De ratiociniis in ludo alea jacta sunt

Description This little treatise on gambling problems is the first printed work on probability theory (even Cardano'sLiber de ludo aleae was only printed in 1663) and appeared as an appendix to van Schooten'sExercitationes mathematicae.

It consists of 14 propositiones and five problemata. In the first three propositions, Huygens introduces the notion of "expectation" for a player of a game of chance. Propositions four to seven deal with so-called "problems of points", a much-debated issue in the early modern era; the question is how to suitably distribute the prize of a prematurely aborted game between two players.

This is extended to three or more players in propositions 8 and 9.

De ratiociniis in ludo alea jacta sunt e

Propositions 10 to 14 deal with dicing problems of various kinds. The propositions always present concrete numerical examples which are also solved for these special cases only; nevertheless, Huygens's general method of recursion becomes clear enough.

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