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)
Theory.- Review of Probability.- Conditional Expectation.- Martingales.- Markov Chains.- Game Theory.- House Advantage.- Gambler´s 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.
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.
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)
Theory.- Review of Probability.- Conditional Expectation.- Martingales.- Markov Chains.- Game Theory.- House Advantage.- Gambler's 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:
"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)
Inhaltsverzeichnis
Theory.- Review of Probability.- Conditional Expectation.- Martingales.- Markov Chains.- Game Theory.- House Advantage.- Gambler's 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.
Klappentext
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.
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)
Includes supplementary material: sn.pub/extras
