Azar game in the book of the dice of Alfonso X The Learned. Its relation with the hazard games of Montmort, Cotton, Hoyle, De Moivre and Jacob Bernoulli

摘要

A game called “Azar” is presented in the second part of the Book “The Book of Chess, Dice and Tables” by Alfonso X El Sabio (The Learned) (1221-1284). The rules of this Azar game depend on two events called “chance” and “azar”. The winning probability in this Azar game implies an event whose probability depends on an infinite number of three-dice rolls. We intend to demonstrate here that this probability is of around 50 %. We associated this game with other games, like the Hazard game by Montmort, Cotton, Hoyle and De Moivre, and also with the Cinq et Neuf game of J. Bernoulli. Finally, we see that the first Hazard game of De Moivre is the famous Craps game.