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

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 Cardano’s [1501–1576] Liber de Ludo Aleae (The Book on Games of Chance, written c. 1565, published 1663), Christiaan Huygens’s [1629– 1695] “De ratiociniis in ludo aleae” (“On reckoning in games of chance,” 1657), Jacob Bernoulli’s [1654–1705]Ars Conjectandi (The Art of Conject- ing, written c. 1690, published 1713), Pierre R ́ emond de Montmort’s [1678– 1719] Essay d’analyse sur les jeux de hasard (Analytical Essay on Games of Chance, 1708, 1713), and Abraham De Moivre’s [1667–1754]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. Preface Contents List of Notation Part I Theory Review of Probability Combinatorics and Probability Independence and Conditional Probability Random Variables and Random Vectors Expectation and Variance Law of Large Numbers and Central Limit Theorem Problems Notes Conditional Expectation Conditioning on an Event Conditioning on a Random Vector Problems Notes Martingales Definitions and Examples Optional Stopping Theorem Martingale Convergence Theorem Problems Notes Markov Chains Definitions and Examples Transience and Recurrence Asymptotic Behavior Renewal Theorem Problems Notes Game Theory Matrix Games Minimax Theorem Utility Theory Problems Notes House Advantage A Single Wager Composite Wagers Volatility Problems Notes Gambler's Ruin Even-Money Payoffs Integer Payoffs Arbitrary Payoffs Problems Notes Betting Systems Examples Conservation of Fairness Problems Notes Bold Play Red-and-Black Red-and-Black with a House Limit Primitive Casinos Problems Notes Optimal Proportional Play A Single Wager Simultaneous Wagers Optimality Properties Problems Notes Card Theory Shuffling Dealing Card Counting Problems Notes Part II Applications Slot Machines Expected Payout Volatility and Ruin Problems Notes Roulette Unbiased Wheels Biased Wheels Problems Notes Keno The m-Spot Ticket Way Tickets Problems Notes Craps Line Bets and Free Odds The Shooter's Hand Problems Notes House-Banked Poker Let It Ride Three Card Poker Problems Notes Video Poker Jacks or Better Deuces Wild Problems Notes Faro The Denomination Bet From Soda to Hock Problems Notes Baccarat Player vs. Banker Card Counting Problems Notes Trente et Quarante Red, Black, Color, Inverse Card Counting Problems Notes Twenty-One Rules Basic Strategy Card Counting Problems Notes Poker Rules and Pot Odds Poker Models and Game Theory Texas Hold'em Problems Notes Results Cited Algebra and Number Theory Analysis and Probability Bibliography Index 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. 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