The Doctrine of Chances

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.

• Operations Research
• Probability theory
• gambling
• game theory
• games of chance
• mathematics
• probability

From the reviews:

“I’m very happy to be reviewing Ethier’s labor of love The Doctrine of Chances: Probabilistic Aspects of Gambling. … Each chapter ends with many exercises and fascinating historical notes and the book ends with a few mathematical appendices. … Ethier’s book is clearly aimed at a more mathematically sophisticated audience … and for that reason I enjoyed Ethier’s much more.” (Peter Rabinovitch, The Mathematical Association of America, August, 2010)

“This textbook on probabilistic aspects of gambling is directed to those already familiar with probability at the post-calculus, pre-measure-theory level. … Each chapter has a good selection of problems … 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.”­­­ (Gerald A. Heuer, Zentralblatt MATH, Vol. 1198, 2010)

“The book by Ethier is unique in the contemporary literature as a university-level mathematical text with a wide coverage of the subject of ‘calculating the probabilities of events in play’. … The book … is highly recommended for every mathematical library. University instructors will find thorough exposition, well suited for undergraduate courses and student projects. … book can eventually be read by everyone familiar with the very basics of probability … . Mathematical fans will be entertained by curious historical precedents and anecdotes.” (Alexander V. Gnedin, Mathematical Reviews, Issue 2011 j)

“This book has been written with great care by someone who loves the applications of probability to the casino industry. … The problems at the end of each of the chapters are extensive and a rich source of motivation for furtherexploration. … The book is very well suited for a mathematical audience. … this book could also work for a course in the mathematics of gambling for a typical cohort of students in a casino management program … .” (Brian Alspach, SIAM Review, Vol. 54 (4), 2012)

• Department of Mathematics, University of Utah, Salt Lake City, USA

  Stewart N. Ethier

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