bluffs: Shallow Stacks With 20bb , BB does far more thin value/protection raising, even against UTG. The low SPR enables them to treat even a 3 with a bad kicker as the nuts and on 322 r. Their strategy on this flop looks almost identical to the 722 r with deeper stacks, featuring many small raises from a pair-heavy range . BB even slowplays some trips now that building the pot is no longer a concern: BB’s strategy vs UTG on A22 r remains largely unchanged, however: Facing a BTN raiser on the same board is a different story. BB’s raising range is actually still polar, even though it’s much wider: Thanks to BTN’s wider range and the fact that BB had a lot of incentive to shove A x and pocket pairs preflop, BB can raise all their A x for value, balancing those raises with many bluffs. In fact, they have no good candidates for calling ! All their hands are either strong enough to raise for value or so weak they must rely on fold equity. Conclusion BB’s response to a continuation bet on paired flops varies with the stack depth , position of the preflop raiser , rank of the pair on the board, and rank of the unpaired board card . It always involves more raising and more folding than on the average flop, but the composition of that raising range can change dramatically with the circumstances. At one extreme are circumstances where the preflop raiser enjoys an especially large range advantage, which is usually when they are in early position and one or both board cards are highly ranked. In these cases, BB mostly raises trips and low equity bluffs for a large size. As stacks get shallower, it becomes easier for BB to check-raise for thin value. Slowplaying trips becomes more appealing with a lower SPR as well. At the other extreme are boards where the preflop raiser’s range consists of many unpaired hands and contains several pocket pairs below the unpaired board card. This occurs more commonly when the raiser is in late position but can arise even against an UTG raiser on an especially dry flop like T22 r. In these cases, BB raises a less polar range consisting of higher equity bluffs, and thin value/protection raises from medium pairs. They also include most of their trips in this range, making it difficult for their opponent to three-bet them. 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…

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How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (read more about ICM here ) in poker impacts their strategy preflop, especially at shallow stack depths near the end of a tournament. But what about postflop ICM? What do the GTO solvers teach us about playing the flop, turn, and river when at final tables or near the money bubble of a poker tournament? Postflop ICM is a relatively unexplored area of poker research . While preflop ICM solvers have been available for a while and postflop GTO solvers have become more prevalent recently, few players have studied postflop ICM. It is only recently that postflop solvers have become “ICM aware”, so it is just now that we are getting a sense of how ICM impacts your postflop strategy. I am the co-author of Endgame Poker Strategy: The ICM Book , which I wrote with poker pro Dara O’Kearney. It is the first book to take a deep dive into the topic of the Independent Chip Model in poker. I have also recently just released GTO Poker Simplified with Dara, which, as the name suggests, turns some of the biggest postflop lessons from the solvers into actionable heuristics. Despite writing a postflop GTO book and an ICM book, we only briefly covered postflop ICM in either for good reason. The topic is vast . Postflop ICM is the topic of our next project together precisely because it merits a whole book. Dara and I were both very excited to discover that GTO Wizard is launching postflop ICM solutions soon! We have discovered several valuable heuristics about postflop ICM that are broadly applicable across various flops, ranges, stack depths, and payout structures. There will no doubt be more lessons, and in some cases, these heuristics are not universal, but they are frequent enough for me to suggest you use them to help guide your postflop ICM study. Postflop ICM Adjustments The covering player can be more aggressive. Downward drift – big bets become small bets, small bets become checks/calls, checks/calls become folds. Solvers take low-variance lines in ICM. Bubble Factor There is a concept in tournament poker called Bubble Factor which is essential to understand when studying ICM. Bubble Factor is a measure of how losing chips costs you more in equity than winning the same amount of chips gains you in equity. Bubble Factor measures ICM pressure. It’s defined as the ratio between how much tournament equity ($EV) you’d lose getting stacked, divided by how much $EV you’d gain stacking another player in the tournament. Big stacks have low Bubble Factors because they can take big risks without being eliminated. Short stacks also have low Bubble Factors because, while they do not want to bust, they still must be aggressive because the cost of inaction is elimination. Middle stacks have very high Bubble Factors; they want to avoid tangling with the chip leader and risk elimination when they could easily ladder to the money or a bigger payout. A higher Bubble Factor indicates a worse risk-reward ratio on

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

as follows : The preflop ICM calculations The preflop ICM calculations Note – Chip% represents the portion of chips each player controls. ICM% shows the portion of the prize pool each player expects to win, on average. As you can see, the BB covers the BTN comfortably. There is also a micro stack in the CO and a very big stack in the HJ, both of whom are having a significant impact on the ICM pressure in this spot, despite neither being in the hand. These are the Bubble Factors going into this hand: Examining ICM solutions can be confusing. A helpful approach is to compare the same situation in both ChipEV and ICM scenarios. This can aid in internalizing ICM. By using ChipEV spots as a reference point and then comparing them to ICM spots, one can better understand the adjustments made in ICM. Preflop ranges comparison Before we look at the postflop lines, let’s take a look at the preflop ranges. This is the BTN opening range: And this is the BB defending range: In the following example, we are using the same preflop ranges in both ICM and ChipEV examples in order to identify the strategic adjustments that ICM compels us to make. However, it is important to note that the preflop ranges would be different in the first place. ICM ranges are tighter on average, and you will see less 3-betting. ICM preflop ranges will be more weighted to suited high card Ax and Kx hands, with fewer small pairs and small suited connectors. Suited Ax type hands serve both as blocker hands to take down more pots preflop and they also make very strong hands by the river. Small pairs do not realize equity well when under extreme ICM pressure, so they are folded more often. You also see less 3-betting in ICM spots preflop. Hands like TT and 99, which are easy BB 3-bets for value in ChipEV spots, are played more often as flat calls in ICM spots. However, we are making an “Apples to Apples” comparison for the following example, so let’s continue with identical ranges. Postflop lines comparison Now, let’s look at how we play the flop in both scenarios. A reminder the flop is A ♣ 8 ♦ 3 ♠ . On this flop the BTN has a significant range advantage, with 63% equity compared to the 33% of the Big Blind. Ax is a bigger proportion of the BTN’s range and he has the strongest Ax, including AA. The Big Blind has some Ax but most of the time misses the flop completely with a very wide range. As such, in both the ChipEV and ICM example, the Big Blind checks 100% of the time. Here’s BTNs c-betting strategy in the ChipEV model: The BTN has such a strong range advantage that they bet with 100% of their hands, mostly for a small size. There are, however, some medium and big bets too. AA always favors the smaller bet sizes because it blocks the Big Blind’s calling range, but hands like