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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
Download PDF [523 KB, 19 November 2013; original version 18 November 2013]

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

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