In a game called red and black, you can stake any amount s in your possession. Suppose you. goal is 1 and you. current fortune is i 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 greater than frac{1}{2} where the player has the advantage over the house. The optimum strategy at any when p>frac{1}{2} is to play timidly, which is to bet a small amount each time. In this paper we perform the simulation study to show that the Timin strategy is optimum.