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You still don't have much, so you should check again. Action: You check. Fifth Street: 7♦ Action: The small blind checks again. Should you check, or try to steal the pot with a $100,000 bet? Answer: Don't bluff here. His check was a setup, and you'll be picked off. Your opponent doesn't think you have anything, for the reason I explained earlier. But if you did have something, you would have bet on fourth street, to prevent him from getting a free card on the river. Since you checked, he was sure you didn't have anything at that point. If you didn't have anything on fourth street, the river card, another seven, surely didn't help you. So now he knows he has the best hand, and he's giving you a chance to lose some more money on the hand 142 by trying to steal. Resolution: You actually bet $100,000, and your opponent calls, turning over K♠4♣. His two pair win the pot. This hand repays careful study, so go over what happened here and make sure you understand it. This is a hand where a top player would have lost about $110,000 less than the player sitting in the big blind, simply by drawing the right conclusions after the flop7 and sticking to those conclusions throughout the hand. Remember that the difference between strong and weak players doesn't lie in how much money they make with their good hands. Anyone can win a big pot when dealt pocket aces, or after flopping a set. A good player loses less money with his marginal hands, and in the course of a long tournament that edge turns the tide. Hand 6-10 Situation: Early in a single-table online tournament. Players B and F are extremely aggressive. Your hand: 7♥7♣ Action to you: Players A, B, and C all call. Player D folds. Player E raises to $60. Player F and the small blind fold. The pot is now $195. Question: Do you fold, call, or raise? Answer: You're the big blind, so it costs you only $30 more to call with $195 in the pot. You should call because of the combination of the expressed and implied pot odds. The expressed pot odds are 6.5-to-l. The odds against your improving to trips on the flop are about 7-to-l against. (You don't have to worry about odds after that, because if you don't improve on the flop with your low pair, you'll be out of the hand.) The expressed odds aren't quite enough to justify a call, but if you hit your trips, you'll likely win a substantial pot, so your implied odds are excellent. If you're alert, you should have one additional concern about the hand. There are three live players who are still to act behind you. If one of them decides to raise, you may not be getting the odds you need when the betting comes around to you again. ----------------------------------------- 7 Of course it could be argued that even the flop probe bet was wrong because it made no sense that your

It quickly became apparent that players didn’t want the delays. The faster their cards arrived, the happier they were. That’s why doylesroom.com and most other online rooms have taken all the air out of dealing and shuffling. There is no delay. You can play many more hands per hour online, about twice as many as you’d play in the real world. That means you can make more money faster. Each hand you play is worth money when you’re playing the way I advise in this book, twice the hands can mean up to twice the profit. Reason #8: Play Two or More Games at Once You see some pretty weird things at poker. I’ve seen players hold seats at adjoining tables and scurry back and forth, trying to play both games for short periods of times. This usually happens when the player has free hands remaining before the blind at one game and has been called to a seat from the waiting list for another game. Needless to say, playing two games at once in the real world doesn’t work well. It’s physically impractical, and you’re almost certain to rudely delay the play of a hand at one table, while completing action at another. But online, it’s much simpler. You just click to enter a second, third, or even more games. When it’s your turn to act, the software notifies you, and you simply click on your decision to fold, call, check, or raise. Since you don’t have to get out of your seat and physically move to the other table, multiple game play becomes practical online. Does this mean more profit for you? It can—if you’re good enough. Try to remember, though, that you won’t be able to focus as closely as you would on a single game. You’ll miss some of the nuances and won’t be able to track your opponents’ tendencies as readily. That means your average earnings per game are sure to suffer when you play more than one. But when you add those slightly diminished profits from multiple games together, you’ll probably find that you’ll earn more total profit. Whether you do depends on your skills. 55 I recommend that you stick to just one game at first, because it can be quite hectic concentrating on two or more at once. But as you get accustomed to playing multiple games, you might find it exciting and rewarding. Certainly, there’s no equivalent in real-world poker. Reason #9: Pre-Select Buttons One of the great inventions of online poker are the early action or pre-select buttons. Since you aren’t being watched by other players, you can decide what to do in advance of the action reaching you. In real-world poker, preselecting wouldn’t be appropriate, because that would let opponents who act before you know how you planned to respond. The early action choices help speed up the play, and they’re especially useful if you’re playing other games simultaneously. For instance, when you know you’re going to fold, no matter what, you can just click the fold button before the action

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a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table tournament and the BB calls. Both… The Art of Bluff Catching Bluff catching—calling a bet with a modest hand which you expect to win only if… Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet… Is Limping Pimping? In a past Discord post, one of our members noted that an upside of implementing… Exploiting Excessive C-Betting by OOP A preflop raiser who continuation bets too often is always a potential target for exploitation,… Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs.… The Worst Turn Card Greetings from GTO land. In today’s article, we will use the Turn Reports feature to… Navigating Range Disadvantage as the 3-Bettor Picture this: We’re playing a NL500 6-max cash game, and we’ve won a few pots,… Mastering Three-Bet Pots In Position in MTTs Playing in position against a three-better is a lesson in playing to your advantages. As… Mastering Three-Bet Pots Out of Position in MTTs Three-bet pots are scary. Playing out of position is scary. Put them together, and you’ve… The Greatest Final Table in Triton History Today, we’ll examine one of the most epic final table battles I’ve ever witnessed! Our… Mastering Thin Value Bets in Checked-Down Pots Valuing your hand appropriately—determining whether it’s strong enough to value bet or so weak you… Maximizing Value on Monotone Flops Monotone flops tend to provoke great anxiety among poker players. It’s easy to imagine that… How to Defend Against Turn Donk Bets Responding effectively to donk bets on the turn is tricky;, there’s no getting around that.… How and Why You Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns of phrase have entered the poker… Should You Ever Cold Call a 3-Bet? When there’s been a raise and re-raise before the action is on you, you will… When ICM Breaks Down If you have read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When

How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most striking was large preflop all-in bets into relatively small pots. Though not unheard of in the pre-solver era, these huge shoves were widely considered fishy, a crude compensation for lack of postflop skill. And in that era, they often were. The underlying principle is correct, however: in the right spot, with the right kind of hand, a big shove preflop is the optimal play, in no small part because of the difficulty of playing these hands after the flop . These big shoves occur most often in late position when opponents’ ranges are widest (any two cards, in the case of blinds who have not yet acted). In such scenarios, it can be optimal to shove with hands too strong to raise-fold but not so strong they wish to induce action . This can incentivize a late position player to shove 20bb into an unopened pot or to shove 30bb or more over a late position “steal”. The blinds especially have an incentive to make these big shoves, as smaller raises would risk contesting a large pot out of position after the flop. For example, here is the BB’s response to a 2.3bb BTN raise with 40bb stacks, using the Chip EV model . The BB shoves 6% of hands with a clear preference for those with robust equity but poor postflop performance at a low SPR : small pairs, AQo, and AJo. These hands value the fold equity that comes from raising and are too strong to fold to a four-bet but not strong enough to want the extra action a smaller three-bet would induce. While it may be fairly obvious what sort of hand you have when you make this shove, there is little your opponent can do about it. While it may be fairly obvious what sort of hand you have when you make this shove, there is little your opponent can do about it: if they call with a tight range, these hands perform less well when called but win more pots without showdown. If they call with a wider range, these hands gain less from folds but have more equity when called. The only way this strategy can go wrong is if the BTN opens an overly tight range in the first place, in which case weaker parts of your range benefit by winning pots they would have lost to a steal from a more appropriately aggressive BTN. Shoving is an Option Many of these shoves are mixed strategies, where the EV of shoving is no better or worse than that of a call or smaller three-bet. Even for many hands that play a pure strategy, the EVs are close. Shoving 88 is worth 3.2bb at equilibrium, compared to 3.15bb for a smaller three-bet. The smaller three-bet with AK o garners 5.68bb in EV, compared to 5.59 for shoving. The key point to remember is not to blindly make big shoves with specific hands at

getting around that.… How and Why You Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns of phrase have entered the poker… Should You Ever Cold Call a 3-Bet? When there’s been a raise and re-raise before the action is on you, you will… When ICM Breaks Down If you have read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be a dicey proposition in single-raised pots. Cold… Dynamic Sizing: A GTO Breakthrough Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Dynamic Sizing Benchmarks Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Understanding The Impact Of Field Size On ICM In Poker When people talk about game selection in multi-table tournaments (MTTs), they invariably talk about the… Defending vs BB Check-Raise on Paired Flops This is a companion piece to Attacking Paired Flops from the BB; you will get… Mastering PKO Final Tables Final tables can be the most exciting and rewarding phase of a tournament, and being… Attacking Paired Flops From the BB Paired flops present unique challenges to both a preflop raiser and a BB caller. The… KK vs QQ vs JJ at WSOP Main Event With only fourteen players remaining in the 2023 WSOP Main Event and blinds of 400K/800K/800K,… Responding to BB Squeezes You open raise, someone calls, and the BB squeezes. How should you construct your strategy?… Crushing a Top HUNL Poker Bot In 2022, Philippe Beardsell and Marc-Antoine Provost, a team of Canadian programmers from Quebec, developed… GTO Wizard AI Explained We are excited to introduce GTO Wizard AI, formerly known as Ruse, the world’s best… GTO Wizard AI Benchmarks GTO Wizard has combined the power of artificial intelligence with traditional solving methods to bring… Table Management in PKOs Perhaps the most important strategic consideration in Progressive Knockout Tournaments (PKOs) is making sure you… Overcalling From the BB In poker, overcalling refers to calling a bet

One chip rule A rule in live poker games that when facing action, a single-chip being placed forward without any verbal declaration is considered a call, regardless of the chip denomination, including if the chip is larger than the raise size.

against these donkeys.” Either that, or they think they’re getting such a good price from the pot that, as the punters say, “Any two’ll do.” And all of a sudden they have all their chips in the pot on an A-8-5 board with A9 and they don’t know how they got into this mess. I’m sure you’ve heard the poker aphorism, “Play tight in a loose game and loose in a tight one.” I’m about to show you why that aphorism is, infact, gospel solid from both a mathematical and a game-theory viewpoint. Let’s look at the math side of things first. The Mathematics of Tight and Loose Imagine you’re playing a game called Biodome stud, seven-card stud played inside an eternal Biodome, where the game never ends and theplayers never die. Pretend that this game has 500 and 1,000 betting limits, but no ante and no bring-in, so that you only put money into the pot whenyou want to; it costs you zero to fold every hand for eternity. Given that you have all of eternity to show a profit in the game, what’s the only hand you’d ever play? Three-of-a-kind to start, where your trips areat least as high as the highest ranked card on the board. If a jack is the highest card out, you’ll play (JJ)J, (QQ)Q, (KK)K, and (AA)A. But if an ace isthe highest card on the board, you’ll throw (KK)K away. With no ante and no bring-in, why would you do anything else? You can just wait and wait and wait until you’re 100% sure you have the best hand and utterly crush the game. Of this game, then, we can say that it has zero risk of ruin. You can sit there forever, never playing anything but the nuts and never going broke. Now let’s imagine the same game of Biodome stud, only this time you have just 1,000 in chips to start and you have to ante 500. What hands doyou play? Almost every hand! Your risk of ruin is so high that you’ll have to play basically any three cards you’re dealt. Now check this out. Like the sliding scale of value to bluff, a sliding scale defines the relationship between the size of the ante and the size of thegame. We’ve seen a game with zero ante and zero risk of ruin. In that case, the size of the game is very big in comparison to the size of the ante. We’ve also seen a game with a huge ante and huge risk of ruin. In this case, the size of the ante is very large in comparison to the size of the game. The games you play will be at neither of these two extremes, but somewhere along that continuum, and once you know where you are on that scale, you’ll know—forever and always—how active you need to be. As the size of the game shrinks in comparison to the size of the ante, risk of ruin rises and you need to loosen up. And as the size of the

Now we know the procedure, let's we plug in our actual hand of 55 and see what happens. Branch 1 EV = +2.25BB. No change here. It's Branch 2 that changes. 55 has 41% equity vs. the top 10% of hands. Hero now gets back 41% of the 41BB pot or 16.81BB. He only loses 19.50 - 16.81BB when called or 2.69BB. His EV then is 2.69 x the 50% frequency with which the branch occurs. Branch 2 EV = -1.35BB Overall EV = 2.25 + (-1.35) = +0.9BB With these assumptions in in place, it's profitable for Hero to put Villain all in, but does he want to do this? No! The problem here is that unlike the last hand, this is not an end of action spot. In the real world, very occasionally, BB will wake up with a big hand and come over the top. In this case, Hero would be forced to lose 20BB if he folded. It's therefore more sensible here to just make a standard 3-bet size and accept that as far as CO is concerned it represents his stack. Even if CO makes the bizarre play of flatting Hero's 3-bet, the measly remainder of the money will go in on pretty much all but the very worst flops. Hero might even save a few bucks on AsKsQs. Hero raises to 9BB 40BB - The 3-Betting Stack Let's turn to an example where Villain has a more common stack size and one that short-stacking Regs like to wield aggressively. The reason that this stack can be played so aggressively pre-flop is that a smallish 3-bet can be used to create a very unpleasant situation for the opener. Take the following situation for example:

today we've released another update to the gto check solver dashboard the equity graph has been revamped to conform more closely to the type of equity graph that many are familiar with which has been implemented in some form in a number of solvers and other tools in the past this graph plots each hand within both players ranges depicting its rank in each player's overall equity distribution the y-axis shows the equity of each plot at hand scaled from zero equity at the bottom to 100 equity at the top and the x-axis shows the percentile strength ranking of such hand from weakest to strongest left to right based on its relative weight within the distribution so for example in this hand which is from a six max cash game where the small blind three bet the button the nuts are pocket eights on this board so if we isolate just the pocket eights we see that the equity of this hand is very high and it's at the 100th percentile of the small blinds range this type of graph can be quite useful to help us understand how ev maximizing strategies are driven in a number of ways for one it provides a very clear visualization of the strength of both players ranges at a glance which allows us to better assess how overall range compositions affect strategies so in this case we see that the ranges are quite symmetrical throughout most of the range up until around the 70th percentile which represents hands with around 60 equity or less the ranges are very similar it's only when we go above this point that the ranges start to diverge where for the next 25 or so of the range the small blind has a clear advantage likely primarily due to its over pair advantage and then at the very top of the ranges the in position player appears to retake the advantage however since this segment represents such a small part of the range it isn't very easy to make out so we've added this zoom bar at the bottom which allows us to hone in on select portions of the equity distribution to take a closer look all we have to do is brush in the area we want to focus on and then this chart will redraw so that the view becomes much more fine-grained and then we can brush this area where the in position player has the advantage which will isolate the specific hands in this region and now we can very clearly see the basis for the imposition player's advantage the buttons range contains more of the sets because he has fours and deuces which the small blind is unlikely to have as the pre-flop 3 better so the result of this dynamic where the ranges are symmetrical for most of the range and the button actually has the advantage with respect to the nuttiest hands coupled with the fact that the small blind is out of position results in a significant amount of checking

Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns of phrase have entered the poker… Should You Ever Cold Call a 3-Bet? When there’s been a raise and re-raise before the action is on you, you will… When ICM Breaks Down If you have read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be a dicey proposition in single-raised pots. Cold… Dynamic Sizing: A GTO Breakthrough Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Dynamic Sizing Benchmarks Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Understanding The Impact Of Field Size On ICM In Poker When people talk about game selection in multi-table tournaments (MTTs), they invariably talk about the… Defending vs BB Check-Raise on Paired Flops This is a companion piece to Attacking Paired Flops from the BB; you will get… Mastering PKO Final Tables Final tables can be the most exciting and rewarding phase of a tournament, and being… Attacking Paired Flops From the BB Paired flops present unique challenges to both a preflop raiser and a BB caller. The… KK vs QQ vs JJ at WSOP Main Event With only fourteen players remaining in the 2023 WSOP Main Event and blinds of 400K/800K/800K,… Responding to BB Squeezes You open raise, someone calls, and the BB squeezes. How should you construct your strategy?… Crushing a Top HUNL Poker Bot In 2022, Philippe Beardsell and Marc-Antoine Provost, a team of Canadian programmers from Quebec, developed… GTO Wizard AI Explained We are excited to introduce GTO Wizard AI, formerly known as Ruse, the world’s best… GTO Wizard AI Benchmarks GTO Wizard has combined the power of artificial intelligence with traditional solving methods to bring… Table Management in PKOs Perhaps the most important strategic consideration in Progressive Knockout Tournaments (PKOs) is making sure you… Overcalling From the BB In poker, overcalling refers to calling a bet or raise after another player has also…

Four straight (4-straight) A drawing hand, which consists of four connected cards such that one card rank will complete a five-card straight and thus create a made hand.

12. Bluffing the Turn and River We discussed c-bet bluffing way back in Chapter 4 where we were striving for fold equity against a wide range that had usually missed the flop. In this chapter we'll start off by discussing: Which parts of our range make sense to continue bluffing on the turn and river after our light c- bet gets called. Delayed c-bets and double delayed c-bets. Spots where we did not have the initiative pre-flop and wish to stab the turn or river after previous streets checked through. Bluff raising vs. river bets. The lines in this chapter are fun and feel good to successfully pull off, but we must remember that the success of a bluff often depends on variance and which part of Villain's range he happened to be holding. It's essential that we work out what constitutes a good bluff so that we can identify them as such independently of results. As always, results over small samples are a terribly unreliable way to measure the EV of a play. The temptation to feel like a poker god due to one bluff getting a fold is an important one to resist!

underdog, or about 3.5-to-l. You have to put in $130 to call this pot, and the pot has $750 in it. That means the pot is offering you a tad less than 6-to-l. So far, it looks like calling is a no-brainer. But there's some additional good and bad news to consider. The bad news is that you're not guaranteed to see the river card for just $130. The big blind and player C are still alive behind you. Neither has shown much this hand, so you're probably not going to see a raise out of them. But it could happen, and if it does your pot odds are wrecked. The good news is that if you hit your flush on the end, you're going to win a lot of money. At least one and perhaps two of them will hit a flush at the same time, and whoever does might lose most of his chips. So your implied pot odds are huge. It's hard to quantify the good and bad news here, but on balance it still looks good for you. So call. Action: You call. The big blind folds, and Player C calls. The pot is now $945. Fifth Street: 9♥ Action: Player C checks, and Player E bets $20. What's your play? Answer: Be calm. You've hit the flush, and since you have the king and the ace is on board, you have the nut flush. And since there's no pair on board, there are no full houses against you, so you have the lock hand. The beginner in this situation is so delighted with having won the hand that he just shoves all his chips in the middle of the pot. Resist this temptation. Your job now is to extract the most money from your opponents. How to do that is often a tricky problem. Your first job is to check out the remaining stacks. Player C started with $970 and now has $720 left. Player E started with $750 and now has $480 left. You are down to an even $600. By the way, this is a key skill to develop if you start out playing online poker and then move to live poker. You can't just look at the screen to gauge how many chips remain; you have to estimate it from the stack sizes. Don't worry - it's a skill that improves with practice. 75 The bad news here is the betting action so far. Player C only checked, and Player E bet $20. With four hearts on board, this action indicates one of three things: 1. No one has a heart. 2. Someone has a heart, but they're afraid of a higher flush. 3. Someone has a heart and has decided to trap. Case (3) is unlikely. It's foolish to check a flush after the last card, because of the danger that the hand simply gets checked down. Cases (1) and (2) are more reasonable. If it's Case (2), and you make a modest bet, the player with the flush will look you up.

THE SKLANSKY-CHUBUKOV RANKINGS 148 and you have an ace, you often have an easy move-in even when your stack is more than ten times the big blind. Tournament pros know that these “loose” move-ins are correct; in fact, that knowledge is the main reason many of them win money at all playing tour- naments. This secret is what separates tourney pros from amateurs. Use the tables starting on page 197 to help you decide when to move in, and you’ll find that your tournament results improve very quickly.

Diagram 21: Skill Edge (p=0.52)

that's small and at this point king nine twenty big blinds deep for top pair okay kicker is a premium hand that you are happy to play for all the money so you're going to check raise and you're going to call it off of your opponent's shoves yes you're going to be beat sometimes but when you are beat you only lose 20 big lines it's not that big of a deal and king 9 in the scenario is very very likely to be the best hand but if we're 200 lines deep in the same scenario where button raises we call big blind we check they bet 25 pot we can no longer raise and look to stack off if we check raise them here and they call or re-raise it's not good for our k9 at all but you see some players making this blunder quite often these are players who are used to playing shallower stat games in general or players who play a lot of short stack tournaments right they get a hand like um king jack on this board you know king jack's pretty good on king seven two they'll check raise it they'll get re-raised they'll just blast their money and they think oh probably the best hand but they're almost always behind and this is even more and more and more true as you get deeper and deeper and deeper so for dripping blind seep it would be a disaster to check raise this flop so this hand goes from being a very premium made hand very shallow stacked to a very clear marginal made hand when you're keeper stack so deeper stacked the plan is just a check call check call flop check call turn check call river and um that's it very clear marginal made hand so sack off threshold changes and essentially this impacts your strategy in a few key ways first on boards where you lack the nut advantage your continuation bet frequency and your check raising frequency or your raising frequency goes down whenever your opponent has more nuts than you or just like a decent amount of hands that are really really high equity and you either don't have those or your high equity range is very very small just because they don't make up much of your range to begin with you're gonna do a whole lot more checking and calling than you are betting and raising also you're gonna find that the cost of reopening the action on the river is higher because if you bet too thin your opponent can just start raising you aggressively let's take a look at a few gto examples here to show a few key adjustments as you get deeper and deeper stacked so on the left we have 100 blind strategy on the right we have 200 big blind strategy so here button raises big blind calls flop comes ten eight six okay big blind checks 100 big blinds deep we are checking 23 of the time betting you

my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players,… C-Betting As the OOP Preflop Raiser Position is an extremely valuable advantage in poker. Most players would describe the comfort zone… Overchoice: Making Sense of Multiple Sizings Solver solutions with multiple bet sizes often involve a lot of mixing between those sizes,… River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI upgrade already has some useful… How To Adjust When Villain Has No Bluffs “They always have it!” is a common, semi-joking expression in poker to describe the tendency… Adjusting on Later Streets After Exploiting Flop The key to exploiting opponents profitably is knowing when to stop. I’m not referring to… C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table tournament and the BB calls. Both… The Art of Bluff Catching Bluff catching—calling a bet with a modest hand which you

weaker players, and you want to win their chips before they give them away to someone else. Even here, you want to choose your starting hands carefully and pick cards that hold some promise. Don't lose sight of the fact that, when the blinds are very small relative to the chip stacks, the theoretically correct way to play is very tight. In order to deviate, you need a very clear idea of what you're doing. The Squeeze Play: Exploiting the Sandwich Effect The existence of the Sandwich Effect allows for a special kind of move called the "Squeeze Play." Imagine you have an early raiser, who may or may not have a strong hand, followed by a caller. When a player in late position now tosses in another raise, the original raiser is caught in a squeeze. The player in late position has shown strength and may have him beaten. But if the original raiser calls to see a flop, the caller, who might have been trapping with a strong hand, can raise as well. Under the circumstances, the original raiser needs a huge hand to continue playing, and will often elect to throw his hand away. Here's a complex example of a squeeze play in an important tournament. Sample Hand: Final Table of the 2003 World Series of Poker. The Players and their chip counts are as follows: Small Blind Amir Vahedi $1,500,000 Big Blind Tomer Benvenisti $700,000 1 Sam Farha $1,460,000 2 Yong Pak $320,000 3 Jason Lester $1,050,000 4 Dan Harrington $575,000 5 Chris Moneymaker $2,800,000 The blinds are $15,000 and $30,000, with $3,000 antes. The starting pot is $66,000. I'm in fourth position, and my hand is K♠ K♦ This was an unusual hand from the 2003 World Series of Poker. Sam Farha raised 60,000 from first position, and I knew from his style and the number of pots that he had been playing that his raise represented a weaker hand than usual from the starting position. When Jason called I still hadn't looked at my hand, but I decided to pull a squeeze and come over the top as long as I had any kind of reasonable holding, like a low pair or suited connectors. When faced with this move, the initial raiser gets squeezed between a reraiser and a caller who might have real strength, and almost has to throw his hand away unless he's latched onto a monster. The caller is then faced with a situation where he's out of position against a reraiser who's shown great strength. He'll Often throw his hand away as well. I'll make this play unless my hand is really hopeless, like seven-trey or eight-deuce. As long as my hand has some outs, this is a great move. 94 When I looked at my cards and saw that I was holding kings, I realized that I'd stumbled into an incredibly favorable situation. I decided to raise $200,000, overbetting the pot. Chris Moneymaker, Amir Vahedi, and Tomer Benvenisti all fold. Sam Farha folds. Jason Lester (with 7-7) calls for another $140,000.

and blinds. You should usually make a bet on the flop whenever you are the last raiser pre-flop, but be ready to put the brakes on if you get called. I don’t usually advocate check-calling after the flop, but even with a very good hand, this is a safer way of playing at this stage of the tournament. It keeps you from getting broke. You have to carefully evaluate your table, particularly if it isn’t going to break for a while. You have to be aware of the size of the chip stack each player has. Remember, the short stacks are more likely to go all-in before the flop with marginal hands than the larger stacks. However, the short stacks 332 can be pushed around more easily after the flop than the big stacks. If it’s apparent that your table isn’t going to break, you want to seem as if you’re unafraid to race by moving all-in occasionally. That is the best image. You try to wait for a favorable opportunity to go all-in, and you are almost always hoping not to get called. If I can double my chips the first day, I’m happy. THE SECOND DAY After the first day, you’ll want to accelerate your play a little more. Not by a lot, because you have to remember that you can’t win the tournament until the last day! But you have to accumulate some chips in order to have a better chance to survive the ante and blind increase. You need to be aware of your own chip count and your position in the tournament. A few years ago, I had an early rush the second day and grabbed $70,000, which put me among the leaders. I had a fast table with several large stacks. On one hand, the player in first position opened, and the player in third position, who had about $50,000 in chips and two WSOP championship bracelets, made a large raise. I looked down at my hand and found two kings. I considered my position in the tournament and then threw them away. I’ve always felt I made the right play, because I was probably either going to win a small pot or lose most of my chips. The player I laid that hand down to was Ron Stanley. He told me later that he had two aces, but he also told a friend of mine that my kings were good. Either way, I believe I was correct in throwing them away, because $70,000 was sufficient to get me comfortably through the next levels, and losing $50,000 would have been disastrous. Ironically, when we were down to twenty-three players, the same Ron Stanley broke me with pocket aces. Here’s one last thought about day two play: Just because you get short stacked, don’t be suicidal late in the day. Remember that the blinds and antes increase again starting the third day, and in major tournaments the prize pools are so big that it’s worth your time and effort to try to catch an early rush. To

The picture is already forming. If we only need 30% equity to call and Villain's value range is so tiny, it won't take many bluffs at all to be in there for calling to be +EV . Let's be conservative and say that Villain only raises the flop with sets and flush draws; this assumes that he uses no bluff combos other than hands with two hearts in them. Let's be even more conservative and say that though we've seen Villain bluff missed flush draws before on the river he only bluffs with them half of the time. Let's see how many combos of bluffs Villain can be estimated to have here. We'll start by seeing how many combos in his pre-flop calling range contain two hearts. Figure 48 - Ranging: Comparing V alue to Bluffs In green are the flopped sets (now boats or Quads) that we already decided were very likely to be a

you have to decide what to do before the big blind and you're in a tricky spot you continue with your middle Pairs and bottom pairs I don't know it's a tough scenario also when you call you are guaranteed to have to pay the rake assuming the big blind calls or folds which again is very bad for you we already learned from the big one you have to play kind of tightly when you have to pay the rake by calling you only get to continue with pretty good stuff both of these are detrimental so because of that you should three bet or fold with all of your hands you want to play from the small blind when you're facing just one razor and I realize this may feel very uncomfortable to only free bet or fold you do not get to call from the small blind but it is definitively the correct play especially in a game where they take a rake so let's take a look at this here we have oh small blind small blind versus race from under the gun small blind versus raised from the hijack and small blind versus a button raids against under the gun we have to be super duper duper duper tight you see we're only three betting Tim's and better Ace 10 suited and better Ace king offsuit king queen suited and a few Bluffs that is depressingly tight but again if the under the gun player is also raising with a tight range this is what you must do simple as that you got to be tight now if you wanted to widen this range a little bit to maybe include a screen off suit pocket eights and better Aston suit in a better King 10 suited and better I think that's probably fine but you really can't get too out of line in this situation if in some world you knew the button would never re-raise and you thought the under the gun player would be pretty straightforward maybe you could start to have a calling range with some of the hands in this region you know the good suited connected type hands and the pairs just to try to flop stats I think that could be reasonable too but again it's not the GTO strategy and I'm trying to show you what the the GTO strategy is here so that you can logically adjust right and hopefully you can look at this chart and realize if I wanted to put in a limping range it'd probably be Studio bases student connectors and pairs it's a good logical adjustment to begin that said three bedroom folding is very very strong and it becomes even better when you're against middle position or late position razors because then you actually get to play a decently wide range you don't have to be super nitty so you see against the hijack Rays we get to three bet something like six isn't better all the good suited connected hands and Ace

Hero reads and masters the technique in the box overleaf at some stage, he should feel free to skip it for now if he prefers to jump straight to the equity table and what this means for c-betting in the hand above.

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we're going to do today is go through just a few mark 10's and then just talk about all the different game theory concepts that are at play we're going to dive into power solver the goal of this is to look at situation develop strong habits and fundamentals such that you can apply these concepts to a bunch of different board textures a bunch of different situations that you're going to face in game so yeah let's uh let's jump right in firsthand comes from a recent 25k uh actually forced to the button this guy raises he's a strong player we call king three of spades trapped in deuce rainbow chuck about 25 pot and that leads us to our first decision point so i think this is a really good hand to show uh how to construct check raise ranges um especially when we're facing a button open because they're gonna have a really wide range they're gonna be betting with a really wide range of bands in these situations come up all the time and anytime you're dealing with really wide ranges it's it's really difficult to defend versus aggression right so um let's first talk about how we want to construct our check raising range and the spot on jack 10 2. so we have a really clear section of hands that that are easy to find right our best jackass king jack jack queen jack nine um even jack gates going to be strong enough and it's going to mix dip down from there with a jackass and then we have like a really um natural draws our natural draws here are going to be some eight nine some queen nine some kingdom right our gut shots are open-ended straight draws but it's just not going to be enough of hands to cut to give us board coverage on enough run outs and so the third hand type that you're going to find in this box is going to be one over card to the jack and after flush draw type stuff like the hand we have here so i go for the check raise in the spot and the opponent calls so let's first look at this flop uh in the solver and start looking at exactly what hands are talking about so two high cardboards button versus big blind forty bigs there's like a bread and butter spot um it's just gonna be a pure small bat from the opponent almost every time um you can find a little bit of bigger bats with like queens kings and maybe a little bit of like king jack off suit and stuff but most people are just going to play a pure small bat strategy um so after about 25 here's our response to the small bet as you can see we're obviously going to raise our strong jackax um and this is typical right it's like our best jacks like king jack we want to raise it every time it's just it's like the nuts

different strategy in the situation just described. Under these circumstances it becomes almost always correct to simply call the initial $10 bet with the next-to-last low card when you have a hand. You are hoping for an overcall behind you since the player is no longer getting sufficient pot odds to gamble on outdrawing you. The difference in strategy is based on the Fundamental Theorem of Poker. By calling, you have not only induced your opponent to make a mistake with a weak hand, but you've given 2 6 0 C h a p t e r T w e n ty - fiv e t h e i m p r e s s i o n t h a t y o u r h a n d i s w e a k e r t h a n i t i s . I f y o u r o p p o n e n t c a l l s , y o u w e l c o m e i t . I f h e r a i s e s , th at's fi n e t o o . T h e i n t e rw o rk i n g o f d i ffe r e n t s tru c tur e s a n d s t r a t e g i e s c an a l s o b e s e e n b y c o m p a r i n g t h e o l d $ 1 0 - $ 2 0 h o l d 'e m g a m e i n R e n o an d th e $ 1 0 - $ 2 0 h o l d 'e m g am e i n L a s V e g a s . I n V e g a s th e fi r s t b e t i s $ 5 , an d a r a i s e r c an m ak e i t $ 1 0 . I n R e n o th e fi r s t b e t i s $ 4 , a n d t h e r a i s e r c a n m a k e i t $ 1 4 . T h e fi r s t e ffe c t o f t h e s e d i ffe r e n c e s i s t o m ak e y o u p l ay s o m e wh at t i ght e r i n V e g a s s i n c e y o ur i n i t i a l i n v e s t m e n t i s a d o l l ar m o r e . H o w e v e

2003. Well, I’ve just explained to you how that happened. I was playing my money, my position, and a particular player—and my hand could have been anything. I hadn’t made a pair the whole day, and I’d had to stay alive by stealing some pots, but on this particular play, my read was wrong. 361 You’ll almost surely have to get some no-limit experience under your belt before you’ll be able to play a pot completely blind. So, in the beginning, I suggest that you restrict the way you play specific hands to the recommendations I make below. However, it’s important for you to understand that those recommendations are what I would do in a normal or medium ante ring game. In different games you’ll have to adjust your play as previously discussed. In order to help you determine what constitutes a normal medium-ante game, you should use the following table as a guide. Nine-Handed Game - Blinds Chart Ante Size $ Ante Single Blind Multiple Blinds Buy-In* 1st seat 2nd seat Very Low $1-$5 $5-$10 $5-$10 $10-$20 $1,000 Low $5-$10 $25 $25 $50 $2,000 Medium $10-$20 $50 $50 $100 $5,000 High $25-$50 $100 $100 $200 $10,000 Very High $50-$100 $500 $300 $500 $25,000 *Twice the minimum buy-ins listed here would be much better. More than twice would be better still. You wouldn’t want to sit down with less than the minimum buys shown. As the footnote states, you should definitely consider buying-in for more. Today, when I play in a game with two blinds of $300 and $500, I never sit down with less than $100,000. What’s more, I like to have as much or more money than any other player at the table. If my stacks are not approximately equal to the guy with the most money, then I couldn’t break him, could I? And I practice what I preach. I start playing fast right away. I’ve always played like that, even when I was just starting out. Back then I’d buy in for a thousand in a small no-limit game, and I’d usually get stuck that first thousand. Then, I’d pull up and start playing tighter, and I almost always got 362 even or won. About three out of four plays, I’d lose that first thousand, but on that fourth play, I’d get on a winning streak or a rush, and I’d more than make up for those first three losses. I mean, I’d be playing so fast and winning so many hands when I was rushing that I’d literally break every player in the game. Because as you know, whenever I hold a bunch of hands, I usually get action on them. I’ve never won a bunch of pots watching the other guys play. If I’m making a bunch of hands or striking, I’m in there—I’m not on the sidelines. If you’re going to have a rush, you’ve got to let yourself have one. You’ve got to sustain that rush. And to do that, you’ve got to get in there and play. It used to be that after

That requires recognizing and refusing to fold the top of your own range . A Dynamic Flop On 9 ♥ 5 ♦ 2 ♦ , UTG actually has the advantage at the very high end of the equity distribution Equity distribution A line graph or scatter plot of a player’s hand vs range equity, sorted from weakest to strongest, such that the equity of every individual combination in the range is represented. Commonly used in game theory analysis. , and donk betting plays a significant role in their strategy: The choice of which hands to bet is not as arbitrary as it appears. With 99 , UTG bets top set without a diamond but checks when they have one. With the other pocket pairs that did not flop sets, they prefer to bet when they do have a diamond. As explained above, the pairs mostly stack off if UTG1 shoves over the bet , as do the overcards+flush draw hands: This flop misses almost all the unpaired hands in both players’ ranges. The pocket pairs aren’t great, but they’re the best you’ve got, and if you’re not going to fold them, there’s a lot to be said for getting the money in early. These same hands are candidates for check-raising , except for the sets, which exclusively slowplay when checked because they are much less in danger than the pocket pairs of losing value on later streets. From a solver’s perspective, it is perfectly viable to either check-shove or donk bet and call off with 66 despite your opponent’s range being thick with overpairs. That’s a consequence of the very low SPR and the fact that this flop misses almost all the unpaired hands in both players’ ranges . The pocket pairs aren’t great, but they’re about the best you’ve got on this board, and if you’re not going to fold them, there’s a lot to be said for getting the money in early . More cards coming down means more chances to get drawn out on or bluffed out. A Moderately Dynamic Board Swapping the 2 for a Q makes the board somewhat less dynamic. Both players have a lot of KQ and AQ , which are much less vulnerable to overcards than equivalent hands on 952 . Both players also have a lot of broadway straight draws , which, even though they won’t come in often, represent a real threat because of the size of the pot. Getting drawn out on, in a pot worth as much as your stack is nothing to sneeze at. Getting drawn out on, in a pot worth as much as your stack is nothing to sneeze at. On Q ♦ 9 ♥ 5 ♦ , the equity split is about the same as on 952 . But with the board being less dynamic and more of the best hands in UTG1’s range, UTG no longer has the incentive to donk bet. They still check-raise aggressively , but on this board, their best hands are the more obviously strong AQ and AA . They balance

are hard to win . Making multiple opponents fold is difficult, so you must often triumph at showdown . But the average winning hand at showdown will be stronger, because you will typically go to showdown against the strongest of several hands that saw the flop, which means you must have an even stronger hand. Being out of position is also more of a liability in a multiway pot. As bad as it is to be out of position to one opponent, it is even worse being out of position to two. These factors lead to poor equity realization , primarily for disconnected offsuit hands when the BB faces a raise and one or more calls. Despite the appealing pot odds, BB folds more often with more players contesting the pot. When they do continue, the callers provide extra incentive to three-bet rather than call . These three-bets are not bluffs; taking the pot down immediately is unlikely. Rather, the BB three-bets primarily strong hands (with “strong” being relative to the position of the original raiser), in the hopes of folding out one or more opponents, trapping dead money into a pot they can contest heads up. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When

Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet too often . The unexploitable, solver-approved strategy is already to bet their entire range. In other cases, it is close enough that simplifying to betting their entire range does not open them up to significant exploitability (though it does make it all the more important for the blinds to respond with appropriate aggression). However, the raiser is not supposed to bet even half their range on less favorable flops. If they bet too often in these spots, their opponent can exploit them in multiple ways, some more intuitive than others. In this article, we will conduct several experiments using the nodelocking feature to learn how to exploit over-aggressive continuation bettors . The Experiment These simulations are based on 30bb ChipEV preflop ranges in a single-raised pot between a BTN raiser and a BB caller . While the general principles of how to exploit an in position opponent who bets too often apply to other scenarios as well, these stack depths and positions bring the principles into a particularly clear focus. The BB, acting first, may check or bet 33%, 66%, or 100% pot. The BTN’s only continuation bet size is 33%, and we will experiment with what happens when we nodelock them to bet their entire range . The BB may respond to this bet by calling, folding, or raising 33%, 66%, or 100% pot. If they raise, BTN has the same options. Options on later streets are determined using the Automatic feature . The Low Connected Flop At equilibrium, donk betting is an important part of BB’s strategy on 6 ♥ 3 ♦ 2 ♣ . They have a lot of 6-x, which is strong enough to play a fairly big pot on the flop but will lose a lot of value on later streets, as the turn and river will almost certainly bring overcards. BB’s Donk Betting Strategy If BB checks, BTN bets 62.5% of their range, after which BB responds mostly by calling , raising just 11% of their range. So many of their best hands went into their donk betting range that they do not have enough value left to balance a wider check-raising range . BB donk bets to prevent BTN from checking behind the flop. If BTN is never going to do that, then BB prefers checking to induce bets. When we nodelock BTN to bet their entire range , BB has no incentive to donk bet. The main reason to bet a hand like J6 would be to prevent BTN from checking behind the flop. If BTN is never going to do that, then BB prefers checking to induce bets from the many weaker hands in BTN’s range. Then, they can raise all those top pair hands to get even more money into the pot and deny equity to BTN’s live overcards: Notice that BB’s primary exploit is raising more , not calling more. Calls do not really “punish” BTN for betting too often because

Hand Range 199: SB vs LJ (40bb) • All-in 1% / • 3-bet 8% / • Call 12.2% / • Fold 78.8%

all-in raise. This is typical and maybe even correct behavior. He’ll reraise with the pocket sevens, hoping that you’ll fold. He’s a favorite over

THE CONCEPTS 178 the rest of your stack on the flop, you don’t offer them enough compensation to call. It’s $110 more to them, but they can win only $845. Getting less than 8-to-1 maximum implied odds, they can’t call profitably with a pocket pair, let alone any unpaired hand. If you raised to $80, however, you’d have the worst of both worlds. It’s an uncommonly large size, so your opponents would expect an excellent hand. But now the implied odds math works out very differently: It’s $70 more to them, and they can still potentially win $845. Now they may have implied odds of slightly more than 12-to-1, allowing them to call profitably with some hands. Usually you should just make the modest, pot-building raise and hope to win a big one. Occasionally you might want to make the large hand-defining raise. But don’t make a raise in the middle. Don’t tell your opponents what you have and then turn around and give them the right price to try to beat it. Concept No. 29: It’s ok to make small raises (2 −3× the big blind) to build the pot or to set up future plays. For some reason, making small raises has acquired a stigma in the no limit community. By small raises, we mean the minimum raise (to twice the big blind) or slightly larger. While there are right and wrong times to make any play, there’s nothing inherently bad about making a small raise. As we discussed in the “Sizing Your Preflop Raises” section, there are a number of factors you should consider when you decide what size raise you want to make. The nature of your hand, the way your opponents play, the stack sizes, your past plays, your image, and more go into each decision. Many preflop raises are primarily intended to elevate the stakes of the game. These raises are based on preflop hand strength or intended as a semi-bluff. You make them only because you prefer the postflop bets to be larger than they would be in an unraised pot. (If you double the size of the preflop pot, you’ll more or less double the size of the postflop bets as well.) Often you should make this sort of raise with “brave” hands – pocket pairs, suited connectors, and suited aces — hands that play well after the flop. The goal is to turn your $5–$10 game (or whatever limit you’re playing) into a $10– $20 or $15–$30 game for this hand only. Say you have A♡T♡in early position in a nine-handed $5–$10 game. You’ve been playing mostly with an $800 stack, but you just won a big pot and now you have $1,500 in front of you. With the smaller, $800 stack, you would usually limp in with the hand. But now that your stack has doubled, you might be better offmin-raising: making it $20 to go. Mostly your opponents will react to your min-raise exactly as if you had limped. They’re not likely to fold their “limping” hands just because you raised.

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

We have 4 hands on Villain, which is a pretty meaningless sample even for stats like VPIP and PFR. However, a player who has already 3-bet (likely one time from two opportunities) and has not yet limped or called an open is more likely to be a Reg than a Fish. His normal Reg-like 3-bet sizing makes this even more likely. Position: Being out of position will cause a great deal of difficulty post-flop. When the pot is larger any mistake made due to lack of information from bad position will be magnified. It is now Villain who reaps all of the benefits and as his EV increases, Hero's decreases. Frequent Strength: 77 has pretty poor frequent strength especially out of position even if Villain's range does turn out to be very light and bluff heavy. We're flopping some underpair, second pair, or more rarely a weak overpair 88% of the time. That's 88% of our potential 6BB investment or 5.28BB that is being thrown into the pot under very negative conditions. This lack of playability is even worse out of position. Versatility: 77 is a completely rigid hand. It either flops the world or very little. Hero will have no aid in the form of semi-bluffing equity. Weaknesses: We don't know of any. Implied Odds: As 77 is an implied odds type of hand, it's worth investigating if these are sufficient to compensate for the other factors all being against us. Hero would be investing 6BB to see the flop and so with implied odds alone would need to be winning back around 60BB the times he flops a set to

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…

evey the first two weeks were frustrating but it's starting to pay off now I'm buying you breakfast and Vegas I like that really appreciate that Kerry let me even I think it's a boring breakfast now it's weird when you're playing a poker tournament you can't eat white carbs because it just gives you this glycemic spike and then you're just screwed right so you have to eat pretty much eggs bring your own avocados Nicholas says why check raise 3x every time and not higher is this to maintain balance or for another reason I find when you go up to 3x Nicolas that's a really good question people just call without thinking Rick says thank you Alex I just superb I just purchased I appreciate Thank You Dakota says thank you is this good for all my also yes sir if you go lower than $100 tournaments excuse me Alex Quinn says how do you deal with tilt in the middle of tourney's I have had a hard time shaking off mistakes or hiccups while I'm still playing thank you by the way for the great content Alex that is uh the first thing you got to recognize alex is your brain is not meant to gamble I would recommend reading any book you can about neuro economics if you ever want to do this seriously your money in your brain is grade Thinking Fast and Slow is great if you enjoyed Moneyball by Micheal Lewis he wrote another book called the undoing project which is all about this the human mind is not made for financial risk and reward so first of all your brain is just not meant for it and you really have to train it away too you got to play with money you can afford to lose three you got to kind of pretend it's loss and a lot of this you know what I realized a lot of times when I tilted it was entitlement like it's really funny we'll enter a tournament with a thousand people in we all for some reason think moi is gonna win think about deeply insane that is now narcissism is actually very natural to the human condition if you think about a baby a baby is very narcissistic it does not think of other creatures because if it were not narcissistic the baby would probably die therefore the narcissistic baby has to cry out for food that is very intelligent right that is an evolutionary by-product that has made us go further but it's really hard to get rid of when we're playing poker we really think these special things are supposed to happen to us so the way I tell it to myself alex is like look if I was going into a fistfight I would expect to get hit if I'm going to play no llem and hold him especially No Limit Hold'em tournaments I'm expecting something goofy to happen every single time you play poker No Limit Hold'em especially things are going to

Diagram 72 UTG c-bets a lot more frequently than the CO. In fact, the CO’s range is in general weaker than the BN’s and CO could easily opt for a 100% checking strategy with minimal to no EV loss. This is similar to the BB vs IP situation where the BB can opt to never donk bet the flop. This strategy works well as an exploit against the population because most players tend to automatically bet the flop when OOP checks to them, whereas the equilibrium strategy is to take a stab at the pot half the time. Checking the flop with all hands allows Hero to play an aggressive check/raising strategy, taking advantage of IP’s aggression, while reducing the effective SPR and positional disadvantage. Many players make the mistake of c-betting way too often when OOP, particularly with weak and trash hands, only to x/f the turn most of the time. This is a serious leak that can be easily attacked by observant opponents who can call the flop bet and then fire the turn 100% of the time when checked to. C-betting Range Strategy Overview: UTG vs BN 40bbs Much as with IP c-bets, OOP c-betting will heavily depend on the board. In this section, we will examine UTG vs BN 40bb deep c-betting to get an overall picture of how the strategies change when compared to playing IP.

Hollywood Refers to an exaggerated or obnoxious way of speaking or acting toward an opponent in a hand, typically to induce a reaction or gain information about a player’s hand strength. Or to try to mislead an opponent's assessment of hero's hand strength.

hereo checks uh C of bets small about one3 he do check races um cut of calls uh there's a six of space on a turn and hero jams and he gets the call by Ace five spades diamonds so um now we want to check out the simulation and see um if here play this hand correctly or if we can improve on it um again start off by looking at the equities so equities run pretty close and given the equities run pretty close again we will see a lot of checking from out of position uh but here interestingly enough if we bet um the hero wants to bet the bigger bet size than uh this smaller one let me see um go back to the Flop now yeah um here the main reason why we are betting this big is because um there are a lot of draws here this uh the beted size is also influenced by uh how much protection do your um strongest hands required right if this was if the Flop was um with a different structure then your um stronger hands will not require as much protection and there's also um a lot of good hands that the impul player can have here to call here the bet now let's look at the uh strong the range polarization and see who has stronger range on the Flop so starting with the out position player he has uh sets about nine comos 3.7% of his range and IP also has um has a little bit less he only has um um Aces and okay yeah he only has Aces but um and yeah so IP only has Aces and out position has nine combinations he has hes 10 and eights so this is a big uh very big incentive for the out position player to use a bigger bet size because he has a lot more noted noted hands than the in position player has and he can get a lot of value from those so betting with a set here um um he he has the sets as protection he can B with with those with some frequency but the hands that really benefit from the um bigger bed size actually hands like top pairs that uh benefit from getting FS or from yeah basically from what we're looking for here is protection betting and the stronger hand like the sets will be more inclined to uh to just check because they don't really need as much protection right they if the opponent has something like a queen 10 if you have a set you're not really going to lose on the turn if your opponent makes two pair you actually want your opponent to make two pairs uh so that uh you can extract more value in later streets so betting with um with a set here will not be terrible if we look at the e but um um just losing little bit less than a chip if we use a

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

♦ Polarized 3-betting: If Villain is more likely to 4-bet or fold than to call, you can increase your 3-bet range to include more hands that have good blockers to their continuing range. For example, AJo, A5s, and KJs can flat call because they are high equity hands that you don’t want to 3-bet/fold. ♦ Linear 3-betting: If Villain is more likely to call your 3-bets than 4-bet, then you want to 3-bet a linear range made of high equity hands that also have great post-flop playability and will dominate Villain’s flatting range. Specific Ranges Playing Versus Open Raises Here we analyse the GTO solutions to playing vs open raises from each position and discuss the key factors that are implied by the construction of the ranges. Hijack The HJ plays a 3-bet/fold strategy with no calling range when facing the LJ’s raise (Hand Range 56). From this position the maximum number of hands you can 3-bet and remain unexploitable is ~8% hands. It might be surprising to the reader that this strategy has a small weight in pocket pairs such as 88 to 22, because if 88 is clearly better than 22 then why not only 3-bet 88 more frequently instead of 22? The main reason is that you want to have good post-flop board coverage and be able to hit sets and other strong hands on many different types of flop texture. Another reason is that if you only 3-bet specific hands, your opponents will be able to use their blockers more effectively against you. Against a LJ 4-bet, you want to 5-bet ~18.4% of the time, but since you have position, your main response is still going to be to call with most of your continuing range, slowplaying AA 52% of the time and just calling pairs that are weaker than KK. Other hands that like taking flops are the small suited connectors, AKo (46%), AQs, AJs, KQs and a small fraction of A5s-A4s (Hand Range 57).

Diagram 67: Low c-bet % and Small Bet-size: BB vs BN on 5♥5♦4♥ (40bbs) Diagram 68 On this flop, the BN doesn’t have a significant range advantage, hence the preference for the smaller bet-sizes. In fact, most of the BN range is made of good hands, giving a depolarized distribution that will result in a low c-bet frequency, as many good and weak hands in the BN’s range will benefit from checking back the flop.

what it was but I'll think twice before betting you again.' I was now at ease. I said, 'I told you you wiggled your ears.' That's good enough for me. How would you like to work for me? Loggy Flick, one of my housemen, is quitting. He's cost me too much money. He plays a poor game of poker and I think he steals from me. When he's running the game he cuts every pot fifty cents, which runs into about ten dollars an hour. He can easily steal two dollars an hour from me without my knowing it. After school and up to bedtime when I'm not playing I'd want you to cut the pots. You can play at the same time you cut.' Monty paused, and when I said nothing, continued. 'I'll tell you what I'll do. I'll back you up to two hundred dollars and you give me one half of what you win. I'll stand the losses if any. You keep one half of the cut. Is that fair?' 'More than fair,' I said. 'But I couldn't let you back me unless I knew more about the game. I'll cut the pot for twenty-five per cent of the cut and will back myself if you will give me lessons in play. When you think I am good enough to risk your money I'll accept your offer.' 'It's a deal, kid,' he said, shaking hands. 'Monty, I want to tell you how I knew you were bluffing,' I said. 'That's your secret, kid.' 'No, I want to tell you. After all, if I’m an apt student we will be partners.' I paused to frame my words. 'Monty, you are left-handed and ordinarily hold your cards in your right hand and bet with your left. Under stress you switch your cards to your left hand and bet with your right. That's how I knew.' 'Well, I'll be a son-of-a-bitch,' he said, and got as red as a beet. 'And you changed seats just to get on my left so that when I raised the shoe drummer you could back in and draw one card. You'll do. You make some bad plays but I can correct that. By the way, what did you have when you drew one card?' 'The same as you - nothing. That's the reason I had to raise.' 'Well, I'll be a son-of-a-bitch!' 'You said you would correct my play. Suppose we start now with the first lesson.' 'Go ahead.' 'Explain the trick you tried on me. Why did you select straight draw instead of deuces wild?' 'Because in deuces if you stand pat you can't make these simpletons believe you have five of a kind or a straight flush. They will think you have a straight, flush, or a full house, any one of which can be beat easily. If you draw one in deuces, though they know the four deuces and the joker are wild, they are silly enough to think you are drawing to a straight, flush, or two pair. If I raise you

perceive you as bluffy, then they call more. If they perceive your range as weak, then they can attack more aggressively. However, if their strategy is unchanging (fixed), your range has no impact on the optimal strategy of your hand. You can simply maximize your hand against their fixed strategy without regard for balance or their perception of your range. Let’s play a GTO bot We’re playing a HU match in the BB. The bot bets 33% on Q95r: The GTO strategy facing this bet looks like this: The bot is playing a fixed strategy. That means we could: Pure raise any hand that’s raised at any frequency Call any hand that’s called at any frequency Fold any hand that’s folded at any frequency These actions are indifferent, and the bot won’t adapt to exploit our mixing imbalances. This is because a fixed strategy like GTO doesn’t punish mixing mistakes, only pure mistakes. This toy game will make you angry Let’s take a look at a BTN vs BB SRP on this T666J: BTN bets 33% on the flop, overbets 175% on the turn, action on BB on the river. Here BB’s best strategy is to rangecheck, regardless of hand strength. Even the nuts should pure check. Here we see the expected value of various actions with Q6s (Quads). As you can see, checking is by far the highest EV action: This is because our range is weak enough that villain should put in a ton of money when checked to. So quads maximize value by rangechecking. What would happen if BB got to this river with ONLY quads, nothing else in range? How should quads play if villain (BTN) will continue to use the same fixed strategy? Should we start leading now that our range is so nutted? A. Should BB start betting? B. Should they mix bets and checks? C. Or should they continue to rangecheck? Click here to see the answer C. BB should continue to rangecheck! BTN is nodelocked to use the exact same fixed GTO strategy on the river. Since checking was optimal before, it’s optimal here, despite our range being comprised of the pure nuts. In other words, we can simply maximize each hand in a vacuum against their fixed strategy. Our own range has no impact on the best move because villain isn’t capable of adapting their strategy. What to take away The three most important takeaways: Understand the difference between mixing mistakes and pure mistakes Learn how each of these mistakes is punished Why it’s important to distinguish between fixed and dynamic strategies Mixed (indifferent) hands are only mixed to prevent your opponents from exploiting you. If your opponents are incapable, unable, or unwilling to adjust, then you shouldn’t be concerned with balancing mixed decisions. Instead, you should focus on maximally exploiting your opponent. It’s important to realize that exact frequencies are less important than overall strategies. So in the Q95r example, it doesn’t matter that J3s is mixing some percentage of folds/calls/raises, what actually matters (in terms of exploitability) is how hero constructs

the line of play that gets those hands to laydown. They won’t fold on the flop, but they might on the turn. If they don’t lay down, oh well. You’re done betting and calling. Not all bluffs work. They’re not all supposed to work. In the face of a heavy bet on the river, just release your hand. But look at the overall price you paid: a small call on the flop and a reasonable raise on the turn. Compare that to the conventional approach to bluffing: a raise on the flop, a bet on the turn, and if you have the chips and nerve, another bet on the river—that proverbial third barrel. The beauty of delaying your bluff until the turn is that’s your first barrel, so if you bet on the river, that’s a second barrel. You never ever have to take a third barrel. Notice also that while AK is likely calling on the turn, he’s definitely not betting on the river. He might make a crying call if you bet—which is why you have to think carefully before you fire again—but he’s certainly not leading into you. That’s such a scary story you’ve told, he’s just hoping hishand is good. Further, no law says you have to bluff at all on the turn. If it goes bet, call on the flop, and your opponent leads into you again, take a read. If youread him strong, you can fold. No harm, no foul. But you got two looks at him for the price of one, and that’s something. Think about your cumulativeedge in decision-making if you’re making all your decisions based on two betting rounds, not one. That’s huge. And you got away from your bluff for 500 instead of 2,000. Further, the way this is set up, to tell such a strong story, you don’t even have to make reads so well. Don’t know if your guy is on AK or AQ? No worries. Maybe they both fold if you raise the turn. Those turn raises inspire fear in some pretty strong holdings. Flop raises? Not so much. If you think your guy will get hip to your tricks and start decoding your bluff patterns, remember, you’re playing your big hands the same way. That’s some effective shit. Your opponent knows that you love to bluff. He even knows howyou bluff. He just doesn’t know if you’re bluffing now. One more myth to explode is the cheap bluff on the flop. Most people try to bluff early in the hand, thinking they’re investing less money by bettinginto a small pot. But I just showed you that you actually invest less money, with more confidence, by waiting. Why don’t most people wait? They’re afraid. They want to take a cheap shot at a bluff and break it off if it doesn’t work. And then what happens? They get re-bluffed, because the price is still pretty low. If you call on the flop and raise on the turn, though, that takes the re-bluff completely away. If they want to re-bluff

3.5 Limping Behind I started this chapter off by warning you about the dangers of open limping. I then discriminated this from limping behind. The call you see Hero make in Hand 11 above is a type of limping behind that can only be done from the SB. This call is called a 'complete.' Note that Hero should generally only complete the SB where there have been one or more limpers in earlier position. Where the action folds to Hero in the SB, he should follow the opening strategy covered in Section 2.7. In Hand 11 we concluded that Hero's poor position tipped the scales away from ISOing. It's unlikely to be profitable to raise such a mediocre hand out of position where fold equity was compromised by the Reg in the BB. This didn't mean, however that Hero was forced to fold. When we've decided that ISOing is out of the question Hero is left with another choice: whether to limp behind or to fold. The answer to this question depends on three main factors: 1. Pot Odds The better the price Hero is getting to call in relation to the pot, the more inclined he should be to come along. 2. Implied Odds Recall that implied odds are the ratio of Hero's investment compared with what he wins on average on future streets from his opponents' stacks. Good implied odds will require a hand capable of flopping something powerful that can extract a lot of value and that there are players in the pot who can pay Hero off should he flop that strong hand. 3. Post-flop Steal Potential Hero should look to limp behind or complete the SB where his opponents are particularly fit-or-fold and where there will commonly be opportunities to take down the pot with a bet on suitable flops,

upon when eight players see the flop: Jacks, no over cards flop: Wins 20.5% of the time; eight of the other hands win 9.9% of the time. Jacks, one over card flop: Wins 14% of the time; each of the eight other hands wins 10.75 percent of the time. Jacks, two over cards flop: Wins 9.6% of the time; each of the eight other hands wins 11.25 percent of the time. Jacks, three over cards flop: Wins 12.9 percent of the time; each of the other hands wins nearly 11 percent of the time. It is interesting that when three over cards flop then the Jacks get a better win percentage. You have the key card to making a Straight if the fourth card, usually a Ten, appears. Actually, Jacks do a little better against over cards for this reason. They can make a Straight up and down while blocking someone with two over cards from completing their Straight. Even if one over card does appear to your Jacks, it does not mean you are beat. It depends on how many opponents are still playing against you and the type of hands they will play. May players will call a raise and even bet out/re-raise with an under Pair to gain information. In this next section, I want to look at your Jacks against different types of hands on the flop. I applied the hand of 8 7s for running these probabilities on Poker Stove. If you have a set on the flop but there is also a three Flush on the board and it completes a Flush for someone else you are a 3 to 1 dog to lose the hand. If you have a set and your opponent has a two Flush and open ended Straight draw (15 outs) you are a favorite 57.88% to 42.12%. If your opponent has a Gut-Shot Straight draw and a two Flush Draw to your set, your win percentage goes up a bit to 65.25% to 34.75%. If your opponent only has a two Flush Draw and a backdoor Straight draw to your set, you are a large favorite: 73.54% to 26.47% an almost 3 to 1 favorite. The odds are about the same if your opponent has an open-ended Straight draw to your set: you are a 3 to 1 favorite. If your opponent has a Gut-Shot Straight draw to your set, you are a 4.5 to 1 favorite to win the hand. Finally, if you made a set and your opponent has made 2-Pair with smaller cards, he is essentially drawing dead. Any pair on the board that makes his Full House (if his 2-Pair are an under Pair to your Jacks) makes you a larger Full House. Of course, this assumes you make your set on the flop. You will hit your set on the flop 10.78% of the time. You will make a Full House 0.98% of the time and quads .245% of the time. One reason that Jacks are difficult to play is the decision making process after the

Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players are incentivized to make high-variance plays for bounties often masks just how complicated they can be. One of the areas where players struggle in this regard is multiway pots. It is often correct to take seemingly wild gambles, and play in a way that would otherwise be unprofitable in regular tournament formats, when multiple bounties are on the line. How much wider can we go for multiple bounties? A lot of the equity in PKO tournaments comes from multiway pots, where you have the potential to win multiple bounties and/or lots of chips. Unlike in regular MTTs where pots tend to be heads-up, it is routine for hands to have three or more players volunteering chips into the pot. A great way to illustrate this is perhaps the most interesting spot in PKO tournaments – the very first hand . The first hand dealt in a Progressive Knockout tournament is unique because it is the only time all the players cover each other. Therefore, everyone can win everyone else’s bounty and, in theory, everyone could win all the bounties simultaneously. If you have read our article on Bubble Factor you will be familiar with this image, which are the Bubble Factors and Risk Premiums of everyone in the first hand of a PKO. Bubble Factors do not go below 1 in regular MTTs, and Risk Premium is never negative, except in PKOs. What this means in layman’s terms is that you are often incentivized to get your money in wider than ChipEV pot odds dictates in PKOs . This is because you win four types of equity when you bust a player in a PKO: You win prizes from the payout structure of the tournament, like in regular MTTs. You realize immediate equity by winning the bounty. You win future equity in the form of the bounty on your own head getting bigger (which you can only realize by winning the tournament). You win future equity because you increase your chance of winning more bounties by covering people. Because you have a greater upside in PKOs compared to regular ‘Vanilla’ tournaments, you are incentivized to play looser, particularly in multiway pots where there is a chance to win several bounties. We can demonstrate this with a simple toy game . This is the first hand of a non-PKO SNG with six players. Everyone starts with 10BBs, 1st place wins $66.66 and 2nd place wins $33.34. The BTN shoves 38.1% of hands with this range: When BTN does shove, SB calls with 17.3% of hands with this range: Finally, when SB calls, the BB over-calls with just 6.1% of hands, with this range: No surprises, SB calls much tighter than BTN shoves, and BB over-calls much tighter than SB calls. Let’s now change the payout structure to a PKO SNG. 1st place gets $33.33, 2nd place gets $16.67 and everyone has an $8.33 progressive bounty on them. Once again the tourney starts

Diagram 45 Diagram 45 shows how often IP should bet in terms of the flop texture. Clearly, paired boards should be frequently min-bet. This will be examined in greater detail in the forthcoming sections. Flop C-betting by Structure The flop structure is one of the key characteristics that drives post-flop play as the strategies differ drastically if the flops feature trips, are paired, or are unpaired. Trips are by far the absolute best flops for IP, who can capture on average 81% of the pot on this texture. Paired boards, on the other hand, give the BB a lot of strong hands, polarizing their range and allowing them some counterplay. This range polarization is one of the main reasons why betting very small is optimal on paired boards. Small bets force the BB to reveal a lot of information about their holding, as there are a lot of trash and weak hands the BB has to fold, regardless of IP’s bet-size, and IP loses the minimum when having to bet/fold the flop with the bottom of their range. In general, small bets are preferred when IP’s range has this type of depolarized distribution with the bulk of hands being good, but not great, and a low frequency of trash and weak hands. In situations where IP’s range distribution is more polarized with a bigger proportion of strong,

practice doing this head over to pokercoaching.com in the challenge section there i have many many many many many challenges that will force you to do this to ensure you know how to do this well at the table i've had a lot of students who've come to me and not even under like knew about this concept and now they are applying this when they're playing and they are crushing the game so go there and study all right so your premium made hands these are just your absolute best hands so this is going to be usually something like the nuts all the way down to strong top pair hands these hands you're pretty much always going to want to be betting with betting in all scenarios and that's because you just want to win a big pot you have the best hand and you want to get money in the pot when you have the best hand don't get fancy and do what's called slow playing where you check a lot of your best hands hoping your opponent's bet because you know they're not always going to bet and even when they do if you check and they bet and then you raise them well you just announced haha gotcha and then they get to fold right so this is a situation where you want to be betting with your best mate hands when you're betting with your best mate hands so you also want to make sure that you're betting with some bluffs and the best bluffs to bet with are your draws and that's because you're betting your draws essentially as a semi bluff it is not the best hand at the moment but it's very likely the best hand if you improve to whatever draw you have so let's say you raise big blind calls flop comes 983 this is a board you should not be betting every single time because the range advantage is going to be kind of close right it's going to be closer to 50 50. so in this spot the when your opponent checks in the big blind you should be betting with your hands like your over pairs like aces kings queens jax tens your three of a kinds your pocket knights pocket eights pocket threes your nine eights for two pairs but then also a bunch of draws like jack 10 queen jack 10 7 suited if you have it so you'll be betting with your best mate hands and your draws that way your opponent will not know if you have one of your best made hands or a draw and that puts them in a difficult spot they're in a guessing game right and you're going to find that draws is a difficult category to really nail down because on a very uncoordinated board a draw may be a backdoor straight draw with a backdoor flush draw meaning you need uh you need to come runner runner you need to turn in the river to be perfect

Ladies A slang poker term for pocket Queens QQ.

Bet to You Whenever we’re sitting with a big draw, like two overs and a flush draw, and there’s a bet to us in a multi-way pot, we have to ask ourselves this question: “If Iraise, can Ireasonably expect to win the pot right here?” If the answer is yes, we raise. If the answer is no, we ask a follow-up: “If Iraisehere, can Ireasonably expect the hand to get heads-up?” If the answer is yes, we raise. If the answer is no, we flat-call. Why do we take these lines of play? For reasons previously discussed: winning without a fight, ginning our outs, and getting to see two cards. If there’s a bet in front of you and you’re next to act, either because you’re directly after the bettor or because players in between have folded, goahead and raise. Raise the whole pot or move in if your stack warrants it. This nearly always isolates the bettor and often wins the pot right there. If exactly one caller winds up between you and the bettor, you can also raise. Raise big. Raise the whole pot. Move in if your stack warrants it. This looks like a classic squeeze play and will work like one. On a highly textured board, it’s unlikely the caller has a made hand. If he did, he’dgenerally raise to protect his holding on such a dangerous board. This means his hand is probably a draw along with yours and that means youactually have that guy beat. It’s unlikely he holds a hand like a set, because that hand is supposed to raise on this kind of board to protect itself. So when you raise, you’re probably ahead of the caller and you definitely put the original bettor in a tough spot. He has to worry about both youand the guy who called him, which makes his marginal lead hands, like one pair, go away. And the guy who’s probably way behind your hand? If he folds, you just won a big pot with no pair.And if he calls, he’s probably calling with a draw and you want that, since you have the draw. No bad result there. The only times you wouldn’t raise when there’s a bet in front of you is if either multiple callers are between you and the bettor or someone beatsyou to the raise. In both these cases, you have to take a read. In the first case, you’ll raise only if you believe you have a good chance of winning thepot right there. Otherwise, you’d never pass up such a good price to draw to the flush. After all, if there’s more than one caller, you’re getting a minimum of 4-to-1 to draw at your hand (assuming a half-pot-size bet) and that’s a bargain you generally don’t want to miss. In the second case, you need to look at the players making the action and make two decisions. If you think a re-raise will win the pot right there, you can try that. It’s kamikaze for sure, but it could win you

least half the pot. In this case, if the first player bets, it likely signifies that he has 212 you beat one way or another, so there isn’t much point in raising. A worse hand behind you will fold, but a better hand will call or reraise, since the only better high or low hand is the nuts. Also, if you raise, you risk the possibility of a reraise from the original bettor. 3. When You’re Last To Act on the River. If you only have the nut low and it’s a bet and a call to you on the end, it is an easy, comfortable play to just call. This is not necessarily the correct play, though. Although you will lose money by raising if you only get a quarter of the pot, you are costing yourself even more money in the long run when you just call and get half. Here is why: Assuming a $10/$20 game, so the last bet is $20: (1) If you raise and win only a quarter of the pot, splitting the low side, you lose $5 on the raise ($20 x 3, you get back $15). (2) If you raise and win half of the pot, you win $10 on the raise ($20 x 3, you get back $30). What this means is that you are getting a price of 2 to 1 on this raise. For raising to be incorrect, you must be quartered more than two out of three times. This will not be the case, especially if you refrain from raising when you are reasonably sure another player has the nut low. Essentially, any time you have a reasonable doubt as to whether another nut low is out there, you should raise. Most players do the opposite in this spot. They will just call, feeling that they might be quartered. In fact, they should raise, because they might win half the pot. When a sophisticated player is in the pot with you, you need to be aware that he may use some of the plays discussed here. He may not always hold what he is representing. He might raise on the river in an attempt to knock you out of the pot, rather than raising just on the strength of his hand. This happens more at the higher limits, though, and a river raise in smaller Omaha eight-orbetter games nearly always signifies a nut hand. If one of these tricky players is in your game and attempts to knock you out, you might call a raise from him on the river with a weaker-than-normal hand, such as two medium pair. However, don’t forget that the original bettor may 213 have you beat, and might choose to reraise. This is a difficult situation to play correctly, and it draws on all your skills as a poker player. Advanced River Play Value Betting When you bet for value, you do so because you believe you have a better hand than your opponents and may be called by one with an inferior hand. You

Jam Used as a verb to describe the act of going all-in. Synonymous with "shove" or "push".

been given a free card, it’s dangerous to bet on the turn, especially from late position. If you bet it, you’re giving someone the opportunity to come over the top for all his money. If you get most of your money in on the flop, it’s fine; but if you make a small bet on the flop and get called, and nothing happens on the turn, then it’s a good idea to check and wait to see what happens on the river. Another reason not to bet a good draw from a late position is that you can be a little more deceptive. Let’s say that you have the nut flush draw with one card to come. You bet from the late position with a club draw and get called. Then a club comes on the river, giving you the nut flush. Your opponent is 287 going to put you on a flush because the board looks dangerous. In other words, it will be harder for you to get paid off. Now, suppose you check the turn and a club comes on the river. Your opponent might check and call when you bet. The point is that you can be a little deceptive by checking a big drawing hand rather than betting it. Don’t Give Free Cards In hold’em, when you have a big hand, you want your opponent to catch up a little, so you’ll get paid off. Therefore, if you are far ahead in the hand, you don’t mind giving away a free card. In Omaha you rarely want to give your opponent a chance to improve and catch up with you. For example, if the flop is A-7-7 and I have pocket aces, I would bet because I’m trolling for a 7. This means I make a bet and hope someone with trip sevens calls. I’m setting a trap. If none of my opponents has a 7, I’m not going to make any money. But if somebody has one and takes the bait, I stand to make some pretty good money. When you give free cards, there’s a chance that an opponent with a pair will catch a two-outer to beat you or that he’ll make a gutshot straight, which happens often. Also, remember that a lot of backdoor hands are possible in Omaha. Backdoor flushes, in particular, don’t always have to be the nuts to win the pot. So, if you have a hand on the flop, you should usually bet it. Also, sometimes you have to be prepared to throw the hand away. Let’s say that the flop comes J-8-2 and you have top and bottom pair. Everybody checks around to you, and you bet it, mainly because you don’t want to give a free card. You want to pick up the pot right there. If you get raised, it’s pretty easy to throw it away. If you get called, you have to be cautious from that point onward. This doesn’t mean that you shouldn’t bet this type of hand; you’re still trying to pick up a

Hand Range 338: OOP x/r vs the 1/3 Bet-size • Bet Full Pot 15% / • Bet 2/3 Pot 28% / • Bet 1/3 Pot 0%/ • Check 57% [0-1] Toy Game Example C If we allow a x/r against all three different bet-sizes, Hero is no longer able to split their range into multiple bet-sizes and will adjust to only use the full pot-size bet, shrinking the value range to KK+ and checking back QQ-66 (Hand Range 339).

a small ante razz game I was playing. On the first three cards I had an: A decent hand but not a great one. The high card brought it in, and a player called with a 5 showing. I was prepared to call or possibly raise. However, a player ahead of me, who was playing tight, raised with a 4 showing. Had the first player with the 5 showing not called the initial bet, I would have called the raiser with my 8,5,2 because, though the raiser was playing tight, there would have been a chance he was semi-bluffing. But since the raiser raised another low card that had already called, it was 232 Chapter Twenty-two almost a certainty he had a better hand than I did; and there was also the probability the first caller had a good hand. Therefore, given the small ante, my hand was no longer worth a call. The same sort of thinking must be employed when deciding whether to call a raise cold. With very few exceptions, you need a better hand to call a raise cold than you would need to raise yourself. The simple logic of this principle can be set forth through an example from draw poker. Let's say in the game you are playing you decide to raise before the draw with aces up or better. You look at your hand and find you have three 2s. You're prepared to raise, but all of a sudden the player to your right, who will also raise with aces up or better, puts in a raise. Now instead of raising, you can't even call. You must fold because the chances are too good that the raiser has you beat. This principle applies to any game. When you have a minimum or near-minimum raising hand and the player to your right, who has the same standards as yours, raises ahead of you, then his hand is probably better than yours, and your correct play is to fold. Summary Reading hands well is a powerful poker weapon because it allows you to play correctly more often, according to the Fundamental Theorem of Poker. The better you read your opponents' hands, the less likely you are to play your hand differently from the way you would play it if you could actually see what your opponents had. Weak players are difficult to read because there is little pattern to their play. Good players are easier because there is logic to their play. However, very tough players are more difficult to read because of their ability to disguise their hands. One way to read hands is to put opponents on a variety of possible hands and eliminate some of them on the basis of their play and the cards they catch from one round to the next, keeping track of the order in which they catch their cards. A second, Reading Hands 233 complementary way is to work backward, looking at an opponent's later plays in terms of how he played his hand in earlier rounds. You can

A PREFLOP STRATEGY 87 From the Blinds In all scenarios, tend to play somewhat tighter than you would in LP. You will be out of position postflop, so most hands won’t be worth playing. In particular, don’t worry about “defending” your big blind. The small amount of blind money usually won’t provide enough incentive to play a weak hand out of position. You should call raises sparingly from either blind. But finally, if several players have limped into the pot, make a big raise occasionally as a semi-bluff. When you do this, choose your worst hands, stuff like J♣4♠, to do it with. There’s no sense in wasting a perfectly good hand like T♡8♡for a bluffwhen you can simply check (or throw in one chip) and see a flop. (Of course, raises will more often be made with your legitimate good hands.) Final Thoughts We haven’t given you a play for every situation, and we don’t intend to. We hope that this strategy will serve you well as a guide and sanity check for your own play. And we also hope that your knowledge and judgment will soon be keen enough that you will never need to refer to this strategy again.

Table 20: Average Fold Frequency Hero’s folding frequency is the highest when playing push/fold (Table 20), which means that this strategy limits the number of hands Hero can profitably play, particularly as stacks get deeper. Conversely, the folding frequency is lower when playing a more complex strategy, especially when having position. With over 17bb, pushing is very rarely used by the BN, but becomes the dominant strategy with fewer than 10bb. The SB pushing frequencies are a lot higher than BN because going all-in diminishes the disadvantage of being OOP. Diagram 4: Hero Push Frequency by Stack Depth

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the third card." Salty pretends to be flustered with having given his hand away. But he hasn't given anything away. He's bluffing. He doesn't have aces back-to-back. He never varies this trick. 'Then he has another habit occasionally during five-card draw of holding the cards close to his face as if to keep anyone from seeing his hand. If he bets, he's bluffing. Once he heard someone say, "Look out for Salty when he picks up his cards like that." You see his cunning is just once removed from Dupin's simpleton.' 'Go on.' 'Well, there's Curley who's a pretty fair player. You can tell when he catches a card that helps him by watching his hands. He has a mild case of palsy and under excitement the tremors increase. 'Then there is Red who plays a great deal and is not too strong a player. In five-card stud watch his eyes and general demeanour. If he helps his hand his eyes will quickly follow the deal as if to say nonchalantly, I did not help. During the betting he will feel his left ear or light a cigarette or do some other thing that we don't normally do during tense moments. You can put it down in your book that the last card helped his hand and judge for yourself to what extent. 'Also there is Shorty, a weak player. If you are setting up a bluff don't do it until you have cured him of calling. Make sure that on every occasion when he calls you beat him. After about the third time you beat him he will give you credit for having the best hand. Not until then can you play odd or even with him for before you cure him he will always call. 'Bluffing should be calculated - just like a pitcher sets up the batter. You may run into a strong hand but you have that risk. In five-card draw a good risk is to raise immediately after someone opens, whether you have anything or not. Raising immediately after someone opens should be proof that you have a strong hand. Either take two cards, pretending you have three of a kind, or stand pat, preferably the latter. Bet at the first opportunity. But be sure that these weak players who always call are not in the pot or that you have taken steps to cure them. 'In stud, even with no pairs, if you hold high cards - and you have no business in the pot unless you do - you will profit by raising an open pair held by your opponent now and then. Most other players will give you credit for having a big pair and will drop their hands. Of course the player holding the small pair, since he has already bet» may go along for another card, especially if he is a weak player. But if he checks, bet, and unless his cunning is less than Dupin's simpleton he will toss in his hand. It is also axiomatic never to try to bluff

the equity gap quickly from the flop to the term so I think you guys kind of learned that on the first example everyone said the imposition player had the equity advantage but then you guys quickly figured out examples that they were very close and then this all allows for the small flop sizing on the flop because of our equity advantage and big polar turn sizes so we made it through it this is very complicated stuff I know this is pretty high-end stuff pretty complicated so we're at an hour in two minutes I'm gonna do 10 minutes of Q&A and then we'll wrap this up so we'll go 10 minutes longer so let's fire in some of these Q&A I'm gonna start from the top so yeah butts I'm gonna go through the top and then keep filing to some questions and I'll try I'm gonna kind of go rapid-fire through some of these questions so earlier real fast is over but still strong on in position player after it goes bet call yeah so this is kind of here what I was talking about these big toy polar sizings I only did a 40% to 80% turn sizing but if I had to add it a hundred and twenty percent sizing or one hundred and fifty percent for in position player it would be used on those brick cards we're in position wants to be polarizing likely an over bet would be used a lot on the turn Bluff to value ratio we talked to that a little bit you're gonna have more Bluffs than value because some of your Bluffs are gonna turn into value on later streets so you need to have a lot of Bluffs more on the flop less on the turn and then less on the river but you're gonna have a most people don't Bluff nearly enough Jason I saw this year asking why did it bet five five but not six six I don't remember what exactly and it was the reason it's certain about fives and sixes was just it's gonna it's gonna betting some of them to turn them into Bluffs on a later street and fives are just weaker than sixes and have less showdown value because sixes can beat fives and fives didn't really beat any pairs because the pair below it was a four on the board so when you see it start to bluff with pairs when you Bluff with pocket pairs you just want to start picking your smallest pocket pairs to bluff with clear out a lot of these comments and answers from earlier a lot of the lot of the bluff to value ratios we've covered that so Michael ass overall big one were to call preflop with a tighter range with a two and a half ex open wouldn't this increases equity range across these hands yes a hundred percent and you would see this when like someone flats in position they normally have a pretty big equity advantage on

This factor can be divided into two sub-factors: flop texture and player type. The more suitable the flop texture for a low to zero equity c-bet, the more likely Villain just bets all his hands without SDV there and then. This doesn't hold true for all player types though: a Passive Fish or a nitty fit-or-fold Reg may well just miss out on too many +EV flop c-bets and end up with too air filled a range on the turn, even on dry textures. If a more aggressive Reg checks back in position on a flop that is normally decent for c-betting air, it's much more likely that he has a more SDV weighted range. Compare the following two flops. Hero has flatted a BU open from the BB and goes heads-up to the flop. He checks each flop and his opponent checks back in each case. What's the difference? When most players check the first flop, they're more likely to be calling the turn with SDV . A Reg will c-bet air on this flop very rampantly and so will typically check back K-high, pocket pairs, 8x and maybe even a poor A once in a while with the intention of calling the turn. This is not to say that he'll never check air either, but on the whole, his range will be weighted more to SDV than air and so Hero's light turn probes will work less often. If an Aggro Fish checks the first flop, Hero should expect very little fold equity on the turn as Villain's range will be full of slowplays; after all, air is an easy bet for him, but he'll do everything to discourage you from folding when he's flopped his mighty trips with A7o... he may well check this hand even at the expense of not building the pot. The second flop is one on which most players feel the need for a check back/give up range that is just too weak to c-bet on such a wet texture. A Reg's flop checking range here will contain plenty of SDV like Jx, 98 etc. that doesn't want to bet for obvious reasons, but these combos will be balanced and perhaps even outweighed by air. Hero should expect more turn fold equity on the second texture. Factor 2: Equity For clarity, equity once again refers to non-made-hand equity since we're dealing with light turn probes for now. It's not always a mandatory requirement depending on the other factors, but it helps a lot wherever the situation is remotely close and can turn poor probe bets into fine ones. Factor 3: SDV You should know what this means by this point. There is no need to bluff with hands that beat everything that will fold to that bluff unless Hero has the best hand a large amount of the time and his SDV is of the vulnerable variety; in this case it can be permissible to bet for protection only. Where the bet is a hybrid of protection and value, the requirements for protecting equity can

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Hand Range 166: BB vs UTG 4-bet (25bb) • Call 57.8% / • Fold 42.2% Defending the BB Versus IP (40bb)

will not bet again without a good hand, then you should obviously fold if he does bet again. So you have risked only $20 and not $60 to win $70. Conversely, if there is some chance your opponent will bet once or twice more without the best hand, then when you continue calling, you are risking $40 to win $90 or $60 to win $110, depending on how many times he bets, You are risking $60 to win $70 only when you plan to call to the end if your opponent bets, even though you assume you have little chance of winning if he continues betting. Summary In sum, reverse implied odds describe situations in which: 1.You're not sure where you're at. 2.You have little chance of improving to beat the hand your opponent might already have or might make. 3.A call commits you to calling future bets all the way to the end. 4.Your opponent can back off at any time. In such cases, you must not think you are getting odds according to what's in the pot and what you have to call right now. You are getting much worse odds — so much worse that it is often better Implied Odds and Reverse Implied Odds 61 to throw your hand away immediately rather than get committed. Such a situation would occur in hold 'em if you held and the flop came A similar situation might occur in seven-card stud if you held two black aces and an opponent with three hearts on board came out betting on fifth street. Whereas implied odds are based on the possibility of winning more money in later betting rounds, reverse implied odds are based on the possibility of losing more money in later betting rounds. Put another way, when you're getting implied odds, you're glad you're not all-in, for you expect to make money on future bets if your card hits. However, when you're getting reverse implied odds, you wish you were all-in so you could see the hand to the end without having to call future bets. Chapter Eight The Value of Deception One approach to poker is to raise when you have a very good hand and fold when you have a very bad hand. But what happens when you follow that approach? Let's say you have three aces rolled up on your first three cards in seven-card stud. That's the best possible hand you could have at that point. You put in a raise, and everybody folds. You have won a very small pot with a hand that potentially could have won a huge pot. The Cost of Giving Your Hand Away This extreme example points up a basic poker dilemma. You want to make the most of your hands by maximizing your gains and minimizing your losses, yet what are you costing yourself when you play in such a way that your opponents should know what you have? The answer to this question is contained in the Fundamental Theorem of Poker, which states that every time opponents play a

Ace-high A hand in which the highest ranking card is an Ace with no pair or higher valued combination of cards possible.

those hands have really good Equity whenever you re-raise those and get shoved on you lose your equity and you don't get to play the hand right you really want to play hands like asex suited eight seven suited Etc so make sure you're not re-raising those at the stack depth from the big blind as we get even shallower the 25 big blinds you're gonna be able to defend even a little bit wider also if Stacks get shallower you're going to be going all in more often that's because you're risking less money to try to win the pot as you're risking less and less money you in turn get to shove wider and wider also obviously as your opponent's range gets wider and wider you get to shove all in more often which is why we're shoving more often against the button compared to Under the Gun 25 big blind zip though we will still have some shoves against razors of all positions but you'll be shoving much wider when the raise comes from a later position also worth noting we're still going to have some non-all in re-raises a lot of players think that they should only go all in or call they think they cannot re-raise small in the scenario and fold to a shove but you most certainly can so let's take a look at against an under the gun race 25 big lines deep we see queens and better and Ace King suited it's amazing offsuit it's amazing Queen offsuit and some Jacks re-raises for value and then calls it off and the Bluffs that are re-raising not all in are entirely some junky asex junkie King X and queen jack off suit as they Bluff these are hands that you're re-raising and then folding so 25 big lines each someone raises a two you make it something like six and a half if they shove you let it go with your non-premium hands the nice thing about this strategy is that your opponents are not going to know if you have the nuts that's gonna easily call off or junk it's gonna easily fold it puts them in a tough spot notice again we are still calling with a whole lot of hands that flop well enough and we're shoving with our hands that are very likely good but vulnerable that's gonna be a mixture of pears King 10 suited Ace King offsuit and Ace Queen offsuit that's a sliver of Ace for off super fun facing a hijack raise we now see the same pattern again lots of pairs are shoving Ace King Ace Queen Ace Jack a few more Ace x a few more suited decent hands we do still have a small re-raising range of mostly nuts and some asex King X Queen X and Jack X offsuit Bluffs from the button or when the button raises this is when we get to shove the white as we see tens and lower shoves every time lots of asex shops Ace clean

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various scenarios i'll show you how you can practice this really quick just to get some examples of how much equity each range has in various spots you can let's say the board is jack of diamonds six of clubs six of spades you see you run it again you see the under the gun range is still a pretty hefty favorite let's say it is eight of hearts seven of hearts four of clubs you see now it's way closer to 50 50 right and doing this in various scenarios with various ranges will go a long way to helping you understand how different ranges interact with different flops we're gonna have some quizzes with this so you are actually gonna have to test yourself to make sure you know how to do this because this is an important concept so in general the player who has the range advantage is going to typically tell you how frequently you want to bet and you want to bet frequently when the flop favors your range and you want to check frequently when the flop favors your opponent's range so when your range has more than about 58 equity you're going to want to be betting very very very very frequently and you're going to want to be checking frequently when the flop favors your opponent's range now i say in this scenario when your opponent has or when you have 54 percent equity or less so that doesn't mean it necessarily heavily favors your opponent's range but you don't have any sort of substantial advantage that allows you just to bet with everything in your range we'll be discussing that a little bit more in depth so if that's um not fully understood or not fully explained we'll we'll get there because we have to put together range advantage nut advantage and position to come up with our strategy so let's discuss a few common board types that you will see typically as the pre-flop aggressor your range is going to contain all of the best hands whereas the pre-flop callers range usually will not contain the best hands because they would have three bet them right so if they just call your pre-flop raise it presumes they don't have aces kings queens ace king in their range anymore so you're gonna find that high cardboards heavily favor the pre-flop aggressor that's what this says which boards favor the pre-flop aggressor next on uncoordinated boards like queen five two let me go over here to show you this right i can type this in we do queen of spades five of clubs two of hearts you see we're still heavily favored as the stronger range let's say the board is seven of clubs four of hearts three of hearts you see here it's much closer right and as we have on this chart low cards boards somewhat favor the pre-flop aggressor not not a huge amount but somewhat and then the middle card boards we already showed back over here middle cardboards

How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical scenarios. As rake increases, ranges typically tighten but are played more aggressively. And in the case of increasing antes, ranges widen. Let’s examine another factor that impacts ranges, which is stack depth. We have already looked at this from an ICM perspective ; a mega stack or a micro stack at a certain table in a multi-table tournament can change the strategies of the players on that same table. But in theory, it can also change the strategy of players on a different table in that same tournament. In this article, we will explore how stack depth changes the strategy of the solutions in GTO Wizard , in common Chip EV Expected Value The anticipated value one expects from any hand, position, or play. EV is calculated as a weighted average of all possible outcomes weighed by the probability of each of those outcomes. scenarios. Same Position, Different Stack Sizes I am going to ambitiously make my point by looking at the same preflop spot in GTO Wizard , each time with different effective stack Effective stack The maximum amount any player can risk in a hand. In two-player situations this will always be the smallest of both players stacks. In multiway situations there are more than one combination of effective stacks. sizes. The difference between each range should tell us how the stack depth has changed the optimal strategy. To begin, this is a 100bb UTG opening range for multi-table tournaments. UTG has a tight linear Linear A range construction that consists of the top-down strongest hands. A linear range might contain nutted to medium strength hands, or value to thin value. range that has decent board coverage. Low boards are covered by the suited Aces and small pairs. This range also has some interaction with middling boards via the occasionally played suited connectors. And being linear, thus high card heavy, the most interaction occurs on high boards . Let’s compare that to an UTG opening range in MTTs, but for 50bb effective: The first thing to note is that the overall percentage of hands has increased from 16.5% to 17.7%. This may surprise some people who think that deeper stacks mean wider ranges, which is a misconception. The reason this range is wider can be explained when we look at how the shape of the range has changed. At 50bb, the open-raising frequency is increased for hands like A3 s, AT o, K8 s, KJ o, and QJ o. There are also new hands like KT o, K7 s, and K6 s that are being added to the range. To keep the overall frequency relatively stable, some hands have to make way by either being completely removed from the range like 65 s, 76 s or being played less like 44 , 33 , and 22 . What all these hands have in common is that they contain cards low in rank. The reason for this is equity realization

Absolute and Relative Position Position is undeniably an important factor in every hand. “Having position” often represents an enormous edge. But many people think that having the button always gives you the ultimate positional advantage. Unfortunately, the position story isn’t quite that simple. Sure, there’s no better place to start a hand than on the button. And on most hands, the button will be an important asset throughout the hand. We’ll call having the button having “absolute” position. That is, you are last to speak no matter what. But sometimes being last to speak isn’t all it’s cracked up to be. Specifically, say you are on the button in a four-handed pot. One player limps, and the next raises. You call, as does the big blind and the limper. What’s likely to happen on the flop? When someone raises preflop, for better or for worse, the early players will often check automatically to the raiser. These checks don’t mean quite what they normally might — weak hands. They merely mean, “Ok, you raised preflop. We’ll let you take first crack at the pot.” So while you are technically last to speak, you aren’t the last to speak meaningfully. If, as the early players expect, the raiser bets, you are, in a very real way, second of four to speak. The first two players checked bad and good hands alike, and you must commit your chips now without any more clues. Of course, having the button is still valuable. If you call, and the two checking players fold, then you go back to having all the positional advantage. Or, for that matter, if you end up heads-up on the turn with any of the other three players, you will be positional king. But as long as the pot is multiway, the player everyone expects to bet is on your right, and that player does, indeed, bet, you are in a poor “relative” position. Absolute position is position relative to the button. The closer you are to the button, the better your absolute position. Relative position is position relative to the likely bettor. The closer you are to the right of the likely better (acting directly before the bettor), the better your relative position. You can have both absolute and relative position at the same time. If a couple of players limp, you limp on the button, and the small blind raises, 63

Many of the hands that would pay off the check-raise will continue betting later streets for value anyway. Despite what we said before about CO folding at higher than MDF, they nevertheless have a lot of counter-intuitive calls and raises when facing a tiny continuation bet on such a dry board. They never fold a pair and rarely fold Ace-high. The stronger Ace-x make good calls, as they dominate some of BTN’s Ace-x. The weaker Ace-x need a backdoor flush draw to continue (which they have three times out of four) and often check-raise, partly because they can fold out dominating Ace-x . CO draws the rest of their check-raise bluffs from gutshots and hands with backdoor straight and flush draws . To be clear, these are not particularly strong draws, and raising them is not especially profitable. But there are no strong draws on this board, and CO needs some bluffs, so they might as well do it when they have an outside chance of improving. Playing Connected Boards On K ♦ 6 ♥ 3 ♠ , CO’s check-raises are exclusively small, regardless of whether there is a flush draw on the board. CO’s check-raises are almost always small , for the same reasons BTN mostly uses a small continuation bet. But there are some exceptions on the most coordinated boards, as can be seen below: This check-shoving strategy is actually more intuitive to implement. Because the raise is all-in, it’s a smaller and more linear Linear A range construction that consists of the top-down strongest hands. A linear range might contain nutted to medium strength hands, or value to thin value. , equity-dense range. For example, on T ♠ 9 ♦ 8 ♦ , CO check-shoves mostly strong draws like AQ and AJ of diamonds and strong but vulnerable made hands like top two pair and the low end of the straight: For the check-calling strategy, we select the weaker draws, including nut flush draws and most straight draws with overcards. Playing a draw passively from out of position is never ideal, but BTN’s bet is worrisome. This is not a high-frequency bet spot for them. Indeed, they check back more than half their range on this flop. So when they do bet, CO gives that bet a lot of respect and raises much less often than on K62 . Playing Flush Draw Boards Similar principles apply when introducing a flush draw, such as on K ♦ 6 ♥ 2 ♦ . CO check-raises less King-x because they have more strong draws with similarly high equity against BTN’s Ace-x and lower pairs. Their weakest bluffs are still gutshots and backdoor flush draws, which now take the form of two hearts or a single diamond. Note that 6 -x of diamonds, for middle pair and flush draw, is an especially poor raising candidate. Yes, it has a lot of equity, but better hands never fold and the weak hands that do fold have little chance of drawing out. It is better to raise weaker flush draws, which value fold equity more

of this is when the flop comes K-Q-6 or A-T-8. Against a large field of opponents, it’s likely that someone has out-flopped you, leaving you with only two outs. You rarely play for two outs in hold’em. Tip # 21 of 52 In a two-way pot, play aggressively when the flop is A-9-3 rainbow. In pots contested between you and only one other player, often the flop helps neither player. Therefore, whoever makes the first bet often wins the hand. Always be on the lookout for flops that contain few or no likely draws, as these boards are more likely to be of little interest to your opponent. A typical such board is A-9-3 rainbow*. Since this flop has no straight or flush draws, and the presence of an ace means that there are no overcards to chase, it is extremely difficult for your opponent to stay in the hand without a pair. Furthermore, if his pair is smaller than aces he may give up if you bet, since an ace is a likely card for you to be holding. So, it is imperative that you play these situations aggressively, particularly if your opponent only called before the flop. If he had raised, that would show a real interest in the hand, and you would probably have to show him the best hand to win. However, if he merely called preflop, then it is often correct to bet if you are first, regardless of what two cards you happen to be holding. The chances are great that he will fold. If you get called, no rule says that you must continue your bluff on the turn. When your opponent is first to act and he checks, you must bet with this board. Again, it is very likely that your opponent is holding a hand like K-Q or 5-5. A-9-3 is a poor flop for these hands, and you should bet when he checks, even if you have nothing. There is free money in the center of the table, and you can make one small bet to lay claim to it. On the other hand, what should you do when your opponent bets at this flop and you are next to act? It is good to have at least some knowledge of your opponent here, as some players bet only when they have an ace, whereas others bet lots of hands (perhaps themselves trying to pick up the pot). All things considered, here are some general guidelines for how to respond to a bet: Tip # 22 of 52 Guidelines on playing a flop of K-Q-3 rainbow. This advice applies to any situation in which the flop contains two face cards and one small card, without a flush draw. Unlike the previous example, this flop is likely to have hit your opponent in some way, either by pairing him or by giving him a straight draw. As a result, you don’t need to feel the same obligation to bet when it’s checked to you as in the A-9-3 scenario. It is still okay

Diagram 39 Strong hands Strong hands are incentivized to bet and increase the size of the pot but, as we know, betting only your high-equity hands and checking your low-equity hands would be a highly exploitable strategy. For this reason, IP also has to bet some weaker hands on the flop so that the c-betting range remains balanced. Sometimes checking back strong hands works well in situations when they don’t need as much protection. When they block the Villain’s continuing range, or when they are so nutted that it doesn’t matter if you give a free card so the Villain can catch a small piece or start bluffing, checking behind with some of your strong hands makes sense. This is referred to as trapping. An added benefit is that checking strong hands also helps protect your checking range. Good hands Good hands also benefit by betting and gaining value from worse hands as well as for protection to get some folds from hands that have equity. However, sometimes it makes sense to check back your good hands when the BB’s range is very polarized to hands that are either stronger than yours or have very little equity. By checking behind, you give the Villain a chance to pick up

Cash Games Tournament poker is not as different from cash game poker as people sometimes assume. Most… How Solvers Work A Game Theory Optimal solver is an algorithm that calculates the best possible poker strategy.… The Most Powerful Play in Poker The central strategic implication of stack depth is the question of how much equity a… When does ICM become significant in MTTs? The Independent Chip Model (ICM) was invented in 1987 by M. Malmuth and is one… How to Study GTO Solutions Tools like GTO Wizard and other solvers should not be used to memorize specific strategies.… Principles of GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds are the value you expect to gain over and above your raw equity.… ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but what… What is

Open limp When the first person to enter a pot preflop does so by calling the big blind.

act after the flop. Flop No. 1: A♠K♦Q♥. A great flop, obviously. Let the other players take the lead in the betting. Flop No. 2: 9♠8♠3♥. Another great flop. Even though your hand isn't made yet, you have 15 outs with two cards to come, so you're the favorite. (Don't make the mistake of double-counting. There are nine spades that help you, plus four sevens and four queens. But the 7♠ and the Q♠ are in both groups, so only 15 different cards help you. The other jacks and tens might give you a winning hand, but you can't be sure.) You should lead out, and not mind a call. Flop No. 3: 8♦5♥2♣. A good flop for texture, although it missed you completely, since at least you have two overcards to the board and it probably didn't hit anyone. If the action in front of you is check, check, try to steal the pot. Flop No. 4. 8♦7♥4♣. This is a little better than the last one since you also have the inside straight draw. With jacks, tens, and nines all good for you, this hand plays well as a semi-bluff. You should take the lead in the betting. Flop No. 5: Q♦9♠3♣. A good flop, with an open-ended straight draw and a backdoor flush draw (needing two running spades to complete it.) An open-ended straight draw is eight outs; the backdoor flush contributes the equivalent of about 11 /2 outs. If the first two players check, you can either bet the hand as a semi-bluff or check and probably see a free card. Starting Hand No. 5: 6♦6♣. You call in fifth position, and the button and the small blind both call. The big blind checks. With a low pair, the number of great flops shrinks. Unless you flop trips, you need to proceed carefully. Flop No. 1: A♠J♦9♥. A bad flop, but it least it won't cost you any money. When someone bets, you fold. Flop No. 2: J♠J♦5♥. This one is moderately good. If no one has a jack, your two pair is likely best. But you have to be careful, and any strong betting will probably chase you out. Flop No. 3: 5♠4♦3♥. A good flop for a bet. Flop No. 4: 7♠5♦4♥. Another good flop to bet. 126 Flop No. 5: A♠Q♦6♥. A great flop. Let someone else take the lead in the betting. Flop No. 6: Q♠7♦2♥. A bettable flop. Be aware that if you meet resistance, the only likely hand you can beat is ace-high. Value Bets There's nothing mysterious or deceptive about a value bet. It is what it appears to be. You started out with two good cards before the flop. The flop helped you in some way, and now you have a hand which appears to be best, such as top pair. How should you proceed? There's no need to be particularly clever here. Unless you've flopped a monster, you don't generally want to slowplay. Just lead out with a hand like top pair and hope that someone with the second-best

(one seat to the right of the button) then a smaller raise may be the best option or if someone has made a big raise before you and you hold a good hand. Why push them out when you have position? Three opponents are the most I can face and be somewhat confident in my hand standing up at the showdown. A Ks (Big Slick) is a completely different monster than the three Wired Pairs just discussed. It could win just by being the most powerful Ace because of the King kicker. Usually it needs some help on the draw. Since it is suited, it can win by completing a Flush but this only increases the win potential by three percent. It is the highest connector so it can win as a nut Straight and it can win as an over-pair if an Ace or King hits. If you hit a King on the flop, you can feel safe that you have Top Pair with the best kicker and bet out to see if someone hit a set, 2-Pair or a drawing hand. If you are in late position and someone bet a probe bet then you should think about re-raising to see how strong his hand actually is. He may be drawing to a better hand or looking to pair the kicker. Same type of thinking if an Ace slides off the deck, you have the best kicker to beat anyone else's Ace and do not want drawing hands to get free cards. Someone could chase the 2-Pair so if an Ace or King flops you want to be aggressive. Some flops can get tricky with A K though. I remember getting A K suited and unsuited in a Limit Hold’em game eight times in one hour. The interesting point is that my A K lost the first five times in a row to opponents who hit a weak 2-Pair or one smaller pair. However, the next three times I won the hands, which made up for all the losses and brought me back to even. If the flop comes K 10 5 or A Q 7 you may have been outdrawn. Why? Because K T and especially A Q are hands that people will call big opening raises (with K T being a loose call). Someone may have flopped 2-Pair. If there was a raise before your raise and they called your raise then you should consider that that person might have A Q or a Wired Pair. You need to be careful and feel out the board with a bet. If someone raise’s back into you then it is decision time. Some things to consider are, that someone is drawing to a Straight instead of having a made hand and betting that the flop missed others and they are trying to win the pot right there, or that someone has a K Q and thinks their K kicker is best. There is a reason A K is called big slick. You have a strong possibility that plays best heads

We know that most flops miss most hands, but where someone's pre-flop range was very wide to begin with, most flops miss even more of the hands in that range. Thus, a weaker player who plays too many hands will actually have air or some very bad pair or draw more frequently than someone who plays a stronger range pre-flop. The stronger range will tend to hit more top pair and better due to having a higher concentration of bigger cards as well as pocket pairs. Weak ranges have to fold more post-flop than strong ones do. It is therefore, all else being equal, better to c-bet against a wide range than a tight one. Look at Hand 20 below and pay attention to the board texture. How would you expect this kind of Villain to connect with it? Let's bust one of the most prevalent fallacies I see in new students. I call it the 'fish flop fallacy'.

Maybe they’re daring you to ask for the clock, so they can be hostile in return. Who knows? The good thing about online poker is that it takes away the awkwardness of asking for the clock. If a player doesn’t click on a decision button, after 10 seconds or so he’ll be prompted to do so. Some sites provide a countdown clock. Doyle’s Room uses gentle chimes to warn that you have 10 seconds left to act. What happens if you don’t act online differs from cardroom to cardroom and situation to situation. If you haven’t put any money in the pot, your hand will be folded. If you have, you’ll usually be treated as if you’re all-in, even though you still have chips in front of you. That means competing for a partial pot. Yes, unscrupulous players sometimes try to use the all-in feature unfairly to their advantage. They’ll pretend to be having Internet communications problems, not realizing that most sites can tell if they’re actually still connected. Sometimes they’ll succeed in getting a free shot at part of a pot, when they would otherwise have folded. That’s why most sites only allow one or two artificial all-ins to be used per session, beyond which hands are folded, no matter what. That’s also why players who abuse the treat-as-all-in privilege are suspended or barred. Despite this timed-out issue, which is hard to deal with and unique to online poker, the presence of an automatic clock keeps the games moving swiftly. It’s part of the reason why there are so many more hands dealt to you each hour online. Reason #14: With More Hands, Your Results Will Even Out More Quickly In most games of skill, the right decisions are quickly rewarded. In poker, the right decisions can cause misery in the short term. If you’re not prepared for the frustrations that go with quick changes in fate, you don’t have the right temperament to be a professional poker player. Although superior players win in the long run, and you hardly ever hear 59 about any full-time pros having a losing year, it’s not hard to spend weeks or even a month suffering a net loss. But the longer you play, the more quickly that familiar law of probability takes hold, and the closer your results get to what really should happen. But even though we talk about chance taking time to even out, it really doesn’t take a lot of time—it takes a lot of hands. What if you could get all those hands played in a short time? Well, suddenly, when you’re playing online, instead of in a physical casino, you’re playing a lot more hands. The deals are amazingly brisk. The action is swift. Expect to get twice as many hands played each hour. And that’s if you only play at a single table. Many winning players regularly play two or three games at once. That’s up to six times as many hands per hour. What does this mean in terms of a bad streak? It means that a

EV calculations are very powerful because they dictate how the game should be played. If players knew the exact EV of each action for every single spot, playing would be trivial as all they would have to do is always choose the highest EV option. Example Game: $100 3-max online Jackpot Sit & Go Stacks: BN 35bb, SB 15bb, BB 25bb Players: 3 (no ante) Pre-flop: (1.5bb) Hero is in the BN with A♠5♠ Hero raises 2x, SB is a regular who goes all-in for 15bb. BB folds and the action gets back to Hero who has a decision. Take your time and analyze the parts of the EV equation one by one. Villain is a regular, so you can assign them a standard 20% rejamming range (Hand Range 9).

two five and one three if you're a one three player but you know you could handle a two five if you just buy in shorter than the max you know buying for 300.25 put your name on both of the lists you never know if the two five games might be fantastic and the one three games are not so hot but by putting your name on both lists you get the choice and you have two lists working for you rather than one now i wouldn't put my name on a plo list because i don't really play plo but just that idea of having your name working out multiple lists is very helpful now i did think that there was a perk to being on a table and then requesting a table change like you were going to get priority and this is worth finding out what the policy is but for most casinos that i've played at the table change priority which you know you'd be at the top of the let's say you're on table 701 your top of the 1-3 list when you want to move to another table you get to move before someone else gets put on a game but it only applies to the limit you're playing so if you go five and instantly request a table change to one three you're not going to get top priority there but you would if you're staying on two five so that's why putting your name on games that on the list for nate games you're willing to play makes sense but for games that are for sure out of your bankroll or out of your comfort zone doesn't make a whole lot of sense the next thing you want to do is check in on arrival because you don't want to get bumped typically your your seat is held for the amount of time they tell you but as soon as you check in now your seat is is good right so if they hold it for 60 minutes and you show up 62 minutes or you show up 40 minutes ahead right you have 20 minutes of wait time if you don't confirm that you're there they won't even call your name as soon as your 60 minutes is up your name just disappears so make sure you check in as soon as you get there so your name goes from being a call-in to someone who's here and on the wait list and then they'll actually call you i've had the experience of missing my seat fortunately i knew the floor person so i was able to get back on the list but you don't want to risk it you don't want to risk it so check it out arrival don't get bumped um because the weight can be very long and then finally know the floor manager or the director if you know the floor manager of the poker room director when little things like that happen where you forget to

pairs only make up 3% so in position has 30 percent hands better than a pair of eight versus only 13% 14% for the out of position and that's basically because the big blonde is defending all this junkie suited stuff because of the price they're getting he's supposed to defend it and that is why sexually range advantage the big blind has ace high or nothing over 60% of the time versus this tiger range here in position the middle I'll always be referring to MP as the in position player has ace high or nothing around 48 percent of the time and we can go ahead and we'll look up here is the simulation on piyo for this hand I'll just go through this really quick because I want to show something on the flop we got the out of position range here same as that I showed you before in position range stock to pot ratio basically effective sex 110 and then various bet sizes kind of just made this as simple simple various bet sizes etc and what I wanted to show you was the equities and if you look at these the coloring here this is the imposition equities the darker green is the higher percent at highest higher percentage of equity the hand has so like for example pocket kings here has 90 almost 95 percent equity against the big blinds range all these kings have you know over eighty percent equity and then as you get into the yellows Theo these are closer to 50% equity hands so like for example as you can see over here ace 9 of Spades has about 43 percent equity ace nine hearts 43 and the one thing I want to show you just for why the imposition has such a big equity there so let's look at the lowest equity hands and the lowest equity hand here for is probably gonna be is the nine ten of Spades in the nine ten of hearts so as you can see in the bottom right here the grade nine ten of spades and nine ten and hearts each have about twenty eight percent equity against the big blinds range so twenty eight percent that's his basically his worst hand for the imposition player and the nine ten still has you know two overs to the eight in back door straight draws and then if we look at the out of position you're gonna see a big thing so look at the imposition lots of green some yellow and pretty much no orange or red which would be the lowest equity hands you can see the grid right here where my mouse is green one hundred-percent red zero percent when I flip it you're gonna see a big difference this is the big blinds range and he has some green and all his green is basically these top pairs king/queen all his pair of kings and just look at all this red that he has just so much he has so

Merged A merged range is often described as a range morphology between linear and polarized. Merged ranges often resemble polarized ranges with some medium-strength hands or polarized ranges with some bluffs. The purpose of "merging" is to make the range more robust. A perfectly polarized range is typically vulnerable to min-raises as you can't call your pure bluffs, whereas a perfectly linear range may be vulnerable to overbets and continued aggression as your medium-strength hands can't effectively realize their equity. A merged range attempts to reduce the exploitability of these extreme range constructions by including some medium-strength hands that improve flexibility.

the amount you must invest to call. (For example, the pot offers 9-to-1 and you think you will win 10 percent of the time.) In these cases, consider an additional factor. When other players remain to act behind the bettor and you, lean towards folding your hand. The reason for this is that someone might overcall, and if that happens, it is almost certain that your longshot hand is no good. If you are the last player to act, you can call more often with your longshot hand if you feel the pot odds are close. Tip # 46 of 52 Classifying your opponents helps you play more effectively against them. Poker is a game of many different playing styles. This is one of the reasons why it is such a fascinating game. If you can learn how each of your opponents plays, you should be able to play with a greater degree of success against them. How can you classify your opponents? In general, every player has tendencies that help define his play. A player can be primarily loose or primarily tight. Overlapping these styles, a player tends to play either aggressively or passively. Loose Loose players enter pots with a wide assortment of hands. They are the ones who cause you to ask yourself, “How could he play that hand?” There are different degrees of loose play to be aware of, as well. Some players play virtually every hand all the way with any possibility (however remote) of winning. Others play for one bet, but tend to tighten up if someone raises. Also, some players don’t necessarily play many hands, but do defend their blinds to the death. Tight Tight players play very few hands. You won’t see a tight player turning over too many marginal hands like K-9 suited, or K-J offsuit. Some players are so tight that the entire table takes notice when they finally do enter a pot. Obviously, when a tight player is in a hand with you, you must assume that he holds quality cards, and that a better than normal hand may be required to win the pot. Aggressive Aggressive players like to bet and raise, even if their cards don’t seem to merit it. They are also more likely to bluff, so you must make more marginal calls against them. As we have seen, a loose-aggressive player is sometimes referred to as a maniac, and he is easily identified by his tendency to play a lot of hands very aggressively. Games with maniacs feature many large pots. Passive Passive players tend to call rather than bet or raise. Loose-passive players enter many pots, and call you down with weak holdings. These players have no chance in a hold’em game. Tight-passive players play only quality starting hands, but don’t get full value from them due to their failure to bet when appropriate. You should be concerned when a passive player bets, as it usually signifies a very good hand. The ideal playing style is tight-aggressive. You want to play tight, as you can’t win

would’ve bet. Of course, I might have to make a further adjustment. If he checked on the flop and then called me, I’d give him credit for something. If there’s no straight or flush draw out there, he’s probably got a small piece of the board. 349 If he had a big piece he would’ve bet. If he checks again on fourth and calls me again, then I’d know I’m going to have to show him a hand on the end. If I’m in the pot with a weak player and I flop a real big hand, say a set of trips, I would check it because I know that if he’d had anything, he would have bet, and I’d be able to break him anyway. Normally, I don’t slow-play that hand. I always lead with it. But against a weak player, I wouldn’t mind giving him a free card if he doesn’t have anything, I want him to improve his hand. I want him to make something so I can possibly break him. It’s more difficult to outplay a strong player. You can’t consistently do simple things against better players; you’ve got to put a play on somebody who knows what’s obvious. And if I see him do something that’s obvious, like I think he’s trying to pick up the pot, I’ll put a play on him and raise him with nothing because he might throw his hand away. Since a good player will understand the obvious, I must try to deceive him. I’ll even put a play on more than one good player. For example, if someone brought it in or raised it in an early position and three players just called it, I might make a big raise with nothing, trying to pick up that pot. Against a good player, you’ll have a lot more tools to work with and many different strategies to use. You’re effectively restricted to a pickax and shovel against a weak player. Never forget that. Don’t try to devise elaborate strategies to use against a bad player. They won’t work against him. Use sophisticated plays against a good player. They’ll work against him. Another point you should note about weak players is that they come in several varieties. They’re not all like the one I described above. Some are the complete opposite. There are some who check good hands and bet bad hands. They like to bluff, and they do it almost all the time. So, when you recognize a player like that, you keep on checking it to him and let him bluff his money off to you. Note that I didn’t say to check-raise him. You don’t want to take the play away from that type of player. In fact, years ago, I rarely used check-raising. In the old days it was a weak play, and I used it only occasionally. I’d usually do it when someone seemed to be trying to take the play away from me. Perhaps, I might have checked it and moved in on him or something like

so in a way that doesn't offer up such massive and obvious counter adjustments. In this chapter we will be creating both balanced unattackable ranges that offer no surface area of exploitation to Villain and also ones that are exploitative and aimed at Villain's own imbalances. The latter ranges will never be more unbalanced than we think we can get away with in the interests of preserving long-term EV at the expense of vacuum EV ; the former is more important. There will be exceptional times against weaker players where we can adopt extremely unbalanced approaches, expecting Villain to be too unaware to find the appropriate highly effective adjustment. Most times against Regs, however, we'll be respecting the prospect of Villain counter adjusting and ending the success of our exploitative strategy if we step too far out of line. Now let's discuss where and why we want to adopt a polar range in the first place. When to be Polar There are two necessary conditions to be met before a polar 3-bet range should be adopted. Necessary Condition 1: Fold Equity If the opener is the type of player to seldom fold to 3-bets, or if there are players behind Hero who are apt to cold call 3-bets with a very wide range, then Hero is not advised to have a 3-bet bluffing range. If it's bad to have a 3-bet bluffing range, then the whole concept of polarity goes out the window. Fold equity is essential for polar 3-betting, but how much is enough? It's time to meet one of the core stats on any serious grinder's HUD, Fold to PF 3-Bet After Open.

How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds are the value you expect to gain over and above your raw equity.… ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but what… What is Equity in Poker? The term “Equity” is ubiquitous throughout poker theory. Equity refers to your chances of winning… Range Morphology “Morphology” is the study of form or structure. You’ve probably heard terms thrown around such… What is Expected Value in Poker? Expected value (EV) is the most fundamental metric in poker. Every decision you make is… Why doesn’t my solution match GTO Wizard? So, you’ve got your own solutions to some spot, compared it to GTO Wizard, and… Understanding Nash Distance Understanding Nash Distance. One of the most common questions when studying with solvers is “Why… Combinatorics Poker Puzzle Today we have a special puzzle for you that will test your intuition as a… The 10 Most Important Concepts for New Poker Players The 10 Most Important Concepts for New Poker Players. Fundamentals are one of the most… What is GTO in Poker? The meaning of GTO in poker is Game Theory Optimal. Game theory is a study… What does GTO aim to achieve? So what exactly is a GTO strategy? What makes it “unexploitable”? What does it try…

up in these exceptions especially if you're playing live or at lower to Mid Stakes remember our real life opponents aren't Clairvoyant like solvers and we aren't playing the same hand against then billions of times over so the same considerations that the computer must take into account when devising its strategies aren't going to be as important against most of our real-life opponents the most important factors that you should be considering in all blocking scenarios are the ones we highlighted in this video foreign

a polar range (strong A x and 66 for value, undercards to the J as the primary bluffs) and small with a linear range consisting of thin value hands and high equity bluffs ( KQ is not merely a gutshot but often two overcards to The Whale’s pair). Conclusion Your opponent’s mistakes are not necessarily your gain. In a multiway pot (which all pots are before the flop), an opponent can make a mistake that costs both of you money, to the benefit of the other players. This is what happens when a player cold-calls your open in position with a widened range. In the case of The Speculator, many of their calls were not that far outside the equilibrium calling range. Once they fade the risks of getting overcalled or three-bet by the blinds, they can play pretty well heads up in position against you. Whether you benefit from their loose calls depends heavily on the flop. On flops that favor you, such as AJ6r, you can bet larger and more often to deny equity to their many weak hands. On less favorable flops, you may have to give up even more often than you would against a tighter player. This is not true at the extremes. A player like The Whale, who plays far too loose, will hold many weak hands regardless of the flop . Some flops are still better for you than others, but even on the worst flops, you can bet larger and/or more often and gain a larger share of the pot than you would against a tighter opponent. Of course, players who are too loose preflop may well make mistakes after the flop as well. The more you can anticipate and exploit those mistakes, the more you may benefit from playing against them, even out of position on the worst flops. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Navigating Nasty Rivers Out of Position Playing out of position (OOP) is hard. It’s fundamentally disadvantageous to act on each street… Crack the Shell of Nut Draw Strategy Nut draws hold obvious appeal as betting and raising candidates. They benefit from fold equity,… Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker

Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach , I regularly encounter common mistakes that players make, affecting their performance and profitability . It’s surprising to see that not just beginners but also advanced players fall into these traps, which can cost them a lot over time. Today, I’m eager to share the top 5 mistakes to avoid when playing the Spin and Go Spin and Go 3-player Sit and Go where only the range of potential prizes is known beforehand but the actual prize is randomized with a ‘spin’ at the start of the game. format. 1) Playing Too Loose From the Button This mistake is particularly prevalent among players transitioning from Tournaments to Spin & Gos. In that format, a playstyle involving around 48% VPIP VPIP An online poker acronym which stands for ‘Voluntarily Put In Pot’, a statistic that measures the frequency with which a player voluntarily puts money into the pot preflop. with limps from the BTN is common at a stack depth of 25bb . However, Spin & Gos require a tighter approach; playing only a 38.5% VPIP without limps . So, why do we play less hands in Spin & Gos? The answer involves the structure of antes ; MTTs often include an extra big blind in the pot preflop, incentivizing more aggressive play. Additionally, the odds for limping on the Button in MTTs are more favorable. Spin & Gos require a tighter approach because of the less favorable pot odds (no antes). Comparing BU opening strategies: MTTs (left) and Spins (right) As a result, many players end up raising too many hands that are simply -EV , negatively impacting their win rate over time. Preflop mistakes are particularly costly due to their frequency. Even minor EV mistakes, when made consistently, can add up quickly to significant losses over time. 2) Making Nash/GTO Calls When Facing an All-In From Recreational Players So, when should we call with GTO ranges when facing an all-in? Exactly when our opponent is pushing GTO ranges. Let’s delve into what these ranges look like at 8bb short in a heads up scenario: On the left, we see the GTO strategy for the SB. It showcases a polarized limping strategy, incorporating the strongest hands with solid postflop playability alongside the weaker part of our range. The hands falling in between are going all-in. On the right, you can view BB’s optimal response to this all-in range, including hands as weak as T9 o, T7 s, and Q4 s. SB opening strategy and BB’s response (vs 8bb open-jam) While many regs will shove GTO ranges preflop, this often isn’t the case for most recreational players. So, how do we adjust our call range against recreational players? A brilliant tool for this is the heads up preflop AI solver . It’s time for some preflop nodelocking! The average recreational player across various platforms and stakes tends to shove tighter than GTO , with the occasional random spazz. I’ve attempted to simulate a tighter shoving range on the left

the out of position on player thank you Jason for the compliment how many hours a month do you study this complicated stuff um right now during the World Series not much at all but in general like I'll spend like five to ten hours a week so basically what I'll do is I can run a script with piosolver so let's say I take this same situation middle position versus big blind and I can just let it run for like a day on my computer it might take like 12 hours I can have it run like 64 different flops and then I can kind of have all of them and I'll export it to a spreadsheet which you can do in the program and it will give me like the frequencies on every flop and what I'll do is kind of use it like flashcards we're on different textures I'll kind of guess what my equity is on different textures and what frequencies I'm using and then when there's like ones that I don't know I can pull up the simulation and kind of look into it how I've looked into it look at the range explore see why we're doing things that we're doing and this is kind of the basic way that I think is really good to use pilo solver to in an effective way not to just cookie-cutter copy the strategy I'm not trying to do that more so you're learning why why is it doing things that it does what factors would you consider for deciding between 80% in versus 1 20% polarising good question benjamin stack depth is the main thing so as stacks are deeper my polar sizings are gonna be a lot bigger and as stacks your shallower your polar sizing for example if you're playing big blinds deep a polar sizing might be 50% pot because there's not much to play but when you're playing like 150 big blinds deep you're polar size you might want to be like 150 percent Rick Ricardo how how are the reeds that you have on players come into this when you know a player's sticky or Bluff e or tight blind defender etc these Trump everything this what we're looking at here is like theory stuff so this is studying theory and what we're trying to learn here is identifying when we have an equity advantage when we have a nut advantage and in general what type of sizings we want to use and like what are kind of general strategies should be on those boards I'm not trying to cookie-cutter copy the strategy that pyro solver does what I'm trying to do is understand range interaction and the composition of ranges so the big takeaway here is now is when the big blank check calls he has something now a lot you know it that's the big takeaway here and that you just don't get a bombs away now on every turn and River so and that you see some players do

as precise and specific as possible. You also want to be creative, as there is often more than one potential exploit for a particular mistake. 4) Determine the Degree of Deviation Ask yourself, “ How far should I deviate from the equilibrium? “ Suppose your opponent doesn’t seem to bluff enough on the river, and you plan to exploit them by folding more often. The next step is to determine how much more often. Does this just mean folding when the decision would otherwise be close? Is it as extreme as folding the second nuts ? Or is it somewhere in between? There’s a strong situational component to this – it’s harder to find bluffs on some rivers than on others – but two factors you can consider in advance are the magnitude of your opponent’s mistake and the degree of confidence you have in your read. Remember that in order to exploit an opponent who seems to be deviating from his equilibrium strategy, you must deviate from your own equilibrium. This, in turn, raises the possibility that you will be exploited if you are wrong about your read. The larger your deviation from the equilibrium, the greater the penalty for being wrong, which is why larger deviations require stronger reads. Demonstration Let’s consider a simplified river scenario where the final board is 22223. The IP player has a range of 44-AA, while OOP has only the middling hands in that range, 77-JJ. There is $100 in the pot. IP may either bet $100 or check. If they bet, OOP may call or fold (even if they were allowed to bet or raise, they would never want to do so). IP’s equilibrium or GTO strategy is to bet anything JJ or better and to bluff with some combination of 44, 55, and 66 (it doesn’t matter which, as all are equally worthless) at a frequency that makes OOP indifferent to bluff-catching. The value bets are all pure strategies , which means betting is definitively better than checking. Even JJ, the thinnest value bet, makes $133.92 by betting as opposed to $98 from checking (it does not win quite the full pot by checking because it occasionally chops with OOP’s JJ). The bluffs are all mixed strategies, which means betting must have the same EV as checking, $0 in this case. OOP must reach a calling frequency of 50% to make IP indifferent to bluffing (very slightly less here because of the blocking effect from JJ). JJ is a profitable call because it blocks some of IP’s value bets, the rest are pure bluff-catchers and indifferent between calling and folding. Although both players have 50% equity, IP’s EV in this game is $67.70, well over half the $50 pot. This is true despite OOP playing as well as they possibly could. The opportunity to bet a polarized range is inherently valuable, no matter how your opponent responds . What do you expect to happen if we node lock OP’s strategy to call at a frequency of 52% rather than 50%? How will IP

Diagram 133 When 10% of P2’s range are traps, P1’s EV maxes out at SPR 1.25 (Diagram 133). After that, their EV starts to diminish and P1 is forced to check more frequently until the SPR is so high that they can no longer go all-in profitably, resulting in a checking strategy 100% of the time. When P1 checks (50% of the time), they win the pot 90% of the time, so their EV is 45% of the pot. Going all-in for a massive overbet when your opponent can have traps is a substantial mistake and will lose you a lot of EV. With low SPRs, the threat of going all-in and occasionally running into the nuts is not as big an issue, but when SPR gets high, it can be costly and P1 should bet smaller than all-in, particularly if P2 can have a lot of traps. The problem with betting smaller than all-in is that P2 will now have the option to x/r the river. When P2 x/r, they will be effectively turning some of their bluff-catchers into bluffs and P1’s value-bets will now turn into bluff-catchers! This situation is particularly bad for P1 as in

you know we are going to fold the best hand every once in a while the bun could also just have like a random bluff like eight seven of clubs and decide to keep bluffing on the ace turn but despite all of that i think we probably just want to make a snug fold at this point unless you know your opponent is overly loose and overly aggressive so we do fold in this scenario and turns out the opponent did just decide to bluff the flop with the ace high but got there on the turn and we end up you know sidestepping a spot where we lose it's important to realize that on this queen jack 3 flop we're actually in okay shape when we check the flop with the jack 10 but when that ace comes that's just very very bad for my hand to the point that we're done with it all right so that's how we play on uncoordinated flops what about coordinated flops so now let's say that we raise pre-flop the opponent calls from out of position they check the flop we bet in this situation on a coordinated flop remember we are going to be doing more checking mainly with our marginal made hands and our junk so when we do bet the flop we probably have one of our best-made hands and or a draw right and the caller's range is going to again strengthen because they fold out the bottom portion of their range this is going to make ranges closer in terms of range advantage but the flop bettors often going to keep betting on the turn in these scenarios because they have either a really good made hand or a draw whereas the opponent has mostly marginal made hands so let's take a look at an example of this here we raise jack ten of spades big blind calls flop comes nine seven six two clubs so now when the opponent checks we want to ask which hands do we want to be betting on this coordinated board and this board should connect very very well with the big blind right big blind has a lot of medium cards so if the player in the hijack the initial razer is betting here it needs to be with the best made hands mostly over pairs three of a kind two pair and some draws and the obvious draws here are flush draws hands with an eight but really we don't have too many hands with an eight besides like ace eight and maybe king eight both both suited um we could bet with also some hands with a ten that have over cards that would be mainly king 10 queen 10 jack 10 and our hand's particularly nice because if we get a spade on the turn we can pretty confidently continue betting and if we get a club on the turn to be fair we can also keep bluffing as if we have the clubs so this is a

Three-bet pot (3BP) A pot that was 3-bet preflop. In other words, someone raised the open-raiser preflop.

range’s post-flop equity distribution and can be more precise about the degree to which a range fits within the different morphologies. It is important to emphasize how a hand’s value is not static but instead dynamic, relative to the ranges in play and the board type (Table 88). Table 88: Sample Hand EQ Values on Various Board Types We can see how a hand such as top pair can be strong with 82% EQ on the AQT flop but has only 60% EQ on the single suited T98 flop. A hand such as two pair on AQT has more equity than a set on T98. BB vs IP Equity Buckets (All flops) Average UTG vs BB and BN vs BB Flop Equity Buckets for GTO MTT Ranges with stack depths 20, 30 and 40bbs (Diagrams 23 and 24).

This time we have a bit more information. First question as always is: should Hero be polar or linear? Never forget to ask yourself this. Adopting the best long-term strategy depends on it. Hero should definitely be linear here not due to lack of fold equity, but due to the fact that having any kind of calling range at all looks horrendous due to the Aggro Reg behind us. Recall that having some kind of calling range is a mandatory requirement for being polar. So given we have a linear range, how wide should that range be? Well, fold equity is extremely good against the opener, but we do have to make sure our range doesn't get too out of hand here for two reasons: Firstly we don't want to ruin the juicy long-term EV of 3-betting a wide range vs. BU by grossly inflating our perceived 3-bet range. Secondly, BB seems like the kind of Aggro Reg aware enough to cold 4-bet us lightly given we're 3-betting an overfolding nitty Reg in very late position. 3-betting A9o would be to 3-bet a very large chunk of hands given that the hand flops poorly, can often be dominated when called and only has one blocker. It might be +EV in a vacuum to 3-bet, but it's not part of the best strategy here, and therefore, this should be an easy fold. Hero folds.