Optimum Stragies for Unfavorable Situation in Red & Black

In a game called red and black, you can stake any amount s in your possession. Suppose your goal is 1 and your current fortune is ｆ, with 0 < f < 1. You win back your stake and as much more with probability p and lose your stake with probability, q = 1- p. Ahn(2000) considered optimum strategy for this game with the value of p less than $\frac{1}{2}$ where the house has the advantage over the player. The optimum strategy at any f when p < $\frac{1}{2}$ is to play boldly, which is to bet as much as you can. In this paper we perform the simulation study to show that the Bold strategy is optimum.