A Game-Theoretic Analysis of Baccara Chemin de Fer

Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 × 2 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his own two-card hand while Player sees only his own total, baccara is a 2× 2 matrix game, which was solved by Downton and Lockwood in 1975 for d = 1, 2, . . . , 8. Assuming that cards are dealt without replacement from a d-deck shoe and that each of Player and Banker sees the composition of his own two-card hand, baccara is a 2 × 2 matrix game, which is solved herein for every positive integer d. AMS 2010 subject classification: Primary 91A05; secondary 91A60.