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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
1 Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA 2 Escuela de Matemática, Facultad de Ciencias Naturales y Matemática, Universidad de El Salvador, Final Avenida, "Mártires Estudiantes del 30 de Julio", Ciudad Universitaria, San Salvador, El Salvador
* Author to whom correspondence should be addressed.
Received: 13 September 2013 / Revised: 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 (CC BY 3.0).

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

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