Ethier The Doctrine of Chances

Probabilistic Aspects of Gambling
1. Auflage 2010
ISBN: 978-3-540-78783-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 816 Seiten, eBook

Reihe: Probability and its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Ethier, Stewart N.

Ethier, Stewart

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.

Leseproben

"Preface (p. v-vi)

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, premeasure- theory level. Gambling motivated much of the early development of probability theory (David 1962).1 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 Conjecturing, 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] The Doctrine of Chances (1718, 1738, 1756).

Gambling also had a major in?uence on 20thcentury probability theory, as it provided the motivation for the concept of a martingale. Thus, gambling has contributed to probability theory. Conversely, probability theory has contributed much to gambling, from the gambler’s ruin formula of Blaise Pascal [1623–1662] to the optimality of bold play due to Lester E. Dubins [1920–2010] and Leonard J. Savage [1917–1971]; from the solution of le her due to Charles Waldegrave to the solution of chemin de fer due to John G. Kemeny [1926–1992] and J. Laurie Snell [1925–]; from the duration-of-play formula of Joseph-Louis Lagrange [1736–1813] to the optimal proportional betting strategy of John L. Kelly, Jr. [1923–1965]; and from the ?rst evaluation of the banker’s advantage at trente et quarante due to Sim´eon-Denis Poisson [1781–1840] to the ?rst published card-counting system at twenty-one due to Edward O. Thorp [1932–]. Topics such as these are the principal focus of this book.

Is gambling a subject worthy of academic study? Let us quote an authority from the 18th century on this question. In the preface to The Doctrine of Chances, De Moivre (1718, p. iii) wrote,

Another use to be made of this Doctrine of Chances is, that it may serve in Conjunction with the other parts of the Mathematicks, as a ?t introduction to the Art of Reasoning; it being known by experience that nothing can contribute more to the attaining of that Art, than the consideration of a long Train of Consequences, rightly deduced from undoubted Principles, of which this Book a?ords many Examples.

We also quote a 20th-century authority on the same question. In Le jeu, la chance et le hasard, Louis Bachelier [1870–1946] (1914, p. 6) wrote,2 It is almost always gambling that enables one to form a fairly clear idea of a manifestation of chance; it is gambling that gave birth to the calculus of probability; it is to gambling that this calculus owes its ?rst faltering utterances and its most recent developments; it is gambling that allows us to conceive of this calculus in the most general way; it is, therefore, gambling that one must strive to understand, but one should understand it in a philosophic sense, free from all vulgar ideas."