The evolution of the game of baccarat

The casino game of baccara chemin de fer is a bimatrix game, not a matrix game, because the house collects a five percent commission on Banker wins. We generalize the game, allowing Banker’s strategy to be unconstrained and assuming a 100α percent commission on Banker wins, where 0 ≤ α < 2/5. Assuming for simplicity that cards are dealt with replacement, we show that, with one exception at α = α0 ≈ 0.140705, there is a unique Nash equilibrium, and we evaluate it. Player’s equilibrium mixed strategy depends explicitly on α, whereas Banker’s equilibrium mixed strategy depends only on whether α < α0 or α > α0. AMS 2010 subject classification: Primary 91A05; secondary 91A60.