Juan Caramuel (1606–1682) and the Spanish version of the Passedix game

Abstract

The game of chance called Passedix was known at least since the Middle Ages around the whole of Western Europe. It is based on the throw of three fair dice. The simplest version, for two players, consists of throwing the three dice once and summing up the numbers on the three upper faces. If this sum is greater than 10, it favours the player; if it is less than or equal to 10, it favours the opponent. A simple calculation of probabilities can show that the game is fair, in the sense of an equal probability of winning for both players. The first time we find explicit reference to this game is in an encyclopaedic work on mathematics, published in two volumes in 1667 and 1670, by the Spaniard Juan Caramuel. In this article, we describe and translate the part of this work which Caramuel dedicates to this game.