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Play Optimal Poker: Practical Game Theory for Every Poker Player

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Think game theory is abstract and incomprehensible? Think again!Play Optimal Poker shatters the myth that game theory is only for elite poker players. Renowned poker pro and coach Andrew Brokos takes you step-by-step through the fundamentals, explaining core game theory principles and how to apply them in real poker situations. Whether you play small stakes or high stakes, cash games or tournaments, Play Optimal Poker provides powerful new tools to help you navigate tricky situations, hold your own against the toughest competition, and exploit common mistakes. Once you understand the fundamentals of game theory, you’ll approach the poker table with the confidence to handle anything the game can throw at you.You will learn how powerful game theory concepts like equilibrium and indifferenceApply game theory principles to everyday poker decisionsBuild polarized and condensed rangesProfit from both aggression and passivityManipulate your ranges to exploit common mistakesHold your own against world-class opponentsAndrew Brokos has been a professional poker player for more than fifteen years, with hundreds of thousands in cash game winnings, final tables in major online tournament series, and three Top 100 finishes in the World Series of Poker Main Event. As a coach and host of the popular Thinking Poker Podcast, Andrew is widely regarded for his ability to explain complex concepts in terms anyone can understand."Working with Andrew instantly leveled up my game, but more importantly it gave me a great foundation on which to build my skills over time by learning to think about the game in the right way. As a rec player the work we did has really had a positive impact on my life because I just get a lot more joy out of poker now that I’m winning much more consistently and moving up the stakes."-Michael S., poker coaching student"There's just a ton of useful stuff here. I'm already starting to think... OK, every hand that I play, I need to be thinking about what hands out of my range am I bluffing here?"-Eric L., lawyer and “serious amateur” poker player

245 pages, Kindle Edition

Published June 4, 2019

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348 people want to read

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Andrew Brokos

22 books14 followers

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Displaying 1 - 26 of 26 reviews
70 reviews1 follower
August 2, 2019
A great mix of theory, toy problems, and applications; stands out among poker books for its effectiveness in quizzing the reading to make information and concepts stick. Rewards both high-engagement (solving every problem) and low-engagement reading. As someone who didn't necessarily think deeply about balancing ranges in spots past preflop, I took a lot from the book & have already felt my thought process changing.
13 reviews
January 6, 2025
Solid intro to GTO that conveys a lot without being overwhelming, teaches crucial concepts well and reinforces with quizzes including answers and explanations
Profile Image for Zach.
36 reviews5 followers
June 29, 2020
It got me thinking about poker in a different way. But throughout the read my little voice inside, the same one that I call the B.S. meter, was tipping. These get kind of intricate which is kind of the point given that this book invites a more intricate look at strategy.

Andrew has some theories or guidance that doesn’t make intuitive sense to me. First, in his simple Ace-King-Queen card game that he builds on, he states a premise that a half pot river bet is effective if it is called 2/3 of the time or less.
• If one was to then back into a frequency of bluffing calculation, this same half pot bet should be made about 1/3 of the time when the dealer is holding the “bad” hand and of course all the time with the “good” hand.
• So the author presumes that the calling player should call 2/3 of the time in order to maximize returns. Fallacy watch: if it’s slightly a good idea to call, isn’t it therefore always a good idea to call? The error in this thinking is that we somehow know ahead of time that the caller is going to call 2/3 of the time. We don’t really know that – this is assumed to be a tuned, or learned behavior. Basically, when the bettor has played umpteen hands, he knows to sneak in a few bluffs. But if the caller begins calling more often, he will bluff less. So, supposedly, given that he is choosing to bet a half pot amount, this equilibrium will tune out at 2/3 calling percentage. I don't buy this - either the opponent is going to call or not. Maybe a select few players have a mental random number generator and say to themselves, "well I am going to now call 2/3 of the time. Which is it this time?"
• There seems to be a trend throughout the book of identifying non-optimum tendencies of opponents. For example, Andrew will say "If a player does not check raise on the river as much as is optimum, then you should do XYZ.". This may work for a tracker when playing on-line. But for a live game, this is ridiculous. If somehow, your brain was tracking to this level, it would be tracking perhaps 4 betting rounds, 4 actions (check-call, check-raise, bet-fold, bet-re-raise) and who is polarized/condensed and then betting amounts (small, medium, large I guess) for 4 x 4 x 2 x 3=96 different situations. If you play for a 4 hour session, you might get 2 datapoints each night on a particular player. Who are we kidding?

Anyhow, it opened up a few new avenues of thinking and for that I am grateful and glad to have read this book.
Profile Image for Hélio Steven.
20 reviews9 followers
April 14, 2023
I think most of those interested in poker by now have already heard about "game theory optimal" poker, usually called GTO poker (GTOP). GTOP basically analyzes the ways in which players seeking to be unexploitable can maximize their gains and minimize their losses; in other words, GTOP studies the results of playing poker optimally. These results are called "equilibrium strategies". In game theory, a Nash equilibrium is a game state where all of the players involved have no incentive to change their strategy set given the strategy sets of everyone else, as they can gain nothing more than what they already have gained by keeping the current strategy. Thus, in poker, to say that players have reached equilibrium is to say that they have no incentive to change the strategies they have settled on, as doing so won't increase their expected payoffs. Being a game of incomplete information with a major chance element, equilibrium in poker will be obtained by players mixing their strategies, which is to say that they won't apply a strict pure rule such as, e.g., "always bet very big on very strong hands and never on bluffs", because then this pattern would eventually be figured out by your opponents and then they could increase their payoffs at your expense by always folding to your big bets when they know their hands are probably worse than what you could have, for example. To preempt exploits, then, a player needs to mix her strategies in a way that makes her unpredictable to her opponents, and this will involve balancing value bets, checks, calls, and bluffs at a given frequency. And of course, by assumption all of the other players will play exactly the same way.

It doesn't take much to realize literal optimal play is impossible for any human player, as the number of possibilities and their relative probabilities are overwhelming to limited beings like us, which is why people interested in figuring out optimal play in many different situations go to computer programs called "solvers" for the answers. Also, the strategies one figures out through GTO studies are based on the assumption that one's opponents are playing optimally, which we know will not be the case even for people who study a lot of GTO regularly. Finally, particular decision points are often compatible with more than one action in an equilibrium set and there will specific such points where the least frequent action will do better. And so from these observations a lot of people complain that GTO is useless and might even be counterproductive, as by relying on it one could be foregoing an exploitative play that would maximize one's returns once they have identified exploitable spots in a given opponent's play. Understandable as it is, this is a bad complaint. As every competent practicing scientist knows, most mathematical models aren't straightforwardly applicable to real world situations because they have a lot of simplifying and unrealistic assumptions, but they can still be relevant if their crucial relationships are approximated or even totally instantiated in real world circumstances. In poker, trying to be as balanced as possible based on GTO thinking will more often than not be more profitable in the long run than using an exploitative approach as a default, and striving to be unexploitable is especially important considering the heterogeneity of opponent types there exists in poker as well as their learning in the game dynamics. To avoid the impression that this is simply a mere assertion, I'll just note that it's not by chance that most top level players on stupidly high stakes games and tournaments (live and online) play according to GTOP, many of them even using solvers themselves to study ways to improve their game. Moreover, GTOP isn't incompatible with exploiting mistakes or weaknesses one's identified in a game: if you know that someone is playing poorly in a particular way, you'll likely increase your payoffs at their expense by exploiting such and such mistake and should do so, and by being aware that this is out-of-equilibrium play you'll be able to more easily revert to equilibrium play if you notice the game dynamic has changed and thus will avoid becoming exploitable.

All of this finally brings me to this book. Brokos manages to give readers a very good introduction to GTO poker. All of the important concepts for playing good modern poker are there: equity, expected value, card ranges, card blocking etc. And all of the concepts are introduced carefully and step by step by using simple toy games so that the reader will be comfortable with them before working with other concepts that build on the previous ones. So I believe there's a lot to be gained by interested lay people and even by those who already have some experience with trying to apply strategic reasoning to poker, as the concepts and perspective the book provides will help both the former and the latter with how to better systematize their strategic thinking. For example, I've benefitted a lot by thinking in terms of range targetting and card blocking, which were concepts I've first seen elsewhere but that are also present in the book.

While I do believe it's a very good and accessible introduction to GTO, I'd recommend that people very unfamiliar with basic statistical and game-theoretic concepts and reasoning get a little grip of these before (or during) reading the book. Brokos does introduce all of the important concepts in the book in the simplest way he can, but I'm afraid it might not be enough for a lot of people too unfamiliar with them, as one can easily struggle with later parts of the book that are counterintuitive if one is not used to statistical and game-theoretic thinking. For example, people used to statistical thinking will quickly see why equilibrium strategies tend to do better given the assumption that a player will play an indefinite amount of games, even if particular out of equilibrium or less frequent equilibrium plays profit in particular instances, while people not used to statistics will probably tend to take particular instances as evidence against the importance of envisioning equilibrium plays, thereby downplaying the very important notion of adopting a pattern of behavior that's better off in the long run with multiple decision points that will be very different from the particular instance one is attending to at any given real life situation. To be clear, here I mean only that one will benefit more if one is comfortable with the logic of game theory and statistics, and so it's not necessary at all that one should also dive into the full blown mathematics of these disciplines. Nowadays there are several youtube channels dedicated to teaching and fixing GTO reasoning, so another way of improving the book's reading experience (and going beyond what you learn there) is to check on them. My favorite ones are Finding Equilibrium and GTOWizard, but there are enough of other options out there for different tastes.

A shortcoming worth mentioning here is that Brokos provides no references, neither did he bother to make a "further reading" list, which is standard practice in introductory books.
Profile Image for Sanford Chee.
559 reviews99 followers
September 4, 2021
Poker Equity:
AKo vs 78s 60/40 but 70/30 vs Axs & 75/25 vs Axo

Bet size/Pot => bluffing frequency where EV = (%bluff*(pot + bet)) - ((1-%bluff)*bet) = 0
1/4 pot => 1/6 bluff
1/3 pot => 1/5 bluff
1/2 pot => 1/4 bluff
2/3 pot => 2/7 bluff
3/4 pot => 3/10 bluff
Pot => 1/3 bluff
1.5x pot => 3/8 bluff
2x pot => 2/5 bluff => bluff < 50% of the time

River bet vs calling station = 1 - (bet/(bet+pot))
1/4 pot => call 4/5
1/3 pot => call 3/4
1/2 pot => call 2/3
2/3 pot => call 3/5
3/4 pot => call 4/7
Pot => call 1/2
1.5x pot => call 2/5
2x pot => call 1/3
3x pot => call 1/4

GTO equilibrium
Out of position bet frequency In position bet frequency
A (nuts) 20% (80% check raise) 100%
K 2nd nut 100% 100%
Q (thin value) 86% 100%
J (thin value) check 37%
T check check
9 check check
8 check check
7 check check
6 bluff 33% bluff 11%
5 bluff 33% bluff 100%

In Position strategy when faced w/ a bet
Call Fold Raise
A (nuts) never 100%
K 2nd nut 90% never 10%
Q 100%
J 87% 12% 1%
T 51% 39% 10%
9 51% 39% 10%
8 47% 42% 11%
7 20% 73% 7%
6 100%
5 100%
How should out of position player exploit in position player who rarely raise as a bluff?
* Don’t ‘ve to worry abt making difficult decision af betting =>fold to raise if you don’t ‘ve the nuts
* => 100% vs [86%/0%] bet w/ Q/J coz not facing difficult decision when these hands are raised yet extract thin value fr villain’s J-7 calls
* 100% vs [80%] check the nuts in the hope of check raising when in position villain bets w/ 2nd nuts (K) or Q or occasional J & river bluffs (6/5). Coz villain when faced w/ bet unlikely to raise K, J-7 as per equilibrium

Out of Position check-calling strategy
Call Fold Raise
A (nuts) 80% check raise (20% bet)
K 2nd nut
Q 14% (86% thin value bet)
J 100%
T 44% 49% 7% raise as a bluff
9 44% 49% 7% raise as a bluff
8 44% 49% 7% raise as a bluff
7 44% 49% 7% raise as a bluff
6 (bluff/fold) 67% (33% bluff)
5 (bluff/fold) 67% (33% bluff)

When in position, how to exploit out of position villain who only value bets w/ K or better (i.e. not enough betting Q for thin value [86%])?
* When villain’s range contains fewer thin value bets, reduce check raising => K (2nd nut) = pure calls vs [10%] check raise
* => < incentive to raise as a bluff

On the under hand, what if out of position villain makes too many thin-value bets (e.g. betting w/ J when it should be a check)?
* value raise & bluff raise > i.e. incr K value raise% vs [10%]
Profile Image for Dustin.
42 reviews1 follower
January 24, 2022
TRUE SCORE: 3.25/5.00

Play Optimal Poker is a somewhat decent introduction to the basics of game theory and how it relates to new school poker concepts. However, as it tries to straddle the line between being a book on game theory and a book on poker, it seems to fail to do either very well. In order to bring everything back to poker the author does a serious disservice to explaining the math behind the game theory that is taught. The math is glossed over so much as to be almost useless. About 25% through the book I realized that I should just give up on trying to understand the specific game theory that was presented and instead only think about the concepts in the abstract. However, because time is devoted to these “toy games,” there is very little time to do anything besides make general statements on how to apply the game theory presented to poker. This book needed to be about twice as long to accomplish what it set out to.

Having said all of that, it is a serviceable jumping off point for a student willing to seek out further information.

On another note, I bought the hard copy of this book and the binding was AWFUL. Pages literally were falling out as I turned them. This didn’t affect my review, but maybe go for the Kindle version if you pick up a copy.
Profile Image for Santiago Mansilla.
Author 2 books4 followers
June 23, 2020
One of the Best Poker Books from 2019.

The author has plenty of experience with 6 cashes (made the money) in the WSOP Main Event and 3 of those ITM were in the Top 100. The player with more cashes has 10.

In Play Optimal Poker he explains in a simple way a very important subject in poker strategy: GTO (Game Theory Optimal). He uses cards games to describe his points and also hand examples to apply the concepts.

If you enjoy this book you should read his other book's: "The Thinking Poker Diaries", were he tells in first person his experiences in the WSOP in Las Vegas.
22 reviews
December 30, 2023
A decent high level conceptual introduction to game theory ideas and how they can apply to Poker. This doesn’t go into much math or specific ranges. It also isn’t meant as a practical guide. Instead you’ll get to understand more of the “why” of Poker and how to think about it.

I would say this is a good book for experienced beginners, or intermediate players who haven’t looked into any game theory yet. If you already know about it and want more specific and practical strategies, I don’t think this will offer all that much.
Profile Image for Connor.
44 reviews3 followers
July 9, 2024
A high quality re-introduction to fundamental game theory concepts utilised in hold 'em. The examples at the end of each chapter aren't always explicitly linked to the concepts within the chapter, and they occasionally lean on recieved knowledge that the reader may or may not be experienced enough to know. This is a small gripe - in general, it was very easy to overlook the rougher edges of the book and just focus on its core lessons. Will certainly read POP 2.
Profile Image for Peter Nielsen.
6 reviews8 followers
September 3, 2019
Excellent read, explaining the concepts of game theory in poker. Brokos uses simplified examples to clarify the strategies and then debates the knowledge gained into typical poker situations.
Polarised vs condensed range was news to me, poker simply serms like a different game due to GTO, and Brokos explains why.

4 reviews
February 5, 2020
Great book for the Rec Poker player

As a recreational poker player I don't have the time or money to invest in solvers like Pio or Monker. Andrew is showing us the power of these solvers and how they can be used to strengthen our strategies. I will definitely be re-reading this many times in the years to come.
Profile Image for Kristin Somsky.
1 review4 followers
February 4, 2020
Excellent introduction to Game Theory

The book leads you through Game Theory concepts by using toy games that increase in complexity to understand basic concepts. While there is still much to learn to apply all of these concepts to No-Limit Hold’em, it is a great start.
4 reviews
Read
October 27, 2021
Best book to understand the complex world of Game theory

I've played Andrew and he's not only a good player but a wonderful funny human. His effort to demystify game theory in Poker is much appreciated.
10 reviews
March 16, 2024
Great book for explaining game theory to poker players with toy games. Good for building some intuition about theoretically optimal play.

Toy games are very simple. Not very applicable to real-life scenarios.
Profile Image for Mingtao Sun.
73 reviews1 follower
February 20, 2021
Definitely the best poker book I've ever read. Up my thinking to the next level.
Profile Image for Jordi CB.
33 reviews
December 29, 2021
It's a good read if you want to get more deep regarding game theory and toy games. Not sure how you imporove your poker game but it will make you think defintely.
Profile Image for Asher Mancinelli.
28 reviews
December 9, 2025
Lots of clumsy wording but some of the walkthroughs of the simplified games were fun and helpful
Profile Image for Mark Donovan.
Author 1 book16 followers
October 15, 2019
Best poker book for advanced players. It could have used more example hands at the end.
Profile Image for Lucas Cavalcanti.
63 reviews4 followers
July 21, 2021
Awesome book to understand the core concepts upon which GTO poker strategies are built. It also gives you a lot of insights about how to deviate from optimal play in order to target specific mistakes from your opponents.

This book is mostly introductory in the sense that although it unveils the fundamentals of GTO and how it applies to actual poker, many questions are left to answer and many decision spots are not explored in great detail. But this is book 1 of a 2 volumes series, so I guess vol. 2 will make up for it.

The main quality of this work is how skilled the author is at breaking down these complex ideas and making them stick through both well written and structured chapters, and engaging questions throughout the book.
Profile Image for Eric Thim.
71 reviews1 follower
February 10, 2021
Great intro to the basics of game theory as applied to poker. Brokos is such a good writer, makes this goofy math stuff so easy to understand. A+!
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