Optimal strategy for the Vardi casino with interest payments

Ilie Grigorescu, Robert Chen, Larry Shepp

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A gambler starts with fortune f < 1 and plays in a Vardi casino with infinitely many tables indexed by their odds, r ≥ 0. In addition, all tables return the same expected winnings per dollar, c < 0, and a discount factor is applied after each round. We determine the optimal probability of reaching fortune 1, as well as an optimal strategy that is different from bold play for fortunes larger than a critical value depending exclusively on c and 1 + a, the discount factor. The general result is computed explicitly for some relevant special cases. The question of whether bold play is an optimal strategy is discussed for various choices of the parameters.

Original languageEnglish (US)
Pages (from-to)199-211
Number of pages13
JournalJournal of Applied Probability
Volume44
Issue number1
DOIs
StatePublished - Mar 2007

Keywords

  • Bold play
  • Gambling problem
  • Optimal strategy
  • Vardi casino

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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