The doctrine of chances: probabilistic aspects of gambling / Stewart N. Ethier

Auteur: Ethier, Stewart N. (1948-) - AuteurType de document: Livre numérique Collection: Probability and its applications Langue: anglaisÉditeur: Berlin : Springer, 2010 ISBN: 9783540787822 Note: This textbook on probabilistic aspects of gambling is directed to those already familiar with probability at the post-calculus, pre-measure-theory level. Gambling is a fitting application of probability theory on which to base such a study, both because of its prominent role in the historical development of the subject and because gambling is one of the few applications in which the probabilistic models are often exactly correct. The book is in two parts of eleven chapters each. Part I, Theory, begins with a chapter on review of probability, followed by chapters on conditional expectations, martingales, Markov chains, game theory, house advantage, gambler’s ruin, betting systems, bold play, optimal proportional play and card theory (shuffling, dealing, card counting). Part II, Applications, has a chapter on each of slot machines, roulette, Keno, Craps, house-banked poker, video poker, Faro, Baccarat, Trente et Quarante, twenty-one, and poker. Each chapter has a good selection of problems (answers, but not solutions, available on author’s web page), and some interesting notes, including some very interesting history. There is plenty of material here for a solid two-semester course, but there is enough independence among the chapters to allow for a variety of one-semester courses covering a subset of the chapters. The book is a welcome and well-researched addition to the field. (zbMath) Sujets MSC: 60C05 Probability theory and stochastic processes -- Combinatorial probability -- Combinatorial probability
60G40 Probability theory and stochastic processes -- Stochastic processes -- Stopping times; optimal stopping problems; gambling theory
60G42 Probability theory and stochastic processes -- Stochastic processes -- Martingales with discrete parameter
91A60 Game theory, economics, social and behavioral sciences -- Game theory -- Probabilistic games; gambling
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This textbook on probabilistic aspects of gambling is directed to those already familiar with probability at the post-calculus, pre-measure-theory level. Gambling is a fitting application of probability theory on which to base such a study, both because of its prominent role in the historical development of the subject and because gambling is one of the few applications in which the probabilistic models are often exactly correct.

The book is in two parts of eleven chapters each. Part I, Theory, begins with a chapter on review of probability, followed by chapters on conditional expectations, martingales, Markov chains, game theory, house advantage, gambler’s ruin, betting systems, bold play, optimal proportional play and card theory (shuffling, dealing, card counting). Part II, Applications, has a chapter on each of slot machines, roulette, Keno, Craps, house-banked poker, video poker, Faro, Baccarat, Trente et Quarante, twenty-one, and poker. Each chapter has a good selection of problems (answers, but not solutions, available on author’s web page), and some interesting notes, including some very interesting history.

There is plenty of material here for a solid two-semester course, but there is enough independence among the chapters to allow for a variety of one-semester courses covering a subset of the chapters. The book is a welcome and well-researched addition to the field. (zbMath)

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