LV Revealed

Review of Optimal Play

Optimal Play: Mathematical Studies of Games and Gambling
Stewart N. Ethier and William R. Eadington, editors
University of Nevada Press

Reviewed by Nick Christenson,

May 11, 2009

About every three years, a conference is held called The International Conference on Gambling and Risk Taking. At this conference professional mathematicians who have an interest in gambling applications meet with professional gamblers who have a background in advanced mathematics. Papers are presented and really geeky conversations take place. Several of these papers selected from multiple conferences along with some papers specifically selected or solicited by the editors have been collected into a single volume by editors Stewart Ethier and William Eadington.

Optimal Play includes over 30 papers written on a variety of gambling-related subjects. Applications to blackjack, sports betting, poker, craps, video poker, horse betting, and other games are covered. Many of the paper authors should be familiar names to well-read students of the gambling literature. Ed Thorpe, Chris "Jesus" Ferguson, James Grosjean, Brian Alspach, and Richard Epstein are some of the more familiar names who have their work included. Other contributors should be familiar to those who have read the academic literature that has been written about gambling.

Without a fairly thorough understanding of college-level mathematics most readers won't get very much out of this volume. Not only do the papers use advanced mathematical techniques, but as is the case for other forms of academic research, the authors are trying to solve new and often unusual problems. While some of these papers might have some direct applications for certain sophisticated gamblers, very little in Optimal Play matches up with the traditional, instructional gambling literature. Some of the results are interesting, but for those who are just concerned with improving their edge at various forms of gambling there isn't enough here to justify the effort required by this formidable book.

The target audience for this volume is really pretty small. Anyone who's not a sophisticated gambler with a background in advanced mathematics who feels compelled to read about some theoretical results with limited applications can safely skip this one. The less mathematically inclined may be interested in some of these results, but it's hard for me to recommend that they shell out the purchase price for this book and wade through 550 pages of explanation to come across the few applicable nuggets. I found Optimal Play to be a very interesting and worthwhile book, but I don't expect the majority of the people who read this review to have the same level of interest as I.

There's one final detail about this volume that I want to point out. I've read a large number of technical conference proceedings on a variety of subjects. This collection is remarkable in two ways. First, in no other collection of papers have I seen so many who acknowledge the editor, namely Stewart Ethier, as as glowingly as I found in this volume. Second, in no other proceedings have I seen so many papers make such well-considered references to other papers in the same volume. These characteristics are overwhelming evidence of the tremendous energy and attention paid toward improving the quality of the included papers, so it seems appropriate to point out what a fine job Dr. Ethier has done in shepherding this project. I found the extent of his involvement to be truly impressive.

It's my opinion that this is an excellent book filled with interesting research, but, again, the target audience just isn't very large. So, I give the book very high marks, but at the same time, I really can't recommend this book to a wide audience. The few people for whom the idea of the book sounds interesting and the level of math isn't daunting should consider checking out Optimal Play.


Optimal Play is a collection of research papers applying advanced mathematical techniques to some esoteric questions about gambling methods. A college-level background in mathematics is required to understand the vast majority of the topics discussed, and the number of distinct and useful ideas that can be directly applied to advantage gambling is quite small. Consequently, most of even the more serious gamblers won't gain enough from this tome to justify the time commitment it requires. However, those who are not daunted by these reservations, are likely to find the research fascinating and the methodologies compelling. This is a very high-quality collection of papers that few will have the background and energy to read.

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