Skip to main content

Gambling, probability and martingales

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


  1. Anderson, C. L.: “Note on the Advantage of First Serve”, J. Combinatorial Theory (A) 23, (1977), 363

    Article  Google Scholar 

  2. Cardano, G.:The Book of Games of Chance, translated by S. Gould, inCardano, The Gambling Scholar by O. Ore, Princeton University Press, Princeton 1963

    Google Scholar 

  3. David, F. N.:Games, Gods and Gambling, Griffin, London 1962

    MATH  Google Scholar 

  4. Doob, J. L.:Stochastic Processes, John Wiley and Sons, New York 1953

    MATH  Google Scholar 

  5. Dostoyevsky, F.:The Gambler, Translated by Jessie Coulsin, Penguin, New York 1966

    Google Scholar 

  6. Kingston, I. C: “Comparison of Scoring Systems in Two- Sided Competitions”, J. Combinatorial Theory (A) 20, (1976), 357–362

    Article  MATH  MathSciNet  Google Scholar 

  7. Kolmogorov, A. N.: “Three Approaches to the Quantitative Definition of Information”, Problems of Information Transmission 1, (1965), 1–7

    Google Scholar 

  8. Li, S. R.: “A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments”, Annals of Probability 8, (1980), 1171–1176

    Article  MATH  MathSciNet  Google Scholar 

  9. DeMoivre, A.: The Doctrine of Chances (pages 51-54). Third Edition, London, 1756 (Reprinted by Chelsea, New York, 1967)

  10. Ore, O.:Cardano, The Gambling Scholar, Princeton University Press, Princeton, 1953

    MATH  Google Scholar 

  11. Ore, O.: “Pascal and the Invention of Probability Theory”, American Math. Monthly 67, (1960), 409–419

    Article  MATH  MathSciNet  Google Scholar 

  12. Packel, E.:The Mathematics of Games and Gambling, published by the Mathematical Association of America, Washington, DC, 1981

    Google Scholar 

  13. Schnorr, C. P: “A Survey of the Theory of Random Sequences”, Part Three of the Proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario (Canada), 1975 (ed. by Butts, R. E. and Hintikka, J.), D. Reidel, Dordrecht and Boston, 1977

  14. Thackeray, W. M.:The Newcomes; Memoirs of a Most Respectable Family, Chapter 28, Page 266, Edited by Arthur Pendennis Esqre. London, Bradbury and Evans, 1853

  15. Thrope, E.:Beat the Dealer: A Winning Strategy for the Game of 21, Random House, New York, 1966

    Google Scholar 

  16. Ville, J.:Étude Critique de la Notion de Collectif, Gauthier- Villars, Paris, 1939

    Google Scholar 

  17. Von Mises, R.: “Grundlagen der Wahrscheinlichkeitstheorie”, Math. Zeitschr. 5, (1919)

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Snell, J.L. Gambling, probability and martingales. The Mathematical Intelligencer 4, 118–124 (1982).

Download citation

  • Published:

  • Issue Date:

  • DOI:


  • Fermat
  • Fair Division
  • Extended Game
  • Walk Away
  • Prize Money