Optimum Strategies When p<1/2 in Discrete Red & Black

이산형 적흑게임에서 p<1/2인 경우의 최적전략

  • Published : 2005.06.30

Abstract

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is ${\Large\;f},\;with\;O<{\Large\;f}. You win back your stake and as much more with probability p and lose your stake with probability, q=1-p. In this study, we consider optimum strategies for this game with the value of p less than ${\frac{1}{2}}$ where the house has the advantage over the player. It is shown that the optimum strategy at any ${\Large\;f}$ is the DBold strategy which is to play boldly in discrete red and black when $p<{\frac{1}{2}}$. And then, we perform the simulation study to show that this strategy, which is to bet as much as you can, is optimal in discrete case.

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References

  1. Ahn and Sok (2002). Optimum Strategies for Unfavorable Situation in Red & Black, The Korean Communications in Statistics, Vol. 9, No.3. 2002, pp. 683-691 https://doi.org/10.5351/CKSS.2002.9.3.683
  2. Coolidge, J. L. (1908-1909). The gambler's ruin, Annals of Mathematics 10, 181-192 https://doi.org/10.2307/1967408
  3. Dubins and Savage (1965). How to gamble if you must, Mcgraw-Hill, New York
  4. Parzen, E. (1962). Stochastic processes, Holden-Day