Session 3-2-F: A Game-Theoretic Analysis of Baccara Chemin de Fer

Abstract

Baccara chemin de fer — review of main contributions Baccara was first mentioned in print by Van Tenac in 1847. It was analyzed by Dormoy in 1872 and Bertrand in 1889. Borel called Bertrand’s study “extremely incomplete,” but it motivated Borel to develop game theory in the 1920s. Von Neumann planned to study baccara after proving the minimax theorem in 1928, but he didn’t. The first game-theoretic solution was by Kemeny and Snell in 1957. In 1964, Foster gave a solution based on a new algorithm, unaware of the Kemeny–Snell solution. A solution under more realistic assumptions was found by Downton and Lockwood in 1975 using Foster’s algorithm. Based on the extensive form of the game, the Kemeny–Snell solution was rederived by Deloche and Oguer in 2007