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This trend continues at 5bb : The shape of the shoving range is based on the raw equity of our hands , which is why small pocket pairs have come back into the range and suited K x hands have reduced. Now the only action our hands take is to shove or fold. We don’t want to min-open, then have to fold to a 3-bet and lose 25% of our stack. Shoving means a maximum gain when we are called, and win, and also makes it more likely we take down the pot preflop. We add 31.25% (1.5 blinds and 1bb ante) to our stack whenever we get everyone to fold preflop, which is very profitable. This is why our range has increased. We play 20% of hands now, compared to 16% in the last example. We play almost 25% of hands, because taking the hand down preflop would increase our stack by 50%. When we get down to 2bb : Now we play almost 36.5% of hands. It would be an amazing result for us if we could take the pot down preflop, but that should never happen. The reason why this range can jam so wide is because the rest of the table is incentivized to call us so wide. The BB, for example, would call with 100% of hands. Therefore the top 36.5% of hands would be profitable against a 100% calling range. Conclusion We have seen today that the impact of stack depth on strategy does not follow a linear progression. Sometimes we widen our range when a stack gets shallower, sometimes we tighten the range. Below, we graphed the percentage of hands UTG plays based on the 21 stack depths between 100bb and 2bb available in GTO Wizard . As you can see the overall trend is for the range to get wider, but between about 35bb and 8bb there are two stretches where the range gets tighter. It may not come as a surprise that the range starts to get tighter around 35bb , this is notoriously a tricky stack depth to play in MTTs – not deep enough to have many options, but too deep to simplify your decisions by playing shove or fold. As stack depths get shallower , stack-to-pot ratio Stack-to-pot ratio (SPR) The effective stack divided by the size of the pot. SPR is commonly used to gauge the value of implied odds and the relative value of made hands. and pot odds Pot odds The ratio of the size of the bet a player is facing in relation to the size of the pot. For example, a player facing a half-pot bet can call risking 0.5 to win 1 (the pot) and 0.5 (their opponent’s bet), and therefore is being laid odds of 3:1. They need 1 / (3+1) = 25% to break even on a call. A common misconception is that the player facing the bet needs 25% equity, when in fact they need to win 25% of the value of the pot. If that player could face future bets

Hand Range 337: No x/r allowed • Bet Full Pot 15% / • Bet 2/3 Pot 14% / • Bet 1/3 Pot 15%/ • Check 56% [0-1] Toy Game Example B If the Villain is allowed to x/r against the 1/3-pot bet-size, they can leverage the information Hero is giving to take advantage of Hero’s range construction. So, Hero immediately adjusts to never use that bet-size and QQ will shift entirely to the 2/3-pot bet-size (Hand Range 338).

and just had like a a king 10 type hand he might make a hero call uh thinking that poker gypsy could have could be betting bricked spades so i think i would have gone for value um verse jackoff i don't think the poker gypsy has to worry about um like but like uh sets here um because i think a set would have raised either the flop or the turn so i think poker gypsy missed out on a little bit of value here all right so let's take a look at a hand between the poker traveler and landon tice so it looks like landon decided to straddle under the gun to 20 i'm sorry decided to straddle 225 and poker traveler under the gun makes it a hundred and five dollars with pocket queens here so folds around to landon and landon decides to make the call with seven four of spades defending his straddle i like it especially considering that they are super deep uh landon sitting with with 4k poker travel has over 10k uh so i like landon's defend here um to poker traveler so uh eight six two spades kind of a fun flop for for uh landon uh if poker traveler had c bet uh i think lennon has a decision whether or not he's gonna check raise or check call he's certainly not going anywhere with his flush draw and gut shot um i think because the fact that poker traveler can represent a lot of the kings ace king king queen king jack king 10 maybe king 9 suited um i think that because of the king on the board uh there is argument for landon to just check call if poker traveler had c bet um if this was like uh let's just say if this was eight six deuce with two spades i like uh a check raise on landon's part if poker traveler had bet because uh then the the texture of the board isn't threatening versus the under the gun range because the under the gun range can have a lot of broadway combos that miss the flop and and landon can certainly represent uh the range advantage there if it was eight six two three six eight six three um so i think check raise for landon uh with a lower flop and a check call with the king high flop um but this is all moot because poker traveler checked back the flop just speaking in you know hypothetically so eight of spades or eight of hearts on the turn here i think if i were landon i would like a lead here uh to me it looks like poker traveler is aware that this is a pretty good board for the big blinds range in which he is trying to keep the pot small um i also think his hand is a little transparent i think uh it certainly does look like poker traveler could have a ham like pocket nines tens jacks queens

Minimum Defense Frequency (MDF) The minimum percentage of your range that must be defended against a bet to prevent the opponent from profitably bluffing a 0% equity hand. Inversely related to alpha; MDF = 1 - alpha. MDF = 1/(s+1) where 's' is the percentage of the pot that is bet. For example, if villain bets half-pot, hero needs to defend 1/(0.5+1) = 66% of their range in order to remain unexploitable against a pure bluff.

Flop and turn were clear value bets. Hero could of course consider going for three streets here, but

IP EQB: 57% strong hands, 37% good, 5% weak and 1% trash BB EQB: 7% strong, 12% good, 0% weak and 81% trash. This situation is commonly known as way ahead or way behind because your opponent will either have a monster or little to nothing, without much in between. In this set-up, IP wants to check back the flop with many good hands for pot control, alongside a big chunk of strong hands as traps. IP also wants to c-bet all trash hands and most weak hands, balanced with the remaining strong and some good hands. This allows IP to often win the pot uncontested on the flop with trash while being able to bluff-catch effectively on future streets after checking back the flop. When facing a x/r, you should always consider your opponent’s range and your hand vs range equity. If the Villain is likely to x/r the flop less than equilibrium suggests, they will probably be missing the optimal bluff. Their range will be heavily skewed towards strong hands and your overall equity will be a lot lower than you would expect it to be. If that is the case, you can exploit the Villain by over-folding the flop. Even if they bluff you once in a while, their frequencies are so far off to the point that it is not worth the risk of continuing with middle strength hands. Depending on the Villain, you can even lay down some strong hands you would never consider folding against someone else. If Villain’s range is skewed towards draws, then you can 3-bet aggressively with your good and strong hands that can benefit from protection. If the Villain’s range is polarized to strong hands or bluffs, your range will play better as a bluff-catcher. Let them keep putting money in with bluffs and don’t raise back with medium strength hands. IP C-bet Examples Flop Strategy Example 1 High c-bet % and big bet-size: BB vs UTG on A♥Q♦3♠ (40bb)

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

of second and third pair so and i can just tell you you can take my word for it like we're gonna have a queen about the big blind and the button are gonna have a queen about equal percentages of the time so if we have a queen about the same amount of time as the big blind okay and they have a seven and a six way more often than us because we don't raise all the sevens to sixes we're at a kind of like we still have a range advantage here but we don't want to bet all the time because we're just losing this seven and six war so you see here we're checking 46 percent of the time why because we don't have all these awesome sixes and we don't have all the offset sevens if i weight them like we're kind of missing most of these offset sevens but the big blind has every offset six in every offsuit seven so you guys see how i'm starting to put this together to learn post flop play so let's take it a step further okay so let's say it goes check big blind checks why do we have the range advantage because we raised like we have a much like we have all the top of the range we probably have like 55 equity on this sport so we're going to say we bet you know they check we bet you know like let's say we bet two thirds who cares on queen seven six that's not the point of this they call let's say the river card is the turn is the jack of hearts okay say that they check let's say we bet okay let's just say we bet whatever the big one calls and let's say the river is the ten of spades okay actually let's say the river is the uh they call i'm just making up a random example cause i don't care the river is the ace of clubs all right let's say the big blind checks i'm not going to show the imposition strategy the big blind checks okay as the imposition player uh and the employee position player shoves how do we know what ranges if any of our opponents are playing you don't but you got to make the best assumptions you can and like probably using these charts are a better assumption than whatever guesses you could think of okay so big blind checks uh big blind checks and all right so someone says it's a better run out for the button yeah of course it is the better run out for the button we got that part when the button shoves what are the worst cards for the big blind bluff catch wit what are the worst cards for the big blind bluff catch with on this run out they check big blind shoves what is the worst cards to have in your hand to what are the worst like ranking of card to have

. If your hand can profit from all your opponent’s bluffs plus a few of their value bets, that will be a solidly profitable call, barring extreme blocking effects. You block value bets and/or unblock bluffs . Because the cards in your hand are hidden information to which your opponent does not have access, they can give you important clues as to which hands they are more or less likely to hold. A player may have a perfectly well-balanced range in theory, but your unique knowledge of your hole cards can nonetheless enable you to conclude they will be weighted toward bluffs or value bets because of what you know they do not hold. Blocking effects are often marginal, but especially on flush and paired boards one or two key cards can block large portions of an opponent’s range. Below is the BB’s strategy facing a third, 85% pot river bet in the scenario discussed above with the A ♠ T ♥ 3 ♠ 8 ♣ 2 ♣ board. A few key things stand out, related to the points above: BB never folds two pair or better . These hands profit from all of UTG’s bluffs plus some of their value bets, making them solidly profitable (as opposed to indifferent) bluff-catchers. BB sometimes folds top pair despite sometimes calling with second pair . In other words, they do not choose their bluff-catchers based on the rank of the hand, because some of their folds are ranked higher than some of their calls. Rather, these calls are chosen based on their blockers. Example #2: After the Turn Checks Through We can observe how dramatically prior action affects river strategy by keeping the early street action and the river card the same and changing only the turn action. When, instead of betting 75% pot on the turn, UTG checks behind, we see much more aggressive river play from BB . BB’s betting frequency is still roughly 50%, but they now prefer larger bets, including some overbets, rather than a 10% pot blocking bet. This is because different turn action leads to completely different range dynamics on the river. In this case, BB’s range is not only more polar but simply much stronger across the board than UTG’s. As a result, it is BB who has the most incentive to force money into the pot. Different turn action leads to completely different range dynamics on the river Below is the equity graph on this river after the turn checks through. Notice how the BB’s blue line hovers well above UTG’s for all but the weakest hands in their ranges; this is why they now prefer to force money into the pot, and why they cannot count on UTG to bet nearly as often when checked to. However, these few strong hands are strategically significant, as the risk of running into them constrains BB from check-raising with abandon. This reduces the risk for UTG of re-opening the betting with small value bets. Even so, UTG needs a fairly strong hand to bet for value: not all

It may also occur that the players’ strategies alternate back and forth and never converge to an equilibrium. In this case, the equilibrium can still be found by making slight changes in the players’ response. Instead of switching all the way to the best response on each iteration, each player can adjust their strategy one step at the time in that direction. The Nash Equilibrium In the poker world, GTO (Game Theory Optimal) is often used as a synonym for Nash Equilibrium. Nash Equilibrium is a set of strategies where: ♦ Players are clairvoyant: each player knows every other player’s exact strategy. ♦ All players are maximally exploiting each other simultaneously. ♦ No player can unilaterally change their strategy to improve their own expectation. Equilibrium strategies are maximally exploitative when played vs an unexploitable opponent, so they inherit all the properties of MES, which are: ♦ Individual hands are always played in the most profitable way possible, and so GTO play never involves playing a hand less profitably than it should be played for the sake of balance. ♦ Strictly dominated strategies cannot be a part of a Nash Equilibrium, as it is irrational for any player to use them. ♦ The only way a hand can be played in more than one way at the equilibrium (mixed strategy) is if multiple strategic choices have the same EV. The following are Nash Equilibrium solutions (generated with HRC) for the previous example when playing heads-up with 10bb stacks where pushing and folding are the only options (Hand Ranges 23 and 24).

Effective stack The maximum amount any player can risk in a hand. In 2-player situations, this will always be the smallest of both players' stacks. In multiway situations, there are more than one combination of effective stacks.

games. Number of players. 34, the two blinds and maybe one or two callers. With few hands dealt, high cards and high pairs increase in value. Opponent's playing style. Predictable and passive. Pre-flop raises are rare and usually mean a high pair or A, K. Bluffing is rare. If you are going head-to-head at the end against someone hoping they've bluffed, you are going to lose. Most lmportunt Factor: Position. Since players are predictable in these games, there is a lot of information available when you have an advantageous position. Acting after a solid player, who only bets strong cards, means that you know the strength of their cards before making a decision on your hand. 84 THE INTELLIGENT GUIDE TO TEXAS HOLD'EM POKER No action on your best hands. You tlop a monster boat :~nd gcr no callers. Your highest ranked hands of the playing session 11iay gcncrate little income. Blinds can whittle away your chip pile. Pots are so small they often don't generate enough income to replenish your blinds. A big win to get yourself firmly in the black is hard to come by. Worse, if you fall behind, it is hard to catch up. A Common Mistake: Becoming too tight yourself. With so little money in each pot, there is a temptation not to bet your moderate hands. It is common in these games to see head-to-head play where no bets are made. The two players check to each other while the dealer runs the rest of the cards. Their thinking is, why risk anything for such a small pot? The problem is, you will not make money with this kind of passive play. If you have a decent hand, bet. Strategv : Make little wins add up. The key is to counter the general passivity with careful aggression. "Careful" is a strange adjective for aggression, but you need a good poker sense to know when to be aggressive. Because the players only play good cards, unrestrained aggression will not necessarily intimidate them. But if you establish yourself as a tight player by being in few hands and showing good cards early on, whenever you sense weakness or hesitation from the opposition, go for the pot, even if it is small. You have to steal a few small pots in these kinds of games or you will never cover your blinds. Knowing how to play your position is key. It is risky to bet ahead of tight players when you have marginal cards. If you act first and bet a marginal hand and a rock solid player calls or raises, its time to fold. STRATEGIES 85 However, if you hold the same marginal hand in last position and the rock solid players check to you, a bet often wins the pot outright. In both these cases your cards may be the same, but your position determines which play is profitable. Typically in tight-passive games, there is not much money on the table. An extreme tight-passive player buys-in for the table minimum and guards the chips, putting money in

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

interested in running their own calculations. Pros ♦ Does not require installation or sophisticated computer requirements ♦ Offers carefully crafted high accuracy GTO strategies developed by experts using the most advanced private and commercial GTO solvers ♦ Easy to use, with sleek and intuitive user interface ♦ Real time advice, so no need to wait for calculations to complete ♦ Large solutions library that grows over time ♦ Multiway pre-flop and post-flop solutions ♦ Requires minimal user input ♦ Rake adjusted cash game solutions ♦ Advanced post-flop analytics Cons ♦ Fixed bet-sizes ♦ Can’t calculate exploitative strategies against weak players (the program only provides a GTO core strategy) ♦ Limited to precomputed GTO solutions, so users cannot make custom calculations Modern Poker Theory and GTO Poker teamed up to offer you a special gift. Please visit (gtopoker.io) and scan the QR code included in this book to get access to a full free month of GTO Poker. I discuss all these tools and teach you how to use them in my training video series available on D&B Poker at dandbpoker.com/book/modern-poker-theory

Hand Range 136: UTG 15bb • Raise 2x 14.1% / • Fold 85.9%

Hero, having read Chapter 7 of this manual and then fired up a poker session has the required equity procedure down to a tee. He reasons as follows: "Well Villain has bet just over half pot. My milestone RE for calling a half pot bet is 25% so I must need just over 25%, maybe 27% or so to call here. Villain should be c-betting all of his air here, so it's very likely that I have easily more than 27% equity vs. his range so I call." This is great reasoning... or at least it would be if villain's 3BB flop bet was all-in. Hero would need just 26% equity to call this c-bet and vs. an opening range of 50% of hands where all of that range c- bets he'd have 48% equity, again, if Villain were all in on the flop for the amount of this bet, then this would be a an end of action spot and Hero's call would be fine. The problem is that Hero is still very far away from showdown and his prospects on the streets between now and then are very poor for a number of reasons listed below.

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

barely +EV chasing call or semi-bluff shove when he picks up a flush draw to go with the gutshot. We can say that Hero has just 8.5% equity that is realisable at no extra cost. 2. Pot Odds are bad. Hero will need to call 7BB into a pot of 9.5BB. We can actually use our method for finding required equity in end of action spots (see here in Chapter 7 for a recap) to determine how often Hero needs to get there on the turn in order for calling to be okay based on pot odds alone. Note we cannot calculate how much equity we need in the hand overall as this is an open action spot and calling this bet does not guarantee us both a turn and river card at no extra cost. Also, the pot odds we get to try to hit the next card do not reflect the full story. The other factors may make the situation better than pot odds suggest. Assuming that Hero had none of these other factors in his favour, i.e he had no implied odds or future fold equity in the hand, he would need to improve ATC / (ATC + TP) % of the time on the turn to profitably call the flop bet. This makes sense as the situation would in essence be the same as that of an end of action spot when simplified in this way. Hero faces a bet and he will win X% of the time and lose the rest of the time due to whether or not he turns one of his outs. This is of course an open action spot, but for now we're ignoring the prospect of Hero's implied odds and future fold equity in order to focus on pot odds alone. If they justify a call then folding is out of the question before we even get to the next factors. Amount to call (ATC)= 7 Total Pot (TP) = 16.5 Required Realisable Equity (RRE) = ATC / (ATC + TP) RRE = 7 / (7 + 16.5) = 29.7% With only 8.5% of turns giving Hero the hand he wants, he is very far away from having the direct pot odds to call. However, this doesn't automatically render the spot a fold because this is an open action spot where implied odds, future fold equity and position are also relevant. Do we have enough of one of these or perhaps a combination of all three to make up for the insufficient pot odds? 3. Implied Odds are not great here. It is certainly true that Villain is rarely folding at any point in the hand and this does guarantee us some decent average payout frequency when we turn our straight. The problem is that Villain's stack is not big enough to generate enough of a reward on the rare occasions when we do get there and our price to call is on the expensive side. As we did when calculating whether we have implied odds to set mine pre-flop, (See Section

If this passive player was to make such a large raise size, or even a smaller one with standard 100BB stacks, Hero would be rather terrified to say the least. The all-in shove however usually sends an entirely more welcoming message. While the raise with deeper stacks from this player type typically means something to the effect of: "I have the nuts and am terrified you might suck out on me The all-in with the shallower stack often says: "I have a pair and or a draw, or possibly a big hand, but I may as well just shove because it's all going in anyway." The shove is far more depolarised and is not weighted towards hands that crush us. The large raise with deeper stacks is a sign that 88 is crushed way too often and is very rarely better than a coin flip.

vs SB’s locked 50% pot c-betting strategy Overall, BB’s folding range has increased significantly from 33% to 50%. For me personally, calling too many hands against recreational players was one of my most persistent leaks because folding so many hands felt very unnatural. 5) Studying All by Yourself This mistake cost me the most money in my poker career. For the first 5-6 years, I studied all on my own. I watched coaching videos and worked with many tools (solvers weren’t even invented back then). However, my development was very slow. Six years later, I was still playing low stakes, making a couple of hundred bucks as a side hustle. It’s not bad for a young student, but there’s so much more potential. It is no coincidence that most successful players at mid and high stakes have a core group with whom they study, create concepts, try things out, etc. I’m not saying that it’s impossible to be successful on your own, but I truly believe it’s much harder and will take more time, which, in the end, will be quite expensive. I recently watched a YouTube video about the rise of the most successful YouTuber, Mr. Beast. When he had around 10k subscribers, he sought other YouTubers to collaborate with. He found 5 other small YouTubers, and they started working together. For 1000 days, they met every day to collaborate. They learned from each other’s mistakes and implemented and tried out new ideas. This way, they all multiplied their learning curves. After that period, all 5 of them had over 1 million subscribers on YouTube. We should learn from this. But where can you find like-minded people to study with? Well, you’re already there. The GTO Wizard Discord group is an amazing place. You can post spots, ask around for study partners, and more. You can also check out my Spin and Go community, Team Bas Poker . Every motivated player who wants to improve their skills is more than welcome. Conclusion Embarking on a poker journey can be a challenging yet rewarding endeavor. As we’ve explored the top mistakes to avoid in Spin and Gos, it becomes clear that continuous learning and adaptation are key to success . Whether it’s revizing your strategy when picking up new game formats like Spin and Gos. Or adjusting against different types of opponents, refining your approach to c-bets, or recognizing the value of collaborative learning, each step forward is a move towards becoming a more skilled and versatile player. Remember, you’re not alone in this journey . Communities like GTO Wizard and Team Bas Poker offer invaluable resources and support for players eager to elevate their game. By avoiding these common pitfalls and embracing the power of community and consistent improvement, the path to poker excellence is well within your reach. Wizards, you don’t want to miss out on ‘Daily Dose of GTO,’ it’s the most valuable freeroll of the year! We Are Hiring We are looking for remarkable individuals to join us in our quest to build the next-generation poker training ecosystem.

quite 100 and on the flip side because the big blind simply called the Rays pre-flop it's unlikely that he has a hand like Aces or Ace King but very likely he has a hand like pocket fours So based on this which player is more likely to hold the strongest hand well right below these grids are bar charts which categorize all the possible hands from above into classes by their strength so in this case the button has a higher probability of holding a set two pair over pair and top pair and when the opponent is much more likely to hold the strongest hand particularly when we're out of position playing passively overall will usually be warranted which is graphically depicted by this last row this row shows how often the big blind should be taking each possible action in this scenario so in other words in this spot button versus big blind in a single raised pot on a king seven Deuce rainbow board regardless of the big blind's specific holding he should be checking 100 of the time now let's move on to the button's decision after the big blind checks as we just established the button has a much higher likelihood of holding the strongest hand what about the likelihood of the big blind holding a weak hand well it's significant the big blind has an over 40 percent chance of holding a hand that is weaker than ace high the combined effects of these two Dynamics means that the buttons should be leveraging this probabilistic advantage to play very aggressively in this case betting nearly 100 of the time including with virtually all bluffing candidates now let's assume that the button bets small here the big blind calls and the turn is the Queen of Diamonds and the big line checks again now we're looking at the hands both players are likely to have on the turn based on the pre-flop and flop action and at each and every decision point we start our analysis all over again so who is more likely to hold the strongest hand well it's still likely to be the button because he's more likely as the pre-flop aggressor to hold Aces kings queens and king queen both suited in an off suit but as to the likelihood of the big blind holding a weak hand the answer has significantly changed from the flop because the big line called the buttons flatbed it means that the likelihood of him holding complete trash on the turn is much lower because he should have folded most of his air on the Flop accordingly overall the frequency of how often the button should continue barreling on this turn is also much lower which means we now need to move on to the next stage of our analysis to determine whether we should Bluff our specific hand but before we do that let's pause for a moment to sum up the first stage of our bluffing analysis by creating a general heuristic if and

hand. Example No. 1. You pick up A♥ Q♥ in early position. The blinds are $50/$100, and you raise to $300. One player in late position calls. The pot is now $750. The flop comes K♦ 9♥ 4♣. (With one card in your suit). Should you bet, and if so, how much? Answer: A continuation bet of $350 to $400 would be a good , move here. It's possible that the king hit your opponent's hand, but more likely it didn't. If your opponent called with a hand like a pair of sevens, he may see the two overcards on the board, realize that his chance of improving on the next two cards is very slim, and throw away the best hand. A continuation bet is a kind of semi-bluff. It's a move which can work in several ways. You may have the best hand, and the bet builds the pot. You may have the worst hand, but the bet ' chases your opponent away. Even if you have the worst hand and your opponent correctly calls, the bet may cause him to check on a later round, giving you a free card. For a continuation bet to be a profitable move, the amount of the bet has to be carefully chosen in comparison to the pot. In essence, you are hoping to buy the pot right now. If you overpay, you'll lose too much money when your opponent calls with a hand better than yours. If you underpay, you'll be offering your opponent correct pot odds to stick around with a drawing hand. Neither situation is good, so the exact amount of the bet is very important. I like my continuation bets to be about half the size of the pot, a small enough amount so that I don't lose too much when I'm called, while still being large enough to chase out a lot of drawing hands. When you bet half the pot, you need to win only one-third of your bets to break even. At the same time, you're not giving great drawing odds to your opponent. Suppose you bet $100 at a pot of $200. From your opponent's point of view, he would now have to put in $100 to call a pot of $300, so he's getting only 3-to -1 on his call. Most drawing situations need better odds than that. Why not bet a little less to get even better odds? If you made a continuation bet of, let's say, onethird of the pot, you'd need to win only one time in four to break even. But now you're offering better calling odds to your opponent (4-to-1 on their call), so many players will now call your bet. On the other hand, if you bet more money to chase people out, you'll lose too much money when you actually are called. Betting about half the pot is a balanced play which gives you the best risk-reward ratio in most situations. Remember, however, that as with all other bets, you must conceal what you're doing from your

Hand Range 188: SB vs BN 4-bet (25bb) • Call 58.2% / • Fold 41.8%

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…

best hand the majority of time and i have a lot of threes whereas they both have very few i realize brock over here in the low jacket usually have ace three or pocket threes small blind could have it but probably not we can have pocket threes or eight three but that's it so i think it's a pretty nice spot to go for a bet and i don't think we need to bet all that big because i'm really only betting here with like very high equity draws made hands that are almost certainly good like this and a lot of threes i bet brought calls rivers of ten interesting spot um we have some draws of course they would love to go for the bluff on the river the opponent definitely has a lot of ace x right could even have some under pairs that decided to get splashy against the small river bet so i think we need to go for a bet i think we can go pretty small when you're out of position you often can go for small blocking type bets with a range of a lot of marginal made hands some nuts some bluffs i think that's the spot it's pretty clear marshall made hand the alternative play is to go big like 50k if i get the vibe as just like a lot of ace king ace queen etc he could just have a 10 which would be a bummer um i think either play is fine either small or big depending on what you want to do depending on read you have on your opponent the problem with small is that every once in a while he's just going to try to blast us i had not played with brock all that much but he's seems to be winning lots of high stakes tournaments i presume he can get after it i did go for the small bat and i think this is probably ideal and i think i would just not even have a big bet size here because i realize my range needs a lot my small betting range needs a lot of protection meaning i need to have a lot of threes here i think i think small bet with everything's good in this scenario he decided to pony up and blast me up to 80k very weird spot because i know i have the threes right so if i have the threes i'm just very well protected because i have a lot of threes and that's basically none hmm he has basically no threes would this player who i don't really know just good kid would he drastically over bluff here into a range that contains a lot of threes i don't know in a spot where he doesn't have very many threes right would he presume either correctly or incorrectly that my small bet range contains almost no threes if that's the case some people will just decide i don't think you have it i'm raising if

if you aren’t already beaten, you may be called by a strong draw and drawn out on or pushed offyour hand later. If you just call, then you allow any of the three players behind you either to raise (forcing you to fold) or call cheaply, leaving you out of position with a

Diagram 94: BB vs BN The BB’s folding range is composed mostly of trash, so the BB’s total number of trash hands is the main factor when determining their overall folding frequency. Diagram 95: BB vs UTG

Heads up When there are only two players at a table playing against each other.

Young How we learn by Benedict Carey A mind for numbers by Barbara Oakley Make it Stick by Peter Brown GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Barry Carter Barry Carter has been a poker writer for 16 years. He is the co-author of six poker books, including The Mental Game of Poker , Endgame Poker Strategy: The ICM Book , and GTO Poker Simplified . Latest article 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 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

We can gain fold equity on the turn or the river where the board texture is likely to worsen for our opponent's calling range. That is to say where scare cards are likely to come down. As if you didn't have enough already, these are two more things to think about when deciding whether or not to make a light c-bet. As this factor is less important than the others that we've covered so far, I'd recommend reserving its use for spots that seem relatively close, especially when you're just getting used to applying the thought processes in the manual. Let's look at a couple of examples. Poor Future Street Prospects This spot might be a fine c-bet in some situations, but it's certainly not due to future street prospects being half decent. This hand fails on both accounts to give hope for later streets. First, it never turns any more equity to aid the firing of future bluffs and secondly, when Villain calls this flop, he likely holds an A or a K quite frequently. Villain's SDV would therefore be stable. There just aren't many turns that are perceived to improve our range. That's not to say that no one will ever fold on the turn here, just that it's less likely especially when we're up against Fish. We shouldn't be bluffing Fish on multiple streets anyway unless we know something specific about their game that leads us to believe that it's a good idea. Good Future Street Prospects

30 big blinds right suppose we do go all in you can click this button right here here's how the cutoff should respond they should Now call with the best hands fold everything else okay but you do see this is a scenario where we are opening very very wide pre-flop which is what I wanted to show you primarily is that when we are going to be raising pretty wide when we get three bet we do have to stick around a decent amount let's say we do raise minimum let's suppose now the cutoff folds and now let's suppose the button goes all in mostly with this range this is the short stack for 15 big lines they should have 15 big lines now here's what we call off with in this situation pretty tight calling range I think for 15 big lines in most people's eyes but it is usually what we're going to want to do in this scenario because we just don't want to find ourselves calling off against a range that should be kind of strong okay let's go back and look at this spot one more time suppose we raise minimum cut off folds notice they are folding a ton notice the button folds they're folding a ton now the small blind the big stack is here with 45 big blinds notice they actually don't do much three betting at all the three bat Almost Never say why are they three betting almost never well they really really don't want to go broke against us and when they do three bet it's almost always with the asex and King X suited blockers say they do actually free bat here's now our strategy we with 60 big wines really don't apply a whole lot of aggression either if we do shove it's literally only with Ace King offsuit and a few low suited asex suits or a few asex students and if we do shove look they have to even fold out stuff like eights and fives and Ace queen against their shove knowing they're going to be very dominating us or they're going to be dominating us right because if they have Ace queen and I just literally announced them I have Ace King and a bunch of low asex students you may be surprised to see ends like nines and eights and sevens folding because they are going to be dominating us or flipping every time but they cannot take the risk of busting before these other shallow stacks let's take a look at a different scenario now um let's take a look at this one here we have 25 big lines in the hijack 30 in the cutoff 10 in the on the button 40 in the small blind and 15 in the big blind what I want to know is what happens when they fold around to us with the big stack and the small blind well you see here when they fold to us with a big stack and the small

Hand Range 288: UTG 15bb (2x vs HJ All-in) • Call All-in 45.7% / • Fold 54.3%

Table 32: Variation of Results with a Wide Spread in Buy-ins In both situations the player invests approximately the same amount of money and has the same EV, but the probability of loss is 10x larger in Situation #1 when they play the schedule with a wide spread in buy-ins and can experience swings from -$262,000 to $1.4 million, while their worst possible run in situation #2 is only -$36,000. I learned this the hard way in 2016 when I had my worst downswing ever. I won approximately $60,000 over the course of 2,000 mid- stakes online MTTs, but lost $120,000 playing fewer than 200 high stakes MTTs, including the $10,000 SCOOP High ME and the $5,000 WCOOP ME when my ABI was $103. Losing just those two tournaments cost me 150 buy-ins! (Ouch!) Table 33 displays actual results for real online players and their respective stats so you can see the correlation between the results and the different metrics. The data is taken from sharkscope.com. Table 33: MTT Results of Some of the World’s Best Players Ability is a rating developed by SharkScope. It goes up to 100 and shows a player’s ability based on an assessment of all the other statistics. Early Finishes refers to the frequency a player has finished in the bottom 10% of tournaments, and Late Finishes refers to the frequency a player has finished in the top 10%. Player 1 is arguably the best online MTT player in the world. After 21,000 MTTs played, he crushed the highest stakes with a 50% Avg ROI, for an astonishing net profit of $2.6 Million! Players 2, 3, 4 and 5 crush the high stakes and are also among the best players in the world.

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

When Hero's competition is weaker he expects to profit by getting into more post-flop scenarios than usual. Hands that struggled to turn a profit at an ordinary table from UTG can quickly become lucrative opens when there are bad players to exploit. So now that we know why we're opening from this seat, let's go ahead and look at our default opening range from UTG. The following range assumes that there are no very aggressive Regulars attacking our opens from this spot by frequently re-raising and no Fish that we're targeting in the blinds. Every default range in this chapter is intended for an average low/microstakes game without conditions of this sort. As mentioned earlier, these ranges are beginner friendly and more competent players can get away with opening wider than advised here. Figure 5 - UTG Default Opening

you checked. This block-bet may even have a negative showdown EV and still be the best play. This is why you’ll sometimes see solvers block-bet OOP with value hands that have less than 50% equity when called. EV relativity One of the most common misconceptions about expected value is that “folding is always 0 EV”. However, this is only true if you choose to define folding as 0. You could also measure EV as the difference in stacks relative to the start of a hand. This perspective is equally valid. Imagine you 3bet to 11bb and face a 4bet of 25bb. If you fold, you’ve just lost 11bb. If you do that 100 times you’ll lose 1100bb! So how can this be if folding is always 0 EV? From the perspective of your decision facing a 4bet, your original 11bb raise is a sunk cost , and folding can be considered 0EV. From the standpoint of your starting stack, folding lost 11bb. Both perspectives are valid . All you’re doing is comparing the EV of different strategic choices at the end of the day. It’s important to realize that EV is always measured relative to something else. If you define folding as 0EV, then the EV of calling is relative to the EV of folding. Here’s an example. You 3bet AQs on the BB and face a 25bb 4bet from the BTN. You have 3 choices: fold, call or shove. If you look at the EV of these options in GTO Wizard , you’ll see something like this: As measured from your decision facing the 4bet: Folding is 0bb, calling is 4.02bb, and shoving is 2.58bb. These numbers above can be misleading. It makes it seem like calling and shoving are both “profitable”. If you instead measure EV relative to your stack at the start of the round: Folding is -11bb, calling is -6.98bb (4.02 better than folding), and shoving is -8.42bb (2.58 better than folding). So regardless of how you look at it, calling is the best option, and it’s better than folding by exactly 4.02bb. But you need to realize that you’re deciding between 3 losing actions and trying to find the one that loses the least! It’s important to recognize this concept to put EV into context. These marginal “try and lose the least” spots constantly happen in poker. EV Units of measurement There are many different ways to measure EV. The most common way is to measure it in “bb” or “big blinds”. However, you can also measure EV in chips or pot share. For example, if you expect to win 3bb, and the pot is 5bb, you could say you have 60% EV (as measured by pot share, the same way we measure EQ). One result of this measurement is that you can have greater than 100% EV. This simply means you expect to win the pot and then some, in the long run. Measuring your EV as a percentage has the benefit of putting things into perspective. For example, is 2bb a lot? Well, if the

For the BB to have a + $EV call with their hand, they need to have 66.44% equity, while for the call to be +cEV, they can call any hand with 47% equity. The difference in equity is the risk premium: Risk Premium Correlation Matrix Risk premium changes depending on the stack sizes of players involved in the hand and is higher when calling big bets, particularly if calling for all your chips and putting your tournament life at risk (Table 41).

Pre-flop: This open is bigger than in the previous hand, but Hero holds a much more playable hand given the added connectivity and two fairly large cards for flopping top pair. This is a clear call. Flop: The first instinct is certainly that this hand cannot be a fold. Though Villain is on the tighter side, his range to open the BU and then c-bet a dry flop like this one is usually still wide and Hero's equity against that range will be way over 50%. When ahead Hero is comfortably ahead. There are no hands in Villain's range that have both two overcards and a draw so the worst case scenario for Hero when he's flopped the best hand is Villain drawing to 6 outs with a hand like KQ/AQ/AK etc. or more rarely 8 outs with 98/45s etc. Often, Hero will be further ahead than this. When Hero is behind, he usually has 5 outs to improve against overpairs and 3 against better Jx. This is not as bad as the dreaded underpair was in Hand 54.

Hand Range 24: BB Nash Equilibrium The value of the push/fold game for both players across the different iterations (Table 9).

wanting to blow opponents out of the pot with the nuts. With 60bb stacks, the SPR will be low enough for BB to treat AA as the nuts on most flops after cold calling, which was not the case with 100bb. The strangeness of BB cold calling with 30bb but not with 40bb is a function of the three-bet size. With shallower stacks, BTN’s open and SB’s three-bet are smaller, making shoving slightly less appealing for BB and calling slightly more. Once again, AA is the strongest contender for this play: ICM In my experience as a coach, the most common explanation for why people call with hands they ought to have four-bet is that they were trying to take a safer, lower variance Variance The measure of how far a set of numbers differ from the mean. In poker, variance often refers to how “swingy” a game or strategy is relative to your win rate or results. Variance can also be defined as the square of standard deviation measured as bb/100. alternative to building a big pot and potentially getting all in preflop. Calling is not the low variance option. A review of ICM simulations, however, makes clear that calling is not the low variance option. In fact, ICM simulations typically involve less calling and more raise-or-fold responses. This is because showdowns Showdown When two or more players remain after the final street of betting, the players will showdown their hands to determine who has a stronger hand and therefore wins the pot. are by far the greatest source of variance , and when you call, you make it more likely that you will see a showdown. There’s no variance when you fold. You know exactly what you’re going to get: nothing. When you raise, you give your opponent the opportunity to fold, which also yields a guaranteed result with no variance. The tradeoff for this decreased variance is missed opportunities to accumulate more chips, which is often a worthwhile tradeoff when ICM is a factor (where a chip gained is worth less than a chip lost). Very strong hands that call instead of raise in ChipEV models take on an increased risk of losing the pot in exchange for the opportunity to win an even bigger pot . Weaker hands that call instead of fold in ChipEV models expect to lose a small or medium pot fairly often in exchange for occasional big wins , which is the opposite of what ICM encourages. Raise Sizing The other reason many human players four-bet less than optimally is due to a misunderstanding about how large to raise. Three-bet sizes tend to be in the neighborhood of three or four times the original raise, and so many players are tempted to apply that same template to four-betting. However, four-bet sizes, especially of the cold four-bets, can be much smaller than this . There are several reasons why: A small four-bet suffices to achieve a low SPR on the flop , even if the effective stack is 100bb. This means your strongest hands–your big

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

Table 66: SB Action Frequencies (60bb) The average SB VPIP is 24%, going from 33.4% VPIP vs the BN to 19.4% vs UTG. As the stacks get deeper, there is a preference towards 3-betting hands with better post-flop playability, given the high likelihood that the play will get to the flop, forcing the SB to play post-flop OOP. Also, since IP is too deep to 4-bet jam, the SB will be able to call many hands vs a 4-bet and play post-flop with high equity hands that play well in 4-bet pots (Hand Ranges 203-210).

not want to put too much money into the pot with this hand but do not give up. The trick from this point on is: A. know what you have and need to make your hand B. What other possible hands are out there to beat you. Chances someone has an Ace before the flop: In regards to our previous example, you will most likely be playing against someone holding an Ace, already hit 2-Pair or a different Straight draw that may beat you. This is why the Flop is a more dangerous. Many hands that are more possible can beat you. Count how many hands could be out there that can beat your Straight draw if you hit or do not hit. Being able to read the board and put it in relation to what your opponent could be holding is the ability to play winning poker. Think about it: in middle to late position, someone could easily be holding K T or K Q in any type of game (loose to tight) giving your opponent a GutShot Straight draw. He would be an underdog to hit the hand, but one side of your Straight draw does complete his hand. This is the type of hand people call in an un-raised pot with all the time. An Ace and a blank card (especially a J = Ajax) is also a common starting hand (Ace small suited is more likely) people enter an un-raised pot with all the time. Someone could have a medium to small Pocket Pair that caught the flop (8’s in this example). Finally, someone could be holding a different diamond draw (this happens less often that two people are holding suited cards of the same suite but it can be expensive if it happens and you are on the short end). You have to get a feel for what your opponents may hold and then guesstimate this according to the betting that is happening on the flop. Put your opponent on a range of hands according to what position they starting in and how they have been betting. In this hand, many different starting hands can beat you now and at the showdown even if you hit your Straight. Deciding on the flop if your hand can become the best at the showdown or folding up camp for another run is where you win or lose money. Of course, not everyone is holding each one of these hands: KT suited or unsuited KQ suited or unsuited 88 wired AJ unsuited Ax unsuited Do you want to invest a lot of you money into this pot if it will get beat? Of course not: you want to save your money for when you hold the best cards and someone raises the pot with the second best cards. I am not suggesting that you fold every time, then you would only be playing the nuts and that would not be the most profitable way of playing. You just need to be aware over the next two rounds what cards help

a look at one more hand we raised with jack 10 of spades hijack and button call flop comes jack 10-4 great spot to bet the flop big right turn is a two we continue betting big because we have one of our best made hands i also had a good draw like queen nine of diamonds nine eight of diamonds eight seven of diamonds nine seven of diamonds i would also keep betting big with those hands if i had three of a kind i'd also keep betting big and we get called and again thinking about the ranges at play we need to now fold if one of our opponents bets if one of our opponent bets notice if we bet the river we're mostly only going to get called by straights and flushes which we lose to which is really bad so if we do let this check through we have the best hand almost every time but if we face a bet we probably just need to get out of the way so we do check the opponent bets and we make the fold and you see how in all these scenarios we're asking ourselves how does our hand line up against our opponent's likely range and this is going to take a lot of practice you're going to find that if you go through a lot of hand examples and you pay attention when you're playing you will get better and better and better at narrowing your opponent's range if you are actively paying attention to that which you really should be because that is a large part of no limit hold up excellent job making it through this entire video you now have many of the tools required to crush post slot poker that will help you beat these small stakes poker cash games don't forget that you can get this entire mastering the fundamentals course for free right now by heading to pokercoaching.com fundamentals course good luck and i'll see you soon

raise to $20. Since your opponents have 19Note that this can invert again if players are relatively likely to call, but not reraise. Then you may again be better offwith a stronger hand in the event that you have to see a flop.

Queen also doing better again I think you can be a little bit wider like king queen and Ace track maybe more asex suited maybe something like 10 9 suited and all these suited connected Broadway hands I think that would be fine pocket six is a better all of them I think that's also reasonable but again three better fold no calling range small blind versus the button who should be quite loose notice we get to play the top 14-ish percent of hands which is just lots of asex suiteds King 9 suited better good suited connect to taipans pocket sixes and better and the best off suit hands and that's it I know that sounds tight I know that sounds actually kind of simplistic just three better fold well that's it that's all you really have to do to play the GTO strategy from the small blind again always logically adjust to take advantage of what your opponents are doing wrong but you have to realize that when you're out of position not closing the action not getting good pot odds well that is basically the most terrible spot you can be in and when you're in a really bad spot you have to be tight but most people don't like being tight they Splash around they gamble they lose the rake they bleed away their money to their opponents and they wonder why they're losing because they're playing too loose in the most disadvantageous scenario and I want to make sure that you do not do that you want to make sure you are putting money in when the spot is good for you you make money when your opponents make mistakes so you want to make sure you're playing in games where your opponents are making a lot of mistakes and on top of that you want to make sure you are sitting in the seat that has the best chance to take advantage of the players who are making the most costly mistakes so we're going to discuss how to find a profitable seat and ideally the most profitable seat in a poker room when you go to play live poker if you're completely new you walk into the poker room and you go to a front desk or a Podium and ask to be put on the list or the stakes you want to play which should be small six if you're just starting and in most games this is going to be one two no limits in most casinos that's the smallest game that runs if you're in a game in a casino that has a lot of different games like one two and one three and two five and five ten especially if some of the lists are very full or you cannot get to see it immediately you may want to be put on a spread of lists for example maybe one two and one three because those games are kind of the same size but if you can get in one

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,

checking and only one player to act behind him, player C might be betting just to try to pick up the pot cheap. Since you can judge this hand to be on the weaker side much of the time, you’re in a great position to flat-call and play the rest of the hand inposition against a hand you’re probably ahead of. Assuming players A and B fold after you call, you play subsequent streets exactly as if you’d gone into the flop heads-up and your opponent bet into you. If he checks the turn, check. If he bets, raise, unless you believe you have the better hand. Why shouldn’t you raise the cutoff player in order to ensure shutting out players A and B? They’ll fold if they have nothing or check-raise if that was their plan all along. And they’ll take these actions regardless of whether you call or raise. And if someone check-raises into two (or more) players, that indicates huge strength, so you get to fold for the price of a call, not a raise. By the way, if you’re thinking that the early-position check-raise is a squeeze play, consider that it’s coming from a player who’s out of position and raising into two players who chose to continue on a board with noobvious draws. That’s usually not a squeeze, that’s strength. Even if player A or B does have a piece of the flop, say middle-pair medium-kicker or top-pair bad-kicker, you don’t mind him calling here. By overcalling your bet, they’ve already paid a price—the wrong price—for improving their hands. Remember, they’re looking at, at most, five outs, so they only have about a 10% chance of hitting on the turn. They need 9-to-1 from a pot that’s probably offering around 4-to-1, so you don’t mind themcalling along. Say they go into the flop with 2,000 in chips in the pot. Now player C bets 1,000 and you call 1,000. That puts 4,000 in the pot for acall of 1,000 by player A or B chasing just five outs. That’s bad math, so you’re okay with him tagging along. Remember, then, that with such a dry board, you really don’t have to worry about thinning the field or denying proper odds on the flop; the tradeoff of running into a check with intent to check-raise is too great. Your controlling idea should be to get maximum information for minimum investment of chips. And the call tells you most of what you need to know, allowing you to get to the turn cheap. Most of the time, the action will go check, check, bet, call (by you), fold, fold. So you’ll end up playing a heads-up pot, which is ideal, for minimal investment. Occasionally, you’ll get a real call-fest, with the action going check, check, bet, call, call, call. When that happens, almost no card on the turn canbe considered a blank. After all, three opponents liked that dry flop enough to call a bet on the flop. Some might have made hands. One or more might have you

an ace is out against him, and there aren't enough strong hands lacking an ace to balance out the odds. In fact, Player B called. Player A showed down Q♥ Q♣ 44 and Player C had A♦ K♦ The Queens held up to win the hand. Observing Yourself While you're carefully observing the other players at your table, noting how many hands they play, what hands they show down, what their betting patterns look like, and any other information you can glean, make sure you pay attention to the most important player at the table - yourself. Player X, sitting at your right, might only be involved in 10 percent of the hands you decide to play. But you're going to be involved in 100 percent of the hands you play, and what your opponents do in those hands will be partially determined by how they see you play. (The better they are, the more their play will be guided by your play.) So keep asking yourself these questions: 1. How many hands have I been playing? 2. What hands have I actually shown down? 3. What would a keen observer think about me at this point? Just because you're trying consciously to play in a certain style doesn't mean that you'll be perceived that way. The perception around the table may be quite different. Let's look at several hands where the key is understanding how the table perceives you, rather than how you perceive the table. Example No. 1: It's the first table of your first major tournament. You've decided to start off playing a tight, conservative game, then gradually loosen up, building on your conservative image to steal a few pots as the blinds get larger. (A perfectly reasonable approach, so reasonable that most of the newcomers will be playing exactly the same way.) In the first 15 hands you have a huge run of cards - a pair of kings, a pair of queens, and a couple of ace-kings. You lead out and bet these hands, catch some good flops, and win all four hands. In no case did you show a hand down. At the end of the first 15 hands, you've doubled your chip count. Discussion: Now what? From your point of view, you've done nothing but play your normal, tight game. It's not your fault you had a great run of cards. But from the point of view of everyone else, you're a wild and crazy guy who's been bullying the table unmercifully. They haven't seen a single hand; they just know you seem to be in every other pot, raising and reraising. If you stick to your original strategy and now try to loosen your playing requirements, it won't work. You'll start playing weaker hands just as your opponents have figured out that you have to be stopped. When you make a move with your suited connectors, the guy behind you will put you all-in with any reasonable hand. You might have started off playing tight, but your table image became loose. Go with it.

relatively simple and straightforward the execution of it is not knowing how to optimally balance your strategy can be incredibly difficult as it will be impacted by numerous factors such as the player's previous actions board cards the stack to pot ratio and position and that's why you'll sometimes see 30 minute long videos going over a single hand on this channel in this video we only briefly touched upon how to rationally differentiate between the weak hands we Bluff versus the weekends we give up or the medium hands we call versus fold or the strong hands we bet versus trap the reality is that there's a whole world of complexity that goes into making these decisions to maximize your Edge if you want to learn more about this world hit that subscribe button and stay tuned for more videos foreign

because you have managed to cost them two double size bets on the next to the last card. That is worth giving up a lot of other small profits. It's Important to be Suited If your hand is suited in these loose games it is a giant advantage. One of the nice things about raising with suited cards before the flop (especially the ace suited), is that when you flop a flush, or for that matter a four-flush, you welcome all bottom pairs calling. They may be right to call, but it doesn't hurt you. They may be making money by calling on the flop because there are other people involved. Biit they are not taking money from you. They are making you money. The Fundamental Theorem of Poker states that if somebody is gaining money they are taking it from you.8 That's true in a headsup pot, but there are exceptions multiway. For instance, in a four handed pot it could be possible that the fourth player in is gaining $l.CO from the second player in, $1.50 from the third player, but giving $0.75 of it back to you. So if you flop a four-flush, especially an ace-high four-flush, and a player calls getting 12-to-1 with bottom pair, he may be costing whoever holds top pair money because of the odds that he is getting, and perhaps even costing someone who holds middle pair a little money, but he is not costing you anything. He is rather making you something. Thus, one of the reasons to raise with these flush cards is because if you flop the draw, by your making the pot bigger, people now play hands that can't win against your hand if you hit it. (This is also why if there ape many players in, it is right to raise with small pairs on the button.) 8 See The Theory of Poker by David Sklansky. 173 174 Part Four: Playing in Loose Games Let's be specific. Suppose you hold: If there are five or more people in front of you who have just called, you should raise if you are in a game where the players are fairly weak. However, if they are tough you should just call, and if they are terrible, you should again just calh When the other players are terrible, there is no reason to make this raise in order to attract their call on the flop because they will stay in anyway. If they are tough, it's not that great a play because they won't play that badly on the flop, and they will have better hands. When many players have limped in (before the flop), a raise with an A484 would be a close decision if you were all in at that point. In other words, if you gave yourself an A484 and you dealt it out against their hands, you probably would break approximately even whether you raised or just called. However, the reason you should sometimes raise is because of how it affects future play. If the raise will get

player's ranges match up we often will not be able to play all of the combos within our class the same way with a pure strategy or else we would be unbalanced and end up losing some ev so to maximize our ev we need to mix the hands in our class between two or more actions and the most logical way to determine this mix in many instances is by availing to blockers and unblockers so let's use this hand as an example to explain further i ended up checking the flop the button c bet i called and the turn was a five of clubs and i checked again now for the sake of discussion let's assume that the button had a random king high and he needed to decide whether he should bear all well if we isolate his king high hands we see that the strategy is mixed although the button has a significant advantage in over pairs this board is not great for him as the cutoff actually has a significant advantage in sets the upshot of this is that the button should not be betting all of his range or else he would be way over bluffing but he still needs some bluffs to support his value and protection bets so how should the button determine which king high hands should barrel and which should check back while on the flop and turn one of the primary drivers of bluffing will be draws and we see that the solve is essentially bluffing all of the king high combos with a straight draw but these draws only comprise a handful of combos so the button will need to find some bluffs elsewhere however when we isolate the king high combos without a draw we see that the ev regret for each available action is greater than one percent meaning that if the button decided to just arbitrarily choose one of these actions over the others or randomly mix between these actions he could potentially lose a significant amount of ev so how should the button decide which king highs he should bet so that he has adequate bluffs and which king highs he should check so he isn't over bluffing well one factor that the solver will often use to differentiate between similar potential bluffing candidates is unblockers that is in a bluffing scenario the solver will often play more aggressively with a hand when that hand does not block the weaker combinations in the opponent's range that are more likely to fold when facing a bet and for those that are newer to the concept of unblockers the gto check solver provides this scatter chart that can be used to help point us in the direction of which hands have better unblocking properties compared to others the x-axis of this chart plots each hand in the button's filtered class in this case king-high combos with no draws based on the hand's unblocker score which is a metric designed to approximate unblocker effects for each such hand

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

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.

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…

Hand Range 215: BN vs CO 4-bet (25bb) • Call 58.9% / • Fold 41.1%

Hand Range 342: BN vs CO 40bb • 3-bet 7.5% / • Call 19.6% / • Fold 72.9%

SWAPPING MISTAKES 120 In practice, your opponents won’t be as dense as the “call them all” player described above. Even bad players who frequently make big mistakes will catch on sometimes if they are getting destroyed. If someone keeps calling and losing, after a while he’ll start folding a few hands. And if someone folds hand after hand to your bluffs, eventually he’ll decide to call. So you will, in practice, always be swapping mistakes with your opponents. They make mistakes, and you attack them, making theoretical mistakes of your own. Sometimes your opponents will hit the spot you left open. That’s fine, as long as you’re trading a little for a lot. Be Vigilant Making mistakes intentionally to exploit your opponents is the right thing to do. All the best players do it. But such a strategy requires vigilance. You are leaving yourself open to attack, and sooner or later, some shrewd player will come along and start probing your weakness. Say you play against people who routinely enter too many raised pots out of position. Position is such an important advantage that no one can win consis- tently playing a great majority of their hands from out of position. Being too willing to play out of position is a big mistake. What mistake should you make to swap for it? When these players limp in, you should play more loosely and aggressively from late position than the perfect strategy would suggest you should. They like to play raised pots out of position; play with them. When they limp in, raise modest hands such as J♡9♡. By maximizing the number of pots you play in position, you can overcome the slight weakness of your starting hands and make more money. Loosening up is the right adjustment to make, but be aware that it is, in comparison to the perfect strategy, a mistake. Someone who sees what you are doing and has a mind to exploit it can do so. Specifically, they can reraise you with weaker hands than they normally might, knowing that you are less likely to have a hand strong enough to call. (That reraising adjustment, of course, is a “mistake” itself, also exploitable by someone so inclined.) The point is, always be aware of basic no limit concepts. No matter who you are playing, the fundamentals remain the same. For every play, try to think of what the perfect strategy might be. Then adjust that strategy to capitalize on your opponents’ weaknesses. Be aware of how your strategy deviates from an unexploitable one, and watch out for opponents who might be trying to exploit your mistakes. Poker history is full of hot shot maestros who quickly racked up big wins by making just the right mistakes to exploit their regular opponents. Unfortunately, their egos usually didn’t allow them to recognize their deviations from perfect play as theoretical mistakes; in their minds, they were natural talents playing an unbeatable game. Then, the sober, seasoned players moved in, systematically targeting the

call. This opponent does not have a history of trying to check-raise. A blank hits on fourth street, and both you and your opponent check. Notice that there is a good chance that he is also on a flush draw and was betting on the flop in an attempt to pick up the pot. If another blank hits on the river and he bets, you may want to raise. If he was on a flush draw, you will probably win the pot. You also can raise as a semi-bluff. For example, suppose you have 98 Part Two: Strategic Concepts the flop is and everyone checks. If the next card is the giving you the nut flush draw and a gut-shot straight draw, you should usually raise if someone bets. A similar opportunity to raise sometimes occurs in a shorthanded pot when everyone checks on the flop and fourth street does not bring an overcard or three to a straight or flush. However, it gives you either a flush draw or an open-end straight draw. Now suppose an early-position player, who you know would try to steal in this spot, bets. Your correct play is to raise in the hope that your opponent will fold. But if he does not fold, you still have outs. Here's an example of this play. You start with and the flop is Raising 99 No one bets, and the turn card is the giving you an open-end straight draw. If an early-position player bets, and he is the type of player who would try to pick up the pot with no hand, you should go ahead and raise. If he calls with a legitimate hand, you still have at least eight outs to win. Another opportunity for a semi-bluff raise occurs almost any time that you pick up a back-door flush draw after calling on the flop with a pair. But again, make this play only against someone who you think is capable of folding. And how likely is it that someone will fold for a raise? The answer is based on the answers to the following three questions: 1. How capable is this person of folding a big hand? 2. How likely is he to be semi-bluffing? (Of course, this is a matter ofwatching your opponent and learning exactly how he plays.) 3. How are you perceived by this particular individual? Specifically, if other players think you virtually never bluff, you are more likely to get away with this play than if they think you are a wild and reckless player. Raising to get a free card is best done when you are in late position and the bet is smaller than the bets on succeeding rounds. But, any hand that is worth a call is conceivably worth a raise. 100 Part Two: Strategic Concepts Finally, raising to gain information should be done only rarely, usually just in heads-up situations. Even in the most favorable spots, this raise probably is not worth it, as you usually have to "pay" too much for the information. However, if

do want to be careful as you add that play to your repertoire in cash games so you want to make sure okay these are truly recreational players they're not paying attention to me okay now I'll open a little bit more if you think the players to your left actually are playing Pretty seriously and there are people that take any buy-in cash games seriously you always have time in cash games to revert back to just solid poker whereas sometimes uh due to ornaments just the blind levels going up so often you will have to make a move at some point table selection will make or break you ninety percent of your job in poker is table selection it doesn't matter if you're the 10th best player in the world if you're sitting at a table with the nine best players in the world then you're going to lose conversely if you constantly surround yourself with weaker players who are not as assertive then you are far more likely to win it is unlikely you'll ever find a table completely without solid players you will have to get comfortable being uncomfortable in pots with them but once you are outside of pots with them you will have to work to clean out a recreational player's money as quickly as possible collect information on the players you're playing against if there is an obvious whale then you should seek to be at every single table they play and you should try to get into as many pots as possible with them if there are obvious killers at your level then seek to avoid their tables if at all possible which is going to be difficult but if the one thing you can do is try to get position on them try to make pots with them as small as possible try to generally stay out of their way it work like that when you're playing tournaments if you're playing a low enough buy-in tournament or if you're playing on a big enough site that attracts a number of recreational players if there's enough players in the field you're it's going to be soft enough if there's 500 runners in a 50 tournament you're fine there's just going to be a lot of people going ah 50 bucks it's a Friday night let's have fun or it's Sunday I'm having a good time let's go ahead and play right so that is table selection is more or less built in if you're playing low to mid Stakes tournaments now obviously As you move up and stakes in tournaments you're going to have to really pay attention to okay who's buying into this what was the promotion like for this tournament were there a number of satellite winners Etc or is this just all killers now when you're playing cash games you can completely change how much money you make in a session based on your table selection it's uh it's amazing to me when you play Live how few how many

final tables, but I've never been to one where I didn't have to hit a perfect card somewhere earlier in the tournament. That's a fact of life in all gaming tournaments, and poker is no different. You go all-in, and your opponent calls. He shows J♣ J♠ and your queens hold up to win the hand. The Problems Problems 4-1 through 4-6 show how to compute pot odds for your hand. Problem 4-2 also gives an example of deciding what pot odds to offer your opponent. In Problem 4-5 you have to adjust your pot odds when facing active players behind you. Problems 4-7 and 4-8 show how to analyze hands based on the cards and betting you have seen so far. 4-8 also gives you some guideposts for extracting the most money from your opponent when you make a monster hand. Problems 4-9 and 4-10 put the whole package together, testing your ability to blend pot odds and hand analysis to arrive at good decisions for your hand. Problem 4-10 shows how to handle a classically weak hand when confronted with great pot odds. Hand 4-1 Situation: Early in a satellite tournament. Players B and E are active and aggressive. Your hand: 7♥6♠ Action to you: Player A folds. Player B raises to $60. Players C, D, E, F, and the small blind all fold. 66 Question: Do you fold, call, or raise? Answer: Call. Your hand isn't much, but you're getting great odds here. It costs you $30 (remember, as the big blind you've put $30 in the pot already) to have a shot at a pot which is now $105. Those are 3.5-to-l odds, and your hand, while weak, is only a bigger dog than that to a high pair. (Even if Player B is holding ace-king, you're only about a 2-to-1 underdog at this point.) Your implied odds make this an even stronger call. Get in the habit of computing the pot odds before throwing your hand away. Many times you'll find you have a compulsory call, virtually without regard to the cards you're holding. Resolution: You actually fold. Hand 4-2 Situation: Single table satellite. Players began loose, but now appear to be playing tighter. Your hand: Q♠Q♣ Action to you: Players A, B, and C all fold. Question: Do you raise $200, $300, or $400? Answer: You're certainly going to raise here. There's no sense in calling, letting the small blind in cheap, then watching an ace or king come on the flop. Make your opponents pay to stick around. Queens are a fine hand, but they can easily get in trouble after the flop. The key question for this hand is - just how much do you raise? The two players left in the pot are the blinds, who already have some money involved. Since you have a strong hand right now, you want action. You don't want to bet so much that you chase moderate hands out of the pot. But you also have to remember The Fundamental Theorem of Poker.6 You want to bet

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…

At the same time, I’m telling him that I “usually” don’t play that hand, making me sound sincere and believable. (At a poker table, it’s perfectly permissible to lie about your hands and about the way you play them. In fact, it’s part of the psychology of winning. And once in a while, you should throw in the truth, just to keep opponents off balance.) But, I’m saying more. I’m claiming that I played the same hand successfully, even though I suggest that I know better. This gives him “permission” to play badly again in the future. If I do it, so can he. It will be fun for him to try to succeed again and be rewarded with more praise. When players make him feel badly about weak plays, they’re prodding him to play better. That’s exactly the opposite of what they should want. And it isn’t fair to other competitors to make their money suppliers uncomfortable about supplying money. TIP 25 While I often praise weak opponents for bad plays, I never praise them for good plays. That would make them proud of “pleasing me.” They might decide to take the game seriously—and wouldn’t that be a disaster? 88 TIP 26 I’ve seen even some of the best players in the world violate the advice shown above. Never forget that recreational players supply most of your profit. They came for the fun of poker, not to analyze it to death or to take it seriously. When you sit at the table discussing the finer points of poker strategy, you’re alerting the players who supply your profit that they might be competing above their league. You’re making them uncomfortable, and it’s quite possible that they’ll either decide to sit in your games less often or to play better. You don’t want either of those things to happen. I often hear sophisticated players debating the technical merits of how a hand was just played in the presence of weak opponents. Serious discussions of strategy can alert these recreational players to the notion that there is strategy. You don’t want to do that. And, even more peculiar to me, the debates are usually over something as inconsequential as whether a call or a raise in a borderline situation was the better choice. These way-too-technical arguments can never really be resolved (except, possibly, by me), because there are too many side factors involved, such as how opponents were likely to respond emotionally at the moment and what the bettor’s image was. The truth is, the discussion is often about which choice is 37¢ better, when just by talking about it in front of a recreational player, the debaters potentially are costing themselves thousands of dollars. Let me put in gently, without insulting some of my poker-playing friends who’ve made this mistake: The economic advisability of discussing advanced strategy at a poker table populated with weak opponents is hereby brought into question. TIP 27 Now I’m going to tell you a story. I’ve told it many times, but I think it illustrates this point so

to keep the ranges reasonably balanced and maintain board coverage. If the changes are too drastic, they won’t go unnoticed, so before making any big changes to the GTO strategies, thinking it doesn’t

you can use it's check raised ace high boards with the best kickers so alright guys we have one more I I tried to keep these a little quicker tonight because your time is very valuable to me and just want to keep it fun so in this hand you were at the beginning of a tournament a hundred big blinds you know nothing about any of the opponents yet you raise on the button the big blind calls you the board comes Ace of Hearts 2 of Hearts 3 of clubs it's check to you what is your bet so Jennifer says 1/3 Chad says 2/3 and we've got a couple E's most people are saying B or D Douglas says this is fine Alex all caps oh ok i mighta my timer is fighting with me a lot tonight because I'm reading your guys's chat ok so most people got their answer in this is a spot we all tend to play the same way but if you think of it's one of those spots we do automatically and we should really think about this a bit more because I think honestly the correct answer is e a the check check let's say you have a hyper aggressive opponent check can work if you think he's just gonna bluff his butt off on the turn in River but that's a very rare situation so I did a sign that a red designation obviously betting one third pot half pot two thirds pot does show a profit but I think three fourth spot is what you want as big as you can get this is one the GTO guys top man and it just makes perfect sense once you think of it the fun stuff about the GTO things in the solvers is sometimes are just any AI you bring into poker is sometimes the computer will say do this and you'll go why why does nobody do that and then you think about it for a while and it makes perfect sense you're obviously betting for value here right what hand is your opponent calling 300 with that he's not calling 550 with a flush draw will call you want all the aces to start paying you big and there's a ton of em his kin highs in Pocket sixes will still likely call you once based on how deep your stacks are if we're not betting big here we're just leaving money on the table now the funny question is people say so what do you do if you miss this flop to me this is the most exploitative life ever right because if you if you want to be balanced you have to pick one back here and go with it right so if you miss you should go big and you'll still turn a profit right and when you hit you should go big and or you can go really small but I honestly think if nobody knows who you are this guy in the big blind

and draw one card you will take it for granted I have four of a kind or you might think I'm bluffing. But not these simpletons. Now, in draw, I can stand pat any time I choose and the player must decide for himself whether I'm bluffing or not. I'll ask you this - if you didn't have the edge of the right-handed betting business - I'll ask you, if you open the pot and I raise and stand pat, are you going to call me if you don't fill your hand, which prohibitive odds say you won't?' 'No - but you make that play so often.' 'Sure I do. You saw Jake, the drummer. I set him up for just that play on which I won his trunks. I wanted him to think I was bluffing.' 'But he might have filled his hand.' 'Sure he might have. They all know I make that fake play by standing pat on nothing. It's like odd or even, as I'll show you in a few moments. First you have them, then you don't. Keep them guessing. And when you think you have them beat, play the hand hard. You don't need a lock to win at poker. It's the law of averages that will win for you. I'd make the same play against a jackass who had just been beaten with a fake pat hand if I held any set of threes as I did against Jake. Set up your man with a bluff. Then knock him down with the winning hand.' As I learned later, Monty worked his bluffing trick at draw on every stranger. His unique conception of the Golden Rule, 'Never give a sucker a break,' paid off. He explained, 'This is a club. I'm collecting initiation fees; then when I work it the second time I call it club dues.' Later, as the years went by, I worked the same trick at every club where I've played, the most recent being the National Press Club in Washington. I was so tight that members would jump to the second table when there was a vacant seat. One radio broadcaster called me Old Adhesive. There was a house rule against looking at face cards but some of the members got so curious that they couldn't resist picking up a player's discards and looking at them. If one is bluffing, this is deadly stuff. So to protect my hand and to try Monty's trick effectively I had to wait until I controlled the discards. This happened to every dealer during the deal. Discards were collected by him so that it was easy for me to hold on to my hand after bluffing and mix it with the other cards. We played two games at the National Press Club - draw and stud. In draw, the dealer would announce his choice: jacks or better, anything opens, any pair, aces progressive, kings regressive and the like. The stakes were $2 limit. In stud there was no ante. In draw everyone anted 25 cents and if

Someone is stealing five gallons out of each drum before you get it and probably selling it on the black market for two hundred and fifty dollars Chinese or twenty-five dollars gold. Multiply this by hundreds of thousands of drums and you get into real money.' 'I'll report this to my superiors,' I said. He advised me seriously against doing so. Then it came home to me that this was not the petty graft of small fry but a gigantic squeeze by government officials reminiscent of official theft in America. What slice Ling got, and for how many drums, I did not know, though I learned later that his father was high in the councils of the Generalissimo. I talked to Ling about this later. He was amused. 'Small thief if caught is executed,' he said. 'If successful he becomes an honoured official and bigger theft becomes a prerequisite of office.' Which philosophy recalls Western wisdom both ancient and modern, to the same effect. Nor did it seem to me on mature thought that I was the one to initiate reforms in China. I said to Ling, 'You ought to throw away that god-dammed dictionary you're always studying and learn how to play poker. How did you learn to speak English anyway ?' 'I studied English under a priest,' he said. 'I told him I was a Christian. English lessons for Buddhists cost five dollars. For Christians only one dollar.' 'The propaganda minister,' I said, 'tells us the Generalissimo is a Christian and reads the Bible every day.' The propaganda minister also gives out -' and Ling smiled sardonically - 'that America loans the Chinese fifty million gold dollars.' 'Ling,' I said severely, 'I didn't know hypocrisy was a Chinese characteristic' He shrugged. 'Ancient ancestor say, "Crows are black everywhere." ' When he let this sink in he said, 'You serious about teaching me poker? You win often?' 'I very seldom lose.5 'You believe in Jesus Christ?* Startled, I looked at Ling's impassive face for some sign of why he asked. Suddenly I knew why foreigners speak of the Oriental as being inscrutable. It was his eyes. They had the same expression as Ruddy Flew's, our home-town baseball pitcher, who lost his eyelashes when he contracted syphilis. 'Missionaries have been good to you,' I said. "They taught you English at cut rates. They teach you hygiene for nothing. Isn't that enough? What does it matter whether Buddhism or Christianity is the true religion?' 'But the missionaries come with the Bible in one hand and rice in the other.' 'Then eat the rice.' Said Ling, 'It is true even as ancient wisdom says that beggars cannot be choosers, but in America I imagine none is so poor as to swallow Buddhism with rice.' 'Then,' I advised him, 'swallow the rice only and don't go around asking people if they believe in Jesus Christ.' Later I was to learn that Chinese students everywhere asked foreigners the same question. It was so late we turned in. I took care to see that my money belt

A pair of kings is obviously a great hand, but it's not invincible. Your alarm bells need to go off when an ace flops. This is especially true in online poker, where players religiously call with acesmall. Flop No. 1. A♠K♦7♥. This is an excellent flop. It's very likely someone at the table made aces, and is ready to lose all his money. Either checking or leading out with a small bet is the recommended play. Flop No. 2: A♠Q♦T♥. A dangerous flop, although it does give you an inside straight draw. It's essential here to define your hand in one stroke. Lead out with a good-sized bet, perhaps twothirds of the pot. Checking here is out of the question, because it will leave you with no idea where you stand if the pot eventually gets bet. Flop No. 3. A♠5♦3♥. Not as bad as Flop No. 2, but still dangerous because of the ace. Once again you need to lead out. If you encounter action, you're done with the hand. Flop No. 4. 9♠7♦6♠ (but you don't have the K♠). You're probably winning now, but the potential drawing hands are too dangerous. Bet somewhere between three-quarters of the pot and the entire pot. You need to squelch resistance immediately and cut off the drawing hands. 125 Starting Hand No. 3. 9♦9♣. There was a raise in fifth position of twice the big blind. The player in sixth position called, and you called on the button. A pair of nines is not a great hand, but so far neither of your opponents has shown much strength. Flop No. 1: A♠9♦4♥. Your ideal flop. Hopefully one of your opponents is in there with acemedium or ace-small. Your problem will be figuring out whether to bet out or trap if they check to you and whether to raise or slowplay if they bet. Flop No. 2: A♠Q♦5♥. A bad flop. You're very likely to be beaten, with little chance of improvement. Fold your hand when someone bets at you. Flop No. 3: 7♠4♦2♥. A good flop, since you have an overpair to the board. If there are two checks to you, definitely bet about two-thirds of the pot. Flop No. 4: J♠J♦6♥. This is also a good flop. If no one has a jack, you are likely best at this point. If both players check to you, bet two-thirds of the flop. If there is a bet and a fold in front of you, just call. You are still all right with the hand until someone shows real strength, at which point you'll have a tough decision. Flop No. 5: 8♠8♦6♥. Another good flop, since your pair is now higher than the board. If there is a check and a bet to you, you can call. If there is a bet followed by a call in front of you, the caller almost certainly has a pair. Again you can call. Hand No. 4: J♠T♠. There are two limpers in front of you, and you call. Another limper comes in behind you. You're third to

Principles of GTO The Exploitative and GTO Frameworks Game theory, or GTO ( for Game Theoretically Optimal ), is best understood not as a rigid set of rules to be accepted or rejected but rather as a framework for thinking about poker, predicting your opponent’s actions, and improving your own decision making. Its objective is to avoid strong assumptions about the opponent’s mistakes, and instead build strategies that will be robust no matter how your opponents play. This makes it especially useful when playing against tough opponents but also against unfamiliar opponents whose mistakes you are not comfortable predicting. Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid set of rules to be accepted or rejected but rather as a framework for thinking about poker. Exploitative thinking is a different way of approaching these same problems. An exploitative approach tries to predict specific mistakes an opponent will make and craft a strategy that takes maximum advantage of those mistakes. This approach works best against weaker players whose tendencies are well-known to you. In the game Rock, Paper, Scissors, each player uses their hands to throw one of these three signs. Rock beats scissors, scissors beats paper, and paper beats rock. The exploitative approach would be to guess what your opponent will throw and then choose your own sign accordingly. The game theory approach would be to choose your throw randomly, with a 33% chance of throwing each. This makes it impossible for your opponent to predict your action, which is the best you can hope for if you cannot predict theirs. In poker, these frameworks are not mutually exclusive. In fact, game theory can help you craft more profitable exploits . You may know, for example, that an opponent calls too many weak hands pre-flop but not have a clear idea how they will play all those bad hands after the flop. Game theory can help you profit from the mistake you’ve identified without opening yourself up to exploits no matter how your opponent plays their weak hands after the flop. Why is Game Theory Useful? Game theory is a tool for making decisions under conditions of uncertainty. In the absence of actionable information about your opponents’ intentions, it assumes they will play as well as possible, rationally pursuing their profit incentives to the best of their ability. While no human opponent will ever play perfectly, it is what most are striving for, so it’s a useful assumption when you don’t have other information to guide you. The first step to understanding game theory is learning to think outside of an exploitative framework. This can be challenging for veteran players, because you may not realize how many assumptions are baked into the strategies you’ve learned or developed over time . In many cases, these assumptions are warranted, and acting on them will yield better results than game theory alone. However, it’s important to recognize that they *are* assumptions so that you don’t rely on them in cases where they are not applicable. Game Theory in Action