The Mathematics of Poker
by Bill Chen, Jerrod Ankenman
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Book Reviews of The Mathematics of Poker
Book Review: If this is poker, I quit!
Summary: 1 Stars
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!
UPDATE Sep 4, 2008: I recently found a computer program that anyone who buys this book really should also seriously consider investing in. No serious poker player should be without a retro encabulator. For more info see this informational video: http://video.google.com/videoplay?docid=5125780462773187994&hl=en
Book Review: I'd love to say this book rocks...
Summary: 2 Stars
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.
Book Review: Can you beat poker with numbers?
Summary: 4 Stars
In the movie 21, which if you will forgive the plug, I have to say is fantastic, a group of MIT students run rampant through Vegas unerringly winning big at the blackjack table. While I'm always skeptical about the way that Hollywood simplifies everything and this was no different. Just because you can count cards, doesn't make you infallible. But still, the general point holds true: if you know the math and can create a math-based system of play around blackjack, you can dramatically improve your chances to win.
I'm sorry for the long lead in, but this is what I thought about when I started reading The Mathematics of Poker. The book doesn't propose that a knowledge of great math will allow you to beat the game, and it really is less immediately practicable than Sklansky's Theory of Poker. But it does give a detailed mathematical analysis of the game that goes beyond the basic pot odds, which have been discussed to death in any number of books by this point. I wouldn't call this calculus, but I also wouldn't call it basic math, by any stretch of the imagination.
The place where this book gets crazy interesting is in the math surrounding less predictable poker concepts like bluffing, and how it should be considered through the percentages of hands won. If you've won too many of your bluffs, it means you're not doing it enough. Too few, and you should tone it down. Bluffing is a break even strategy. It is in ideas like this where the book extends beyond Sklansky's idea that there is a proper play for each situation, assuming you have total awareness of all the cards. MoP tries to take this thinking to a different level, to where there is a mathematical benefit to near optimal play, and that the human dynamic of poker can be understood, if not fully accounted for through math.
So to get back to my original point. Can you beat poker with numbers? Of course not. The game has far too many variables to allow for a purely mathematical approach to be as successful as it would be in blackjack. That being said, when you're facing a tough river call, I would rather have Chen, Ankenman, and their math by my side, than to just rely on gut instinct.
Book Review: If you take poker seriously, buy this book
Summary: 5 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.
Book Review: Beginner's Beware
Summary: 3 Stars
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.