The Doctrine of Chances Probabilistic Aspects of Gambling [Hardcover]

Three centuries ago Montmort and De Moivre published two books on probability theory 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.

Theory.- Review of Probability.- Conditional Expectation.- Martingales.- Markov Chains.- Game Theory.- House Advantage.- Gamblers Ruin.- Betting Systems.- Bold Play.- Optimal Proportional Play.- Card Theory.- Applications.- Slot Machines.- Roulette.- Keno.- Craps.- House-Banked Poker.- Video Poker.- Faro.- Baccarat.- Trente et Quarante.- Twenty-One.- Poker.

From the reviews:

Im very happy to be reviewing Ethiers 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. & Ethiers book is clearly aimed at a more mathematically sophisticated audience & and for that reason I enjoyed Ethiers 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 mathemls£