A Game-Theoretic Analysis of Baccara Chemin de Fer, II

Stewart N. Ethier () and Jiyeon Lee
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Stewart N. Ethier: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
Jiyeon Lee: Department of Statistics, Yeungnam University, 280 Daehak-Ro, Gyeongsan 38541, Gyeongbuk, Republic of Korea

Games, 2023, vol. 14, issue 5, 1-25

Abstract: In a previous paper, we considered several models of the parlor game baccara chemin de fer , including Model B2 (a 2 × 2 484 matrix game) and Model B3 (a 2 5 × 2 484 matrix game), both of which depend on a positive-integer parameter d , the number of decks. The key to solving the game under Model B2 was what we called Foster’s algorithm, which applies to additive 2 × 2 n matrix games. Here “additive” means that the payoffs are additive in the n binary choices that comprise a player II pure strategy. In the present paper, we consider analogous models of the casino game baccara chemin de fer that take into account the 100 α percent commission on Banker (player II) wins, where 0 ≤ α ≤ 1 / 10 . Thus, the game now depends not just on the discrete parameter d but also on a continuous parameter α . Moreover, the game is no longer zero sum. To find all Nash equilibria under Model B2, we generalize Foster’s algorithm to additive 2 × 2 n bimatrix games. We find that, with rare exceptions, the Nash equilibrium is unique. We also obtain a Nash equilibrium under Model B3, based on Model B2 results, but here we are unable to prove uniqueness.

Keywords: baccara; chemin de fer; sampling without replacement; bimatrix game; best response; Nash equilibrium; Foster’s algorithm (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
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