Review: The Mathematics of Poker

5 Star, Book Reviews

July 28, 2007

Author: Bill Chen & Jerrod Ankenman

Publisher: Conjelco

This book attempts a fundamental methodological shift in the way scholarly players approach the game of poker.

A brief history lesson is in order here. The first method of developing poker skills was simply to learn by experience. Certain smart players can do that very well. However it’s a slow process – a given situation has to occur several times before you develop an understanding, and in the meanwhile those with a better grasp of the game are taking your money. Lessons were expensive back then even if you were smart, and if you weren’t that sharp, well, you were screwed. The second method of developing poker skills was to learn from books containing the distilled experience of others. This method is typified by the first Supersystem book, and it fundamentally revolutionized poker. Now the lessons weren’t so costly (even at $100, the book was comparatively cheap) and you could benefit from the experience of some very sharp players. The third method was typified by Sklansky’s Theory of Poker, and essentially amounted to using algebraic & logical thinking at the poker table to make decisions. The benefit of this system was that it could be applied to situations not covered in the book or that the player has never seen before. Unfortunately, certain kinds of decisions (which are very mathematically complicated) are beyond the scope of this sort of thinking. For example, Theory of Poker has little to say about how to open you hands in multi-street forms of poker.

The Mathematics of Poker, while it shares something with Sklansky’s philosophy in the early chapters, is really trying to develop a fourth way of thinking and learning about poker. The new philosophy is game theoretic simulation. When you encounter one of those problems too complicated to reason about directly, create a new “toy” game that contains that one troublesome aspect in it’s entirety but simplifies as much of the rest of the complexity of poker as possible. Then use sophisticated mathematical techniques to “solve” that toy game and determine a “optimal” strategy for it. The details of how this is done are beyond the scope of a review, but suffice to say a ton of math is involved. Then take the solution to the toy problem, and see what it has to say about the original real-game problem.

It’s very difficult to say whether this method will in the long run come to dominate poker thinking at the highest levels, or be solely an academic sidelight. Chen’s very strong world series of poker results in 2006 might be an indication that he knows something the rest of us don’t, or it might just be coincidence and/or strong conventional play on Bill’s part. Only time will tell.

A significant concern for most prospective readers of this book is exactly how mathematically literate you have to be to make use of the book. It’s a difficult question – Chen & Ankenman assume only algebra skills and develop everything else in-book. However, to really grasp what they’re getting at, you need “mathematical maturity” which is usually developed in classes far beyond algebra. In my opinion, to really “get” this book you would ideally have already studied and excelled at algebra, statistics, boolean logic, probability, game theory, basic algorithms, and some sort of abstract algebra or other foundational math. You can get some benefit without that background, but you’ll have to do a lot of work and outside reading in places where more prepared readers can cruise.

Now, as to whether you should buy this book or pass on it, well, it depends. If you’re looking for practical tips to improve your beginner or intermediate game, I suggest you pass. The gulf between the kind of thinking that Chen & Ankenman are engaging in and actual play is pretty wide and there’s many books that will help you more. If you don’t like or aren’t good at math, pass. If you aren’t an experienced player, pass unless you’re reading out of pure academic/mathematical interest. If you’re an advanced player looking for a new way to think about the game & get a possible edge, it’s worth your time. However, be aware that this book is in some sense the birth of its philosophy, not the fruition. If you want to get the full value out of it, you need to be prepared to extend Chen & Ankenman’s work to answer questions about the poker problems you face rather than the ones they chose to tackle. In other words you need to be prepared to dive in and do novel graduate-level mathematics. Realistically, few readers are going to be that skilled or motivated.

In the end, I struggled with how to rate this book since the value of the information contained within is still unclear and the audience that will fully benefit may be only 100 people in the entire world. But I can’t in good conscience give it anything less than five stars. It’s rare that a book revolutionizes its field, and such works are not easily dismissed.

Rating: 5/5 stars

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