Doctrine of Chances, The

Antecedents

De Moivre was not unusual in concentrating the bulk of his book on games of chance. This emphasis was apparent from the very first work on probability theory. The mathematician Gero-lamo Cardano, who was also a professional gambler, wrote Liber de ludo aleae (Book on Games of Chance), in which he discussed the computation of probabilities. However, because Cardano's work was not published until 1663, the beginning of probability theory is traditionally assigned to 1654. In that year Blaise Pascal and Pierre de Fermat began a correspondence on gaming problems. This letter exchange led Pascal to write Traité du triangle arithmétique (Treatise on the Arithmetical Triangle), in which he arranged the binomial coefficients into a triangle and then used them to solve certain problems in games of chance. De Moivre was evidently among the first to refer to this geometric configuration as Pascal's triangle (even though Pascal did not really introduce the schema).

In 1657 Christian Huygens published Libellus de ratiociniis in ludo aleae (The Value of All Chances in Games of Fortune), an extended discussion of certain issues raised by Pascal and Fermat. Within a half century, Huygens's work was largely superseded by two works that appeared shortly before de Moivre's book. The first was the 1708 Essai d'analyse sur les jeux de hasard (Essay of Analysis on Games of Chance) by Pierre de Montmort and Ars Conjectandi (The Art of Conjecturing) by Jakob (or James) Bernoulli, published posthumously in 1713. By the time de Moivre wrote The Doctrine of Chances, he was familiar with all these efforts as well as derived works. This body of knowledge put him in a unique position to create a truly comprehensive treatment of probability theory.

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