The Mathematics of Games and Gambling
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 | |
| Author | Edward Packel |
|---|---|
| Language | English |
| Series | New Mathematical Library |
Release number | 28 |
| Subject | |
| Genre | Mathematics |
| Publisher | Mathematical Association of America |
Publication date | 1981 |
The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006.
The book has seven chapters. Its first gives a survey of the history of gambling games in western culture, including brief biographies of two famous gamblers, Gerolamo Cardano and Fyodor Dostoevsky,[1] and a review of the games of chance found in Dostoevsky's novel The Gambler.[2] The next four chapters introduce the basic concepts of probability theory, including expectation, binomial distributions and compound distributions, and conditional probability,[1] through games including roulette, keno, craps, chuck-a-luck, backgammon, and blackjack.[3]
The sixth chapter of the book moves from probability theory to game theory, including material on tic-tac-toe, matrix representations of zero-sum games, nonzero-sum games such as the prisoner's dilemma, the concept of a Nash equilibrium, game trees, and the minimax method used by computers to play two-player strategy games. A final chapter, "Odds and ends", includes analyses of bluffing in poker, horse racing, and lotteries.[1][4]
The second edition adds material on online gambling systems, casino poker machines, and Texas hold 'em poker.[3] It also adds links to online versions of the games, and expands the material on game theory.[5]