The Mathematics of Poker

• #31 in Best Gambling Books
• #36 in Best Poker Books

36 Reviews

Sort by: Most Helpful ▲ Date Rating

Here is a quote from the book, "This is the general recursion that describes the relationship between successive values of Rp. To find specific values, we can use the fact that we know that Rp converges on r as P goes to infinity (since this is an approximation of the no-fold game as shown in Example 16.4). Hence, we can choose an arbitrarily large value of n, set it equal to square root of 2 - 1, and work backwards to the desired P. As it happens, this recursive relation converges quite rapidly. Of course, we can see that for the no-fold case, Rp simply is r for all thresholds, and this game simplifies to its no-fold analogue."

Of course! Duh, who didn't know that! If you enjoyed reading that, there are 375 more pages of this stuff. Oh, and in case you get bored with such elementary level stuff, there are sections throughout the book, where the authors have "marked off the start and end of some portions of the text so that our less mathematical readers can skip more complex derivitions." I can't even give you a quote from one of these sections because I don't have those keys on my keyboard...

I have been buying poker books for a while now and I finally found my limit. While I did slug my way through this book, I doubt it will make any difference in my game. I don't see how knowing that, quote, "skew instead sums the cubes of the distances, which cause the values to have sign," will improve my game. Whatever the heck that even means!

My advice, save your money and time, unless you want to put this book on your shelf and use it to intimidate your opponents. If one of them asks for advice you could give them this book, tell that it is a "must read" if they ever want to be a good poker player, and say that you LOVED IT! If they read it, they'll never look at you the same way again, I guarantee it. And they might just quit poker all-together. Like I said above, if THIS is poker, I might quit myself!

I finished this book last week and was pretty amazed. I think, at least for non-mathematic experts like this reviewer, going through it a couple more times is the best way to make use of the author's endeavor. This book is not huge but its pages are swelled with information. It is broken down into five major parts; each of these support the central theme of maximizing average profit. By the second page of the Introduction--in which the common misconceptions of play are examined--readers will discern that there is no fluff in these 350+ pages. Parts II and III embody its intellectual core as they outline the mechanics of both exploitative and optimal play. Exploitative play is defined as maximizing expectation in lieu of your opponent's strategy; whereas, optimal play makes use of fundamentally sound strategies which are independent from your opponent's actions. While most players strive to be exploitative with their play, the better ones compete at a "near-optimal" level which is an evolutionary advancement over taking advantage of mistakes. Other than Roshambo [rock, paper, scissors] and the The Jam or Fold Game for no limit, many examples will not be familiar to the average person. A lack of familiarity is not a problem, however, because studying games like Clairvoyance, AKQ, Cops and Robbers, and Auction strengthen the mind and provide valuable perspective. Of course, novices should be forewarned to put off this purchase until they become fully grounded in the elementary facets of poker. This text does not address the majority of the decisions one makes at the table. In this way, Chen and Ankenman are more Plutarch than Sklansky by treating the mind as "a fire to be kindled, not a vessel to be filled."

Poker fans may be worried about the difficulty of the math presented, and whether or not the possession of serious quantitative skills mandatory for getting something out of it. Not surprisingly, the answer is, "It depends." Assuredly, most members of the book consuming poker public meet the author's criteria in this area, which is the completion of eighth grade algebra. Although, what Chen and Ankenman may forget is that many of us no longer remember most of what we learned during those dark days of middle school. Understanding the proofs so prevalent hinges on the retention of information that might have been long deleted from our memory banks. Furthermore, a rudimentary background in statistics is also necessary for apprehending the meaning behind the equations. Those with no knowledge of statistics and algebra will be slightly stunned by the extent of the quantitative detail on display. The math impaired might become slightly demoralized, but the good news is that some amazing ideas are presented above and below the ubiquitous expressions. The sections concerning bankrolls, backing agreements, and tournaments will be of value to everyone as will the chapters devoted to the Risk of Ruin model, the use of math to improve play, and a no limit hold `em case study used as the basis for justifying the precepts of game theory.

Yes, this book is quite challenging, but self-improvement is rarely accomplished via easy endeavor. It is important to recall that this text is not an end point. Mountain ranges worth of mathematical information remain in need of interpretation. The Mathematics of Poker is a thorough introduction, and there is little doubt that future works will build upon its foundation. Chen and Ankenman offer something here that is totally unique due to its avoidance of felt level tactics and its emphasis on strategy--which is its essential virtue.

Wow, I'm very impressed with the book. I think it's touched ground that isn't available anywhere else. I'm sure that many programmers (myself included) have attempted to solve this game, and have discovered how burdensome the simple odds calculations are, nevermind the strategy and decision trees. Poker will not soon be solved by computers, like chess is. However, Bill Chen's ideas of "Toy games" help humans get insight into the character of the solution.

Anyone picking up this text should be warned of several things:

1) It is not for beginners. Strong poker takes judgement and experience, and basic hand/situational values cen be best learned from Dan Harringtons books or Sklansky's No-Limit book. I've read over 20 poker books, and Harrington and Sklansky stand out as the best. Harrington's books are very practical, with detailed analysis of situations.
2) It is not for the timid, foggy headed, or undisciplined. The new concepts in his books require for you to stop and think. If your instinct is "gee, this sounds complicated", then give up now. Some people will have the same backlash that regular people have with math. If you're from the "Math is hard" philosophy, this is not for you.
3) This book does not read fast. You should read it 3 times slower than a normal book to really appreciate it. The math shold not just be understood, it should be questioned.
4) The book highlights theory behind game strategy, but does not connect the dots with real hands or real situations. It would be good to connect the check-call, check-raise, check-fold, bet-raise, bet-call, bet-fold, bluff, check-raise bluff, etc... thresholds with actual cards. What would be most cool is for software to perform this analysis, although I imagine only one-street analysis could be performed, but it would still be insightful.
5) Personally, I cannot recommend the first 40 pages of this book. They really didn't dig into the meat of the game and I found it quite mundane.

That said, here are the good things I can say about it:

1) It is nothing like you've ever read in any other poker book before! Many poker books overlap eachother, reminding pot odds, hand values, tournament phases, etc. This book dives into the fundamental theory. The interesting math of poker is not related with mundane matters of probabilities, pot odds, etc. The interesting math is the math behind bluffing, calling, and value-playing. BTW, there is a math essay by Chris Ferguson about game theory and poker.
2) It will remind you about why you bluff. One of the most practical lesson I learned from this math is that if you are bluffing optimally, YOU SHOULD BREAK EVEN ON YOUR BLUFFS! That was revolutionary for me. If you're winning on your bluffs, you're not bluffing enough. If you're losing, you're bluffing too much. If you break even, you get paid most on your value. This is not exclusively true, but becomes more true the more solid your opponent is. If your opponent is weak tight, then you should probably profit on your bluffs. Exploit appropriately.
3) Optimal play gives you your "center game", which you use before you know your opponents. When you adapt to exploit your opponents, be aware that you are opening holes in your own game to perform the exploit.
4) The material covered in this book is shore of an undiscovered land. It is only the beginning. Since the game appears unsolveable, there are riddles and puzzles at every corner. New insights can drive a stronger game. Who knows? You may have some clever insight beyond what the author discovered.


I hope he writes a sequel to this book. Material I would love for him to research for the sequel:

1) Preflop single-full-street play, but with real holdem. For a given bet-size some actual card thresholds would be given for bluff, check-fold, checkraise, bet-fold, bet-call, etc... Translate this basic game concept to card thresholds. Include the fact that hands only have equity, not some automatic ranking (like 0-1 game).
2) Actual single-street post-flop play for some example flops. Again, card thresholds would be great. Ideally, if some representation could be shown for card thresholds as a function of bet & raise sizes. Maybe a few pages of tables are required. There should be at least 10 distinct flop examples and this should probably consume more than 30% of the book.
3) Optimal exploit as a function of opponent's deviation from optimal play. Again, make it practical with card thresholds.
4) The math of Caution vs. Aggression. I know that the deeper the stacks are, the more that play should steer towards caution. At 30 blinds, top pair is a push-push-push hand. At stack=pot middle pair is an allin hand. At 200 blinds, suddenly top pair seems like it should be sometimes checked, because it's tough to fold later. My question is, how does caution show up in the math? And how does it balance with the common notion that Aggressive play is best? I know it's often better to bet-fold a medium hand, but definately sometimes it's smartest to check-call it, to make your opponent indifferent to bluffing.
5) The math suggests that you should be check-calling and bet-calling with some expected losers to make your opponent indifferent to bluffing. What is the real threshold for these check-calls? Are check-calls with 2nd pair smart? bottom pair? What is really the right threshold? How does this change with multiple "bullets"?
6) The math suggests you should only bluff your trash. But then in multi-street poker with draws, we put many of our bluffs on medium drawing hands. How do the partially made hands with draws fit in?
7) More analysis about mult-way pots. Try to solve the full street 3-way 0-1 game. In a multiway pot, which player will take the burden to bluff-call and make the opponent indifferent to bluffing?
8) Any deeper material which cannot be described absolutely with math can probably be backed only by simulation. The readers are pragmatic people (just trying to improve their game) and do not need a systematic analysis for everything.
9) Figure out every secret that Chris Ferguson knows and squeeze it in here! lol


I very much believe there needs to be a sequel to this book. A foundation was layed, but the dots were not completely connected together. It's kinda like a movie where you're left in the middle, waiting for the sequel. The theory needs to be grounded to some practice.

As a math major, I can tell you that this book is not for the math-handicapped out there. I was expecting some strategy, but instead got tons and tons of analysis. It'd take hours and hours to fully grasp what they went over, but I just feel it is not worth it in terms of improving ones game.

I just finished my first complete reading of the book. It is absolutely extraordinary.

Those looking for specific advice playing particular forms of poker will not be happy with the book (with one important, and possibly extremely profitable exception). Those who are looking to really understand the depths and complexity of the game, in all its forms, will be rewarded with an absolute masterpiece.

I am a professional poker player, and I've read and studied everything worth reading (and many others not worth reading!) about poker many times. In my opinion, nearly all of the worthwhile stuff is 2+2 books, with a few important exceptions. As stellar as I believe the 2+2 books are, I feel that Mathematics of Poker (MoP) deserves its own category.

Its major departure from most good poker books is to explore the notion of "optimal play" in a great deal of depth. The most powerful tool of this exploration is game theory, and the book contains an extremely rigorous application of game theory to poker using exemplifying "toy" games that illustrate strategic principles of real poker games. Except for what Sklansky has briefly written on the subject (Theory of Poker), this is the only book containing this kind of information that I am aware of.

While the game theory sections seem to be causing the most comments, MoP also contains excellent sections on what the authors call "exploitive play". While optimal play intends to make our own play unexploitable, exploitive play intends to maximally profit from the deficiencies in our opponent's strategies. To do so, we must ourselves deviate from optimal play, which opens us up to be expolited ourselves (what the authors call counter-exploitation). The discussion of identifiying opponent's strategic weaknesses and developing maximally exploitive strategies is fantastic. Related to this whole discussion is the notion of strategic "balance", which is the bridge to the discussion of optimal play -- and the defense against counter-exploitation.

I can't say the book has taught me any new "plays" or given me any one specific thing to improve about my game (I am not a tournament player, the domain of the important exception I mentioned above). Instead, this book has given me something orders of magnitude more valuable: a more sophisticated way of *thinking* about poker. One reading has already prompted me to think about some pretty important aspects of my game -- balanced strategy on the turn in cash NL holdem, in my particular case -- in an entirely different paradigm. This is absolutely NOT just another book showing you how to calculate pot odds and reminding you to consider future action or the chance you'll catch and lose (my opinion of Yao's "Weighing the Odds"). There is some new and very sophisticated stuff here.

The book has introduced me to thinking about poker at the level beyond what's described in the existing literature. As soon as I finished the last page, I started reading it again...

One final comment about the math. I have an extremely strong math background (though not post-graduate level), and I am comfortable reading ideas in a textbook style of writing. However, the math is not difficult in this book, and the most "advanced" math employed is probably finding a minimum by finding the zero of the first derivative. That is calculus, but anyone who's taken basic differential calculus will be able to follow all the math in the book (this includes quite a few high school students). If you're someone who thinks that NL Holdem is a "people game" and so you don't need to know about equity of hands, pot odds, and draw probabilities, skip this book. This book is for people who have that stuff down cold, don't need any clever new ways to think about it (DIPO?!?), and want to go to the next level.

The beginning of the book has a nice introduction to probability and statistics, but I feel that a good understanding of how the authors analyze poker will require some basic training in statistics, particularly a degree of comfort with the idea of distributions. I think that studying the first half of a first-term college statistics book is valuable for gamblers whether they read MoP or not, but it will definitely help you with this book.

This book is difficult for people without an advanced math background. It is a theoretical book that will evolve your thinking about the game. The content however is ground breaking as it is the only book that brings game theory into the game of poker.

I am a 2-4nl online regular (6-tabling) and have every poker book worth mentioning. This is a must have!!! Having a master in theoretical physics obviously helped me understand the notation but I don't think you need to understand all math to get something from reading this book. It has lots of good stuff that can be applied like, how fast does my win rate (BB/100) converge to 95% probability.

If you are interesting in game theory but not so familiar with the math, then I could recommend some of the less technical books on the subject (just search on game theory) and get a feeling for the subject. If you haven't already reached an advanced level in poker (or have a master in mathematics) I recommend that you first make sure you have read: Harrington, Sklansky, Supersystem II and Maybe Phil Gordon's green book.

I'd love to say this book rocks, but I guess I'm just not smart enough. If you're REALLY into math, specifically statistics, discrete math, and game theory, AND you're a poker player, you'll get a lot out of this book. (As long as you read the errata and don't take all the examples as gospel - there are some mistakes in there even the authors didn't spot)

The truth is, I'm just not smart enough to enjoy this book. I'm a 30-something, college educated computer programmer (so I have the discrete math education already and I'm certainly not taking the short bus to work) - but the sheer volume of pure hardcore math and formulas in this book made my brain itch. I'm definitely very interested in the math behind the game, but unfortunately I can't muster the mental energy to dig deep enough in this book to find any entertaining poker anectodes or even any tongue-in-cheek dork humor to keep me reading. There are definitely more than a few concepts in the book that you can take and roll with at the table - in fact, if you can manage the read, it's all very useful information, but don't expect to find any epiphanies in there that will make you insta-rich.

Having said all this, if you're looking to write a poker bot to cheat- er... play online for you while you're, say, shopping for Dungeons and Dragons figurines in the game store and buying more 20-sided dice (you can never have too many), this is probably useful. With it, you'll be able to load your bot with all the information it needs to make sound, statistically correct playing decisions which will give you a sufficient decision-making edge over the competition, get you in the black sooner, and minimize deviation from your profit plan.

Yes, there will still be many pits and troughs in the graph where ex-Party Poker players will take out your bot on their typical colossal suck outs that encourage them to keep depositing their money every month. But don't worry - your bot will beat them 3 out of 5 times and that's really what it's all about, right?

Enjoy!

PS - No, I didn't write nor will I write a bot. I have a real job which I actually enjoy going to, a family, and... oh, yeah... I'm not bereft of morals.

Bill Chen and Jerrod Ankenman, The Mathematics of Poker (ConJelCo, 2006)

I should start this review by saying I'm not a math guy. I never was. I failed calculus the first time and had to take it twice (I squeaked by with a C- the second time). Years as a horseplayer, though, made me understand that I was a stats guy, and that the math inherent to the stats was workable even for an English major like me. Then I started playing poker seriously. Probability? Kelly criterion? Game theory? Yeah, I had all that. Then I read The Mathematics of Poker. And there's my old nemesis... calculus.

Chen and Ankenman say in the intro that the book is geared towards laypeople, and that they try to keep the math to a minimum (they separate out the more complex proofs and the like for non-math-guys to skip over). In short, they don't succeed. They can't; in order for you to grasp concepts later in the book, you have to get the math earlier in the book. There's no way to keep it to a minimum, really. There might be a way to make it more palatable, though. I've read probably seven or eight books on horse racing for every poker book I've read. (I was a horseplayer for a decade before I started playing poker with real, honest-to-goodness money.) One thing many of the good ones have in common is that they err on the side of excess when it comes to examples. If there's tricky math involved, the author will take you through it with four or five examples. When you're reading a book on horse racing, sometimes it seems like overkill, and I know I've remarked on that in some reviews of horse books I've written. I am now reformed, and see the light. Had I had that many redundant examples here, I'd probably have gotten it. Theory is great and all, but it's fundamentally useless unless you can put it into practice. Which is the stated goal of the authors here. What's missing is the gateway between theory and practice those examples provide.

One other thing (and this, too, is addressed by the authors towards the end of the book)-- even if you don't get the math, unless you're Daniel Negreanu or someone who plays like he does, you're likely to look at Chen and Ankenman's conclusions and say "whoa, that's some seriously aggressive play." Academically, yes, there will be times when it's right to call a raise with a suited five-deuce. (For that matter, with three-deuce offsuit as well.) There will also be times when it's right to push all-in with it. Would anyone actually do it at the table? The authors say they've been accused of maniacal play, and I have to say that after reading this book, I can see why. So be prepared: if you plan to put the lessons this book teaches you into practice, you're probably going to find yourself well outside your comfort zone for a while. ***

Two brilliant minds who also happen to be brilliant poker players have written a challenging but accessible explanation of what truly lies beneath the surface of the game of poker - the numbers. They begin with the basics of probability, then move to exploitative play (taking advantage of your opponents' errors), then to optimal play (playing so that no one can take advantage of you). The book also includes an important discussion of bankroll size, bet size, and risk of ruin, concepts rarely seen in the poker literature. Finally, they wrap up with an "Other Topics" section that provides critical insight into proper poker tournament play.

If you want to get beyond what you can accomplish by rote memorization of starting hand charts, give this book a try. It should not be the first poker book you read, but it may be one of the most important.

P.S. Unlike many poker books, this one is beautifully put together, without the typos and bad sentences that make me cringe as I read.

P.P.S I received my copy today. Why does Amazon still say "it's not available yet and we'll e-mail you when it does become available"???

For the first time, poker strategy and analysis advances past the simple mathematical concept of pot odds to incorporating more subtle and sophisticated mathematical tools to refine your game. As with the best poker books, this is a book that will require repeated readings to fully absorb. The book covers basic game theory, applications to poker strategy, optimal play in poker, managing risk to one's bankroll, and misc. topics including tournament play concepts.

That these concepts work is evident by the fact that the authors cashed in 7 WSOP 2006 events and won 2.

In the beginning, God created Supersystem.
The final "Revelation" in poker books is 'The Mathematics Of Poker".
With the release of this book now underway, the collective body of poker authorship is now complete. There needn't be any more.

With the boom in pokers popularity, a lot of books have recently come out that do nothing more than repeat what other authors have already said. At best, many of these books are simply pages upon pages that reflect the individual game-play philosophy of that particular author. Are such books useful? Sure. The more perspectives you understand as a player, the better. You really can't blame someone like Annie Duke for getting her piece of the poker boom pie by writing a book, but it isn't like it's going to make any difference in your game if you bother to read it or not...

Such is *not* the case with this book.
In my opinion, "The Mathematics Of Poker" is the first poker book in a long time that conveys information about the game which is truly essential. Kinda shocking that such a book hasn't been written before, but it was worth the wait.

This is not the first poker book you should read, but in my opinion, it is definitely the second or third.
Five Stars.

I really didn't expect to like this book. Honestly, the only reason I bought it was because I like to read everything that my opponents possibly have read. I don't want them to have an edge simply because I slept on something. So I thought: "Fine, I'll read this book. But I'm not going to like it." Boy, was I wrong. This might be the most thoughtful and intelligent poker book that I have ever read.

I learned poker by using my instincts, not math. So I expected to disagree with a lot of what this book would present. On the contrary, the opposite took place. Not only was I agreeing with the authors, it also reinforced what I had figured out intuitively on my own. Instead of contradicting my play, it reinforced that what I was doing was usually correct.

I haven't taken a math class since high school pre-calc in 1998, and I did alright. I didn't understand ALL the math in these pages, but one doesn't need to. As long as you get the gist of what they're saying and can apply it to poker, which an intelligent person should be able to do, you'll be fine. If you find yourself lost without a map (which you probably will at some point in the book), take a break and come back to it.

Flipping through this at your local book store, you might be intimidated by all the charts, graphs and equations. Don't be. Just buy it, read it with an open mind, and watch your poker game soar.

Chris Ferguson states that if he ever teaches a poker related math class he'll use this book. That observation really fits what this book accomplishes. The book is very much like a text book. A fair amount of study is required to fully understand what's in this book. Most of the information is quite terse and, like other reviewers have mentioned, you get out of it what you put in. If you're looking for specific advice for specific poker situations then this isn't for you. If you do want to gain a deeper understanding of the maths behind poker, with some effort, this book will help with that.

The two stars that I give the book is not, by any means, a way of rating the quality of the material within. It is meant to illustrate a different problem with the book - lack of any real target audience for it.

I am a rather mediocre poker player (who has read all of the basic poker theory books out there, but who has little practical experience and almost no time to improve on that) and a reasonably competent math user (having graduated in Computer Sciences). However, this book is of no interest to me in either aspect. For the poker player part of me, it is too detached, too much time is spent analyzing the theoretical aspects, too little intuitive data is given on how to actually improve your game (you might say that some of the game-theoretic results given within are something that cannot be inferred from the other poker books out there, but those pearls of wisdom could be easily compiled in a 10-page article). Maybe for a really world-class poker player, one who has mastered all the basics, can count all the relevant odds and take into account all the factors, this book might provide the pieces of intuition that might give him the competitive edge, but how many players like this are there?

For the math-user part of me, this book is too specific. I do not specialize in probability or game theory and even if I did, this text has actually little scientific value. The results contained within, from a scientific point of view, are not very interesting (which is why it's a 'popular' book and not a scientific publication). Most of this describes calculations that actually lead to nowhere because, as the authors themselves admit, poker is a too complicated game to solve by game-theoretical means with the current computing power. The few special cases which are actually broken down in the book are too specific to be actually used without modifications in real-game situations, which can be seen in the case of poker-playing bots, who cannot beat even a fair poker player in 1-1 situations in limit games. In what is currently probably the predominant game type on the internet, 10-seat no limit hold'em games, they are practically helpless. Human intuition quickly closes the gaps left by the increasing number of factors a computer program cannot cope with.

If you're the specific case of a math person who's recently done a course in probability, this subject interests you and you play poker competitively, this book is for you. If you're not, it's probably not. Hence the two stars: it represents the rough average of the usability of this book for the standard reader out there.

This book is ridiculous. It does not deal with "poker math" (hand winning percentages, odds and outs, etc). Instead, it goes into a bunch of limit formulas that deal with expected value and ways to mathematically figure out if your opponent is bluffing, etc. It really takes poker math to a ridiculous level. As an intermediate poker player, this book is not a necessary part of a poker player's library. There's nothing in this book that cannot be found with a little research online or by reading a different book...perhaps one of Dan Harrington's tournament books (awesome read), or something by David Sklansky if you want poker math.

I am by no means finished with this book yet, and I'm having to dust off a lot of mathematics I haven't used since college (a while ago), but I have already learned a great deal from this book.

I would encourage anyone who seriously wants a better understanding of how to play this complex game to take a look at this book, but be forewarned, it isn't a quick read. You will get out of this book in proportion to the amount of work you're willing to put into it.

I purchased this book based primarily on Chen's reputation. My first thought on opening it was that "this is math, not poker."

I had expected something on the order of King Yao's "Weighing the Odds in Hold'em Poker" on steroids. Instead I got a rigorous exploration of the mathematics of this fascinating game.

The authors point out quite rightly that one may get more insight into poker through exploration of what they call "toy games" than by tackling the monster head-on. This is much like the dilemma posed in performing quantum mechanical calculations - either solve an exact equation approximately or solve an approximate equation (toy game) exactly.

Some reviewers express disappointment in that they apparently wanted a book that would show them directly how to win at the poker table. Instead they got a book that will give them insight that will increase their probability of winning, provided they are willing to work through the math.

If you want the "smart pill" that produces instant understanding this book probably isn't for you. However, if you want to rigorously explore the mathematical underpinnings of the game I strongly recommend it.

much good.
This book has lot of interesting mental games. So it is a good book if you are into math, game theory and this kind of things. You probably will be disappointed if you want to improve your poker skills through reading this book.

Very little information relevant to poker players. Hard to separate the formula derivations from the concepts of the book.

The book examines a multitude of toy games with some similarities to poker and find the optimal strategy for each. There is one chapter (6 pages) on applying the conclusions to poker, it is not very concrete though. I haven't read the tournament section (28 pages) because I only play cash games so I can't comment on it.

For a No-Limit cash game player, there is very little value in this book. In fairness, it can teach someone to think in terms of a balanced strategy and playing different types of hands the same way. The example where they describe a player that raises a lot but folds too much to a reraise can open to eyes of some players. Anyway it could fit on a 2-pager instead of an almost 400 pages book using small fonts.

This book takes around 15 very narrow specific "toy games" (ie. i can only make one bet, and you can only call or fold), and runs thru some very dense, mathematical calculations to draw some conclusions and principles for real poker play. I found the principles and math to be very valuable, and I learned alot about how to play drawing hands, and how to think about what actions to take with a range of hands.

But it took alot of thinking and re-reading to get there. and it is not presented in an easy-to-digest way. However, if you are pretty smart, mathematically-oriented, like to study things to get better at them, then this is a very good book because it is the only one i've found that applies games theory to poker and gives you advice on how to holistically play across many hands (as opposed to advice on how to play one specific hand). but this book is only for the serious advanced player.

Make no bones about this, this book contains some pretty complicated and esoteric stuff, but then again, poker can be a pretty complicated game!

First off, not for beginners. Sup bro.

No need for a long-winded review here, this book is flat-out excellent. You should have some ability with mathematics to gain full benefit, but if not, some of the conclusions the authors draw will still be more than enough to make this book an excellent value.

My initial impression is that this book will become as essential as TOP is to serious players, and again, I will need to reread this many times before I'm able to fully grasp everything, if even then.

Less important: the text is relatively tiny, which I prefer, but some people may not. The end result is that each page has a lot of information on it. If the typography were that of other poker texts, the book would need twice as many pages.

Got this on a recommendation. It's been a while since I've used my brain to this extent. I've read other reviews saying that you don't need much math to get through it - don't believe it. I'm only halfway thru the book - there are nuggets of information, and hopefully some very useful info later on...but it's the type of book one would likely have to read a few times to get the gist of it. Unless you've got a math brain like Jesus Ferguson. Recommended to a certain extent.

As an engineer, I was very excited to start reading this book, then as I started to read, I realized I was in serious trouble. I am the type of player who loves to read strategy poker books, (i.e Harrington on Hold Em, Theory of Poker) but this book in my opinion cannot teach you much about strategy because most of the math presented in the book is very abstract. The authors tell you in the first few pages that if you want to question the material or better understand the material you should refer to a math text because they don't want to scare readers away. However, it is the fact that they cannot present each mathematical truth in detail which causes the book to fail most readers who do not have a mathematical background. If a book could show you how to make the right play in a 3 handed poker game with a simple calculator as opposed to setting up multiple equations using graphs with several variables to accomplish the same goal, a reader would probably go with the calculator.

Overall, the book is very well written and presents great examples of mathematical proof of why a certain play is correct and why others are not correct. If you love mathematical proofs, poker, and working out equations, then you'll probably love this book. However, the book, in my opinion, uses very complicated equations to prove what many poker players probably already understand in a simpler, more straightforward context.

This may be a great book, for a few players.
But for the average poker player, its a very tough read.
With difficult math. However, if thats what your looking for...its the book for you .

After picking this book up three times, I realized that this book is not for me.
1. The font size is too small for easy reading.
2. The presentation assumes that the reader has a significant amount of mathematics background; alternatively, even if this interpretation is incorrect, it is not easily understood.
I give up.

Bought this book to understand the finer aspects of the math behind poker. Knowing that Bill has won a couple of WSOP bracelets led me to be confident that the book was worthwhile.

My statistics knowledge is quite rusty, so the reading is slow-going for me to this point. My eyes have honestly glazed over quite a few times in the early going...

Vanessa Russo, an up-and-coming poker pro, basically endorsed this book on one or more occassions on TV, citing the value of reading the latter chapters of this book. Admittedly, she teaches a poker course on Game Theory, so the material probably comes easy to her :)

Just finished the book after laying it down many times; it's not an easy read. The authors do a fine job of laying the theoretical groundwork for how to think about your play. I liked the concepts, but the details are quite tedious. I'm glad I read it, but I don't think it's going to be too useful to players that are looking for specific advice on how to play certain situations that arise.

I bought this book thinking it was going to contain analyses of poker. It does not. Let me repeat that. IT DOES NOT. What it does contain are analyses of simple poker-like games, the optimal strategies of which are easily determinable by anyone with a rudimentary knowledge of game theory. The authors, after wasting your time with simple, near obvious results then proceed to draw no useful conclusions applicable to the real game of poker as played for real money in the real world. But if you think having it on your bookshelf will make your poker library complete, then buy one today.

The concepts presented by Mr. Chen should be intuitively obvious to the most casual observer. There is of course, an intimate relationship of the concepts presented in this book to the geometric progression of the aging of our planet. The general recursion that describes the relationship between successive values of ozone percentage in the ionosphere is a function of the standard deviation of annual mean temperature at sea level at the Arctic Circle.

This book contains overwhelming mathematical evidence that the laws of nature are being geometrically accelerated by pollution on the earth, most importantly, the greenhouse effect.

As for poker, many experts consider poker to be a people game played with cards.

I wish that an expert mathematician, such as Mr. Chen would write a book that applies the principles of mathematics to cooking. Possible topics could include optimization techniques, which modify inexpensive meats, poultry, and fish to taste as good as expensive cuisine.

If this book was the poker bible, I would find poker as much fun as enlisting in the Army.

Some advanced players may like this book. I recommend first browsing the book before buying, to determine if it is of interest to you.

Complex, yes, but nothing beyond high school algebra is necessary to grasp the essentials. Teaches you a way to think about poker that is unlike any other book. The best poker book in my library.

There is nothing more to say other than this book is the complete math book of poker. Nothing is left out and some of the material is fairly advanced. So, if you've not taken a college-level math course, you may be lost.

Soooooo much material but so very, very good. Chris Ferguson said it right ... if there were ever a university-level class on poker, THIS would be the textbook.

Intriguing and thought-provoking analysis of bluffing, mostly in no-limit hold'em, although some analysis of limit hold'em. Focuses on toy examples that are nonetheless educational. Writing at times a bit choppy and elliptical. Nevertheless, full of fun and entertaining examples that will at a minimum give much scope for future research.

This book is a must have. Ive read many books on poker and this book alone is worth more than the rest of them. Of course if you are going to read it you have to be rather smart and have some poker experience. If you have those characteristics then my advice is: Throw the rest of the books away and read a master book on poker

I bought this book and that was a big mistake. The beginning of the book was fine to me. Because almost everything was explained well. but, the more I read into the rest of the book, the more headaches I got.

When it comes to the everyday poker player this book gets ZERO stars!!
But - the title does say The Mathematics of Poker. and if you look at it as A complex math book with poker as it's subject then this book gets FIVE stars. unless you're working on, or have, A college Math degree then this book is not for you! The books you should read instead are "Texas Hold'em Odds and Probabilities" by Matthew Hilger - or "Killer Poker By The Numbers" by Tony Guerrera both of these books are way more practical!!!