Two-person red-and-black games with bet-dependent win probability functions

May Ru Chen, Shoou Ren Hsiau

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In this paper a two-person red-and-black game is investigated. We suppose that, at every stage of the game, player I's win probability, f, is a function of the ratio of his bet to the sum of both players' bets. Two results are given: (i) if f is convex then a bold strategy is optimal for player I when player II plays timidly; and (ii) if f satisfies f(s)f(t) ≤ f(st) then a timid strategy is optimal for player II when player I plays boldly. These two results extend two formulations of red-and-black games proposed by Pontiggia (2005), and also provide a sufficient condition to ensure that the profile (bold, timid) is the unique Nash equilibrium for players I and II. Finally, we give a counterexample to Pontiggia's conjecture about a proportional N-person red-and-black game.

Original languageEnglish
Pages (from-to)905-915
Number of pages11
JournalJournal of Applied Probability
Issue number4
Publication statusPublished - 2006 Dec 1

All Science Journal Classification (ASJC) codes

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

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