Gambling by the Numbers: Frain du Tremblay and Barbeyrac on the Moral Uses of Probability

Abstract

The invention of probability mathematics in the seventeenth century added a novel element to the long European cultural discussion surrounding gambling. While the mathematicians regularly used gambling games in setting up and solving problems, they were often reluctant to make broader moral claims regarding the practice beyond establishing if a game was fair. Two French-language moralists, however, drew on probability in their explorations of games and the morality of play, although in contradictory ways. Jean Frain du Tremblay’s Conversations morales sur les jeux et les divertissements attempted to use probability mathematics in order to argue that chance did not exist. Overstating probability’s claims, Frain du Tremblay argued that the results of games of chance were predictable and that they thereby demonstrated God’s order. By contrast, Jean Barbeyrac’s Traité du jeu criticized the inability of probability to predict unerringly what would happen next. Based on this perceived flaw, Barbeyrac similarly rejected probability’s claim to establish the morality of games of chance, although his purported proofs show his own inability to master the implications and mechanisms of the new ‘geometry of chance.’ Together the two authors show the struggle for non-mathematicians to understand the implications of probability for early modern concepts of chance.