© 2010

The Doctrine of Chances

Probabilistic Aspects of Gambling


  • The Doctrine of Chances appears in 2008, the tercentenary of Pierre Rémond de Montmort’s [1678–1719] Essay d’analyse sur les jeux de hasard (Analytical Essay on Games of Chance, 1708, 1713)


Part of the Probability and its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Theory

    1. Front Matter
      Pages 1-1
    2. Stewart N. Ethier
      Pages 3-73
    3. Stewart N. Ethier
      Pages 75-94
    4. Stewart N. Ethier
      Pages 95-117
    5. Stewart N. Ethier
      Pages 119-158
    6. Stewart N. Ethier
      Pages 159-198
    7. Stewart N. Ethier
      Pages 199-240
    8. Stewart N. Ethier
      Pages 241-274
    9. Stewart N. Ethier
      Pages 275-316
    10. Stewart N. Ethier
      Pages 317-356
    11. Stewart N. Ethier
      Pages 357-390
    12. Stewart N. Ethier
      Pages 391-425
  3. Applications

    1. Front Matter
      Pages 427-427
    2. Stewart N. Ethier
      Pages 429-460
    3. Stewart N. Ethier
      Pages 461-482
    4. Stewart N. Ethier
      Pages 483-500
    5. Stewart N. Ethier
      Pages 501-524
    6. Stewart N. Ethier
      Pages 525-544
    7. Stewart N. Ethier
      Pages 545-572

About this book


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.


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

Authors and affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

Bibliographic information

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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 further exploration. … 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)