International Journal of Game Theory

, Volume 2, Issue 1, pp 109–119 | Cite as

The Fundamental Theorem of Card Counting with applications to Trente-et-Quarante and Baccarat

  • Edward O. Thorp
  • William E. Walden
Papers

Abstract

The Fundamental Theorem of Card Counting is a unifying principle for the analysis of card games of chance which are characterized by sampling without replacement. The Theorem says (roughly) the “spread” in distribution of player expectations for partially depleted card packs increases with depletion of the card pack. Furthermore, average player expectation is non-decreasing (increasing under suitable hypotheses) with increasing depletion.

The Theorem is used to prove that significant favorable strategies based on card counting do not exist for Trente-et-Quarante or for “tie” bets in Nevada Baccarat. This is in sharp contrast with previous results for Blackjack and for Nevada Baccarat side bets on natural eight and natural nine.

Keywords

Economic Theory Game Theory Sharp Contrast Fundamental Theorem Card Game 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boll, M.: La Chance et les Jeux de Hasard. Librarie Larousse, Paris 1936.Google Scholar
  2. Epstein, R. A.: The Theory of Gambling and Statistical Logic. Academic Press, New York 1967.Google Scholar
  3. Poisson, D.: Mémoire sur L'Advantage du Banquier au Jeu de Trente et Quarante. Annales de Mathematiques Pures et Appliqueés (“Gergonne's Journal”), Tom. XVI n∘ VI, Décembre 1825, 173–208.Google Scholar
  4. Thorp, E. O.: A Favorable Strategy for Twenty One. Proceedings of the National Academy of Sciences47, 110–12, 1961.Google Scholar
  5. —: Beat the Dealer. Random House, New York 1962; revised, 1966.Google Scholar
  6. —: Optimal Gambling Systems for Favorable Games. Review of the International Statistical Institute37:3, 273–93, 1969.Google Scholar
  7. —: Probabilities and Strategies for the Game of Faro. To appear, J. Am. Stat. Assn., 1973.Google Scholar
  8. Thorp, E. O., andW. Walden: A Winning Bet in Nevada Baccarat. Journal of the American Statistical Association61, Part I, 313–28, 1966.Google Scholar
  9. —: The Solution of Games by Computer. Prebook.Google Scholar

Copyright information

© Physica-Verlag Rudolf Liebing KG 1973

Authors and Affiliations

  • Edward O. Thorp
    • 1
  • William E. Walden
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Dir. of Systems and Computing Washington State UniversityUSA

Personalised recommendations