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A Game-Theoretic Analysis of Baccara Chemin de Fer

Author

Listed:
  • Stewart N. Ethier

    (Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA)

  • Carlos Gámez

    (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)

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 2 88 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 2 484 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 2 5 x 2 484 matrix game, which is solved herein for every positive integer d.

Suggested Citation

  • Stewart N. Ethier & Carlos Gámez, 2013. "A Game-Theoretic Analysis of Baccara Chemin de Fer," Games, MDPI, vol. 4(4), pages 1-27, November.
    • Handle: RePEc:gam:jgames:v:4:y:2013:i:4:p:711-737:d:30534
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    References listed on IDEAS

    as
    1. N/A, 1968. "Gaming," Journal of Conflict Resolution, Peace Science Society (International), vol. 12(2), pages 222-223, June.
    2. N/A, 1968. "Gaming," Journal of Conflict Resolution, Peace Science Society (International), vol. 12(1), pages 82-82, March.
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    Cited by:

    1. Stewart N. Ethier & Jiyeon Lee, 2015. "On the Three-Person Game Baccara Banque," Games, MDPI, vol. 6(2), pages 1-22, May.

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