Optimal Play: Mathematical Studies of Games and Gambling
• Optimal Play: Mathematical Studies of Games and Gambling, edited by Stewart N. Ethier and William R. Eadington.
• Published by Institute for the Study of Gambling and Commercial Gaming, December 2007.
• Text on back of dust jacket:
This collection of peer-reviewed articles contains 32 mathematical studies of games and gambling, including
• "The Endgame in Poker" by 2000 World Series of Poker champion Chris Ferguson and UCLA mathematician Tom Ferguson.
• "Backgammon: The Optimal Strategy for the Pure Running Game" by Edward O. Thorp, author of Beat the Dealer: A Winning Strategy for the Game of Twenty One.
• "Parrondo's Principle: An Overview" by Richard A. Epstein, author of The Theory of Gambling and Statistical Logic.
• "Much Ado about Baccara" by James Grosjean, author of Beyond Counting: Exploiting Casino Games from Blackjack to Video Poker.
• "Kalman-Filtered Radial Basis Function Networks for Horserace Odds Estimation" by David Edelman, author of The Compleat Horseplayer.
Other games analyzed herein include blackjack, craps, video poker, slots, lotteries, backgammon, sports betting, le her, and faro. Theoretical issues addressed include gambler's ruin, loss rebates, house advantage, and proportional betting. Mathematical tools include game theory, group theory, stochastic analysis, Markov chains, branching processes, renewal theory, control theory, Kalman filtering, and multivariate statistics. In short, for those mathematically inclined readers fascinated by how games should be conceptually viewed and how strategies are developed, or just by how to find the edge, this volume is a treasure chest filled with intellectual nuggets.
• Text on dust jacket flap:
Serious mathematical analysis of gambling games can trace its origins to correspondence between the acknowledged founders of modern probability, Pascal and Fermat. They were asked to explain why a dice wager from the Chevalier de Méré had gone awry. From that beginning, interest in the probability of gambling games and opportunities has been of two distinct types. First, mathematicians have wanted to better understand, model, and analyze underlying probability structures of gambling games and playing strategies. Second, players have wanted to use these results to find ways that would allow them to consistently make winning wagers and fulfill the gambler's fantasy of finding an edge.
This volume continues that tradition, with mathematically rich and pragmatically enlightening discussions on blackjack, poker, baccarat, video poker, backgammon, racing, and sports betting. Other discussions touch upon the Kelly criterion, proportional betting, Parrondo's principle, poker bots, and rebates on losses. The analyses presented herein often use mathematical tools and computational strategies that have evolved only in recent years.
Contributors to this collection include individuals who have been among the top theoreticians in the analysis of gambling games, and include a few who have become well-known as practitioners of the gambling arts.
• BibTeX entry.
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