The Doctrine of Chances

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 Cardanös [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.