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Calculated Bets: Computers, Gambling and Mathematical Modeling to Win

Steven Skiena
Mathematical Association of America and Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Andrew Perry
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Steven Skiena's Calculated Bets describes a clever computerized betting system which the author uses to scientifically and systematically "beat the odds" betting on jai alai games. In addition to describing his betting system, Prof. Skiena frequently digresses into various topics of mathematics and computer science which have some relevance to the betting system. In so doing he brings academic topics to life, showing, in the words of Mark Balestra, "how mathematical theory extends far beyond the academic boundaries in which so many of us attempt to contain it". Skiena's lucid and engaging writing style together with his seamless integration of disparate topics makes Calculated Bets a true masterpiece.

In order to explain the mechanics of his system, Skiena gives his readers a crash course in jai alai; I will try to summarize only the very basics. The game is played in an indoor court somewhat like a squash or racquetball court, only larger. Instead of racquets, curved baskets called cestas are used; the ball is small and hard, and can fly up to 180 miles per hour. Rather like tennis or racquetball, a player wins a point when he forces his opponent to misplay the ball . Eight players (or sometimes, eight pairs of players) compete in a sequence of head to head contests (points). Initially, player #1 plays a point against player #2, with the other six players waiting in a queue. The winner of a point plays the fellow at the front of the queue next, while the loser goes to the end of the queue. It continues in this way until someone has scored eight points, and this person is then declared the winner. Second and third place finishers are also decided using a complex tie breaking system. A variety of bets are possible, the most popular being the trifecta, a bet on first second and third place finishers in order. All betting uses the pari-mutuel system, where bettors effectively bet against one another and the house taking a percentage (perhaps 20%) of all winnings.

Of course, the earlier players in the queue have a distinct advantage, as they will tend to have more opportunities to score points before the game ends. To minimize this advantage, every "point" or volley starting with the eighth counts double. Player #8, for example, is guaranteed to win the entire match by winning his first four volleys (worth two points each). One might think that this doubling rule would make for a relatively fair game. To determine the relative advantages of the different starting positions, Skiena constructs a computer simulation of one million jai alai matches using theoretical players of equal ability. It turns out that players #1 and #2 retain a distinct advantage over the rest of the field, and are almost twice as likely as player #7 to win the match. Amazingly, the most frequently occurring trifecta (1-4-2) is nearly 500 times more likely than the rarest one (5-8-7).

Real life jai alai players, of course, vary in ability. A good player, for example, may win 60% of the points he plays. First Skiena constructs a mathematical model of jai alai matches between players of unequal ability, and in so doing he digresses into interesting discussions of functions, curve fitting, correlation and other topics. He describes how he built a parser for WWW files to automatically read the results of past matches from the internet into his computer. This leads into discussions of Perl, HTML and other computer-related issues. By the end of the book we see how Skiena's computer can download data, choose favorable bets, and place bets using a touch tone telephone, all without needing any human intervention... and that it makes a steady profit!

The one minor complaint I have regarding this book is the way it is marketed (judging from the back cover, at least.) The marketing blurbs suggest that this book can teach anyone, even a mathematical novice, how to money betting on jai alai. In reality only an extremely knowledgeable and skillful person could execute a system like Skiena's, and then only with months (or more likely, years) of intense labor. In fact, this book does provide some sound advice on how not to lose too much money at the jai alai fronton (always make the minimum bet, for example); however these tidbits of advice aren't by any means the meat of the book. Calculated Bets is an inspirational tale far more valuable than advice on how to make a quick buck or two.

Calculated Bets should hold great appeal to a wide range of readers. Readers who aren't well versed in math or computers should find this book both educational and entertaining. More sophisticated readers will be mesmerized as Skiena finds ingenious ways to make connections between familiar topics and demonstrates convincing applications of mathematical theory. As a reader of MAA Online, I think it is fair to say that there is a high probability that you will love this book.

Andrew Perry ( is Assistant Professor of Mathematics and Computer Science at Springfield College in Springfield, MA.

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