The Doctrine of Chances: Probabilistic Aspects of Gambling (Probability and Its Applications)

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 20 th -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. I have found many thousands more readers than I ever looked for. I have no right to say to these, You shall not ?nd fault with my art, or fall asleep over my pages; but I ask you to believe that this person writing strives to tell the truth. If there is not that, there is nothing. William Makepeace Thackeray, The History of Pendennis This is a monograph/textbook on the probabilistic aspects of gambling, intended for those already familiar with probability at the post-calculus, p- measure-theory level. Gambling motivated much of the early development of probability the- 1 ory (David 1962). Indeed, some of the earliest works on probability include Girolamo Cardanos [15011576] Liber de Ludo Aleae (The Book on Games of Chance, written c. 1565, published 1663), Christiaan Huygenss [1629 1695] De ratiociniis in ludo aleae (On reckoning in games of chance, 1657), Jacob Bernoullis [16541705]Ars Conjectandi (The Art of Conject- ing, written c. 1690, published 1713), Pierre R emond de Montmorts [1678 1719] Essay danalyse sur les jeux de hasard (Analytical Essay on Games of Chance, 1708, 1713), and Abraham De Moivres [16671754]TheDoctrineof Chances (1718, 1738, 1756). Gambling also had a major in?uence on 20- century probability theory, as it provided the motivation for the concept of a martingale. Front Matter....Pages I-XIV Front Matter....Pages 1-1 Review of Probability....Pages 3-73 Conditional Expectation....Pages 75-94 Martingales....Pages 95-117 Markov Chains....Pages 119-158 Game Theory....Pages 159-198 House Advantage....Pages 199-240 Gambler’s Ruin....Pages 241-274 Betting Systems....Pages 275-316 Bold Play....Pages 317-356 Optimal Proportional Play....Pages 357-390 Card Theory....Pages 391-425 Front Matter....Pages 427-427 Slot Machines....Pages 429-460 Roulette....Pages 461-482 Keno....Pages 483-500 Craps....Pages 501-524 House-Banked Poker....Pages 525-544 Video Poker....Pages 545-572 Faro....Pages 573-595 Baccarat....Pages 597-621 Trente et Quarante....Pages 623-642 Front Matter....Pages 427-427 Twenty-One....Pages 643-687 Poker....Pages 689-744 Back Matter....Pages 745-816 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 book, 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. --Book Jacket