Game-Theoretic Solution of Baccarat

The famous gambling game of baccarat has been the subject of many mathematical studies. There is, however, considerable variation in the solutions offered and it is now clear that these variations have come from trying to solve a game of strategy without a precise meaning for the solution of such a game. The theory of games has made this precise; it is now interesting to carry out the solution of baccarat in terms of the modern concepts of game theory and to compare the solution obtained with the earlier attempts based upon the more vague ideas previously available. Baccarat is usually played by three men, one banker playing against a pair of players. But there is a popular variant of the game, known as chemin de fer, in which the banker plays against a single player. This is the version commonly discussed in the literature, and we too will take this two-person version of baccarat as our subject.