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Optimal Gambling Strategies

  • Martin Beckmann

Summary

Optimal Gambling Strategies are defined as those that maximize the expected utility of the gambler’s fortune after a given number N of trials, at each of which he can bet at most his current wealth. They are discussed in terms of betting on a biassed coin with probability p > 0.5 for heads. We also develop a Bayesian approach to the case of an unknown bias. Dynamic Programming is the principal tool of this analysis.

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References

  1. Bellman, Richard (1957): Dynamic Programming; Princeton: Princeton University Press.zbMATHGoogle Scholar
  2. Bernoulli, Daniel (1730/31): Specimen theoriae novae de mensura sortis; Commentarii academiae scientiarum imperialis Petropolitanae (for 1730 and 1731) 5 (1738) pp. 175–192; cited after Savage, Leonard: The Foundations of Statistics. New York: Wiley & Sons, 1954.Google Scholar
  3. Courant, Richard (1955): Vorlesungen über Differential- und Integralrechnung; 3. Auflage, Heidelberg: Springer Verlag, Band I p. 317, Band II p. 301.Google Scholar
  4. Durbins, L. E./Savage, L. J. (1965): How To Gamble If You Must; New York: McGraw- Hill.Google Scholar

Copyright information

© Physica-Verlag Heidelberg 1995

Authors and Affiliations

  • Martin Beckmann
    • 1
  1. 1.Institut für Statistik und UnternehmensforschungTechnische Universität MünchenMünchenDeutschland

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