Skip to main content

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

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.

This is a preview of subscription content, access via your institution.

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.

  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.

Download references

Author information

Affiliations

Authors

Additional information

This paper was supported in part by Air Force Grant AFOSR 70-1870 A, B, C.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Thorp, E.O., Walden, W.E. The Fundamental Theorem of Card Counting with applications to Trente-et-Quarante and Baccarat. Int J Game Theory 2, 109–119 (1973). https://doi.org/10.1007/BF01737563

Download citation

Keywords

  • Economic Theory
  • Game Theory
  • Sharp Contrast
  • Fundamental Theorem
  • Card Game