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Games 2013, 4(4), 711-737; doi:10.3390/g4040711
Article

A Game-Theoretic Analysis of Baccara Chemin de Fer

1,*  and 2
Received: 13 September 2013; in revised form: 6 November 2013 / Accepted: 6 November 2013 / Published: 18 November 2013
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Abstract: 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 x 288 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 x 2484 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 25 x 2484 matrix game, which is solved herein for every positive integer d.
Keywords: baccara; chemin de fer; sampling without replacement; matrix game; strict dominance; kernel; solution baccara; chemin de fer; sampling without replacement; matrix game; strict dominance; kernel; solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Ethier, S.N.; Gámez, C. A Game-Theoretic Analysis of Baccara Chemin de Fer. Games 2013, 4, 711-737.

AMA Style

Ethier SN, Gámez C. A Game-Theoretic Analysis of Baccara Chemin de Fer. Games. 2013; 4(4):711-737.

Chicago/Turabian Style

Ethier, Stewart N.; Gámez, Carlos. 2013. "A Game-Theoretic Analysis of Baccara Chemin de Fer." Games 4, no. 4: 711-737.

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