Advertisement

A Distribution Inequality For Martingales with Bounded Symmetric Differences

  • Loren D. Pitt
Part of the Trends in Mathematics book series (TM)

Abstract

We discuss (with some generalizations) the question of optimal strategies for the game of red-and-black with a fixed goal, with fixed subfair odds, and with both the size of legal bets allowed and the playing time limited.

Keywords

Optimal Strategy Playing Time Legal Limit Stochastic Game Flawed Treatment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B84]
    D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 1984, 647–702.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [C08-9]
    J. L. Coolidge, The Gamblers ruin, Annals of Math. 10, 1908–1909, 181-192.Google Scholar
  3. [DS65]
    L. E. Dubins and L. J. Savage, How To Gamble If You Must: Inequalities for Stochastic Processes. McGraw-Hill, New York, 1965.zbMATHGoogle Scholar
  4. [HK88]
    D. Heath and R. Kertz, Leaving an interval in limited playing time. Adv. Appl. Probab. 20 1988, 635–645.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [K79]
    M. Klawe, Optimal strategies for a fair betting game. Discrete Appl. Math. 1 1979, 105–115.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [MS96]
    A. Maitra and W. Suddreth, Discrete Gambling and Stochastic Games. Springer, New York, 1996.zbMATHCrossRefGoogle Scholar
  7. [MW96]
    D. McBeth and A. Weerasinghe, Finite-time optimal control a process leaving an interval. Jour. Appl. Probab. 33 1996, 714–728.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [Y96]
    Z. Yang, Optimal strategies for a betting game. Discrete Appl. Math. 28 19790, 157–169.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Loren D. Pitt
    • 1
  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations