Three person baccarat

Baccarat and the closely related game Chemin-de-Fer are played for high stakes in casinos around the world. Optimal strategies for the player and the banker in the two person game have been developed by Kemeny and Snell. Similar strategies are now the rules of play in Nevada. Thorp and Walden developed card counting strategies to make certain side bets profitable but these bets are no longer allowed. Hence, the game is essentially a Bernoulli trial with a banker edge of 1.24%. For the three person game we determine the banker's strategy that optimally counters the two players fixed rules of play. It is optimal for the players to collude and place indentical bets in which case the game becomes a Bernoulli trial with banker's edge of 0.82%.