The Mathematics of Poker
by Bill Chen, Jerrod Ankenman
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Book Summary Information
Author: Bill Chen, Jerrod AnkenmanEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 2006-11-30
ISBN: 1886070253
Number of pages: 382
Publisher: Conjelco
Book Reviews of The Mathematics of Poker
Book Review: Bill, you gottta write a sequel
Summary: 5 Stars
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.
Summary of The Mathematics of Poker
In the late 1970s and early 1980s, the bond an option markets were dominated by traders who had learned their craft by experience. They believed that there experience and intuition for trading were a renewable edge; this is, that they could make money just as they always had by continuing to trade as they always had. By the mid-1990s, a revolution in trading had occurred; the old school grizzled traders had been replaced by a new breed of quantitative analysts, applying mathematics to the "art" of trading and making of it a science. Similarly in poker, for decades, the highest level of pokers have been dominated by players who have learned the game by playing it, "road gamblers" who have cultivated intuition for the game and are adept at reading other players' hands from betting patterns and physical tells. Over the last five to ten years, a whole new breed has risen to prominence within the poker community. Applying the tools of computer science and mathematics to poker and sharing the information across the Internet, these players have challenged many of the assumptions that underlie traditional approaches to the game. One of the most important features of this new approach is a reliance on quantitative analysis and the application of mathematics to the game. The intent of this book is to provide an introduction to quantitative techniques as applied to poker and to a branch of mathematics that is particularly applicable to poker, game theory. There are mathematical techniques that can be applied for poker that are difficult and complex. But most of the mathematics of poker is really not terribly difficult, and the authors have sought to make seemingly difficult topics accessible to players without a very strong mathematical background.Poker Books
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