The Doctrine of Chances

Three centuries ago Montmort and De Moivre published two books on probability theory emphasizing its most important application at that time, games of chance. This book, on the probabilistic aspects of gambling, is a modern version of those classics.

Three centuries ago Montmort and De Moivre published two of the first books on probability theory, then called the doctrine of chances, emphasizing its most important application at that time, games of chance. This volume, on the probabilistic aspects of gambling, is a modern version of those classics. While covering the classical material such as house advantage and gambler's ruin, it also takes up such 20th-century topics as martingales, Markov chains, game theory, bold play, and optimal proportional play. In addition there is extensive coverage of specific casino games such as roulette, craps, video poker, baccarat, and twenty-one. The volume addresses researchers and graduate students in probability theory, stochastic processes, game theory, operations research, statistics but it is also accessible to undergraduate students, who have had a course in probability.

The Doctrine of Chances appears in 2008, the tercentenary of Pierre Rémond de Montmort's [16781719] Essay d'analyse sur les jeux de hasard (Analytical Essay on Games of Chance, 1708, 1713) Includes supplementary material: sn.pub/extras

Inhalt
Theory.- Review of Probability.- Conditional Expectation.- Martingales.- Markov Chains.- Game Theory.- House Advantage.- Gambler's Ruin.- Betting Systems.- Bold Play.- Optimal Proportional Play.- Card Theory.- Applications.- Slot Machines.- Roulette.- Keno.- Craps.- House-Banked Poker.- Video Poker.- Faro.- Baccarat.- Trente et Quarante.- Twenty-One.- Poker.