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 f, with 0＜f＜N. 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 greater than $frac{1}{2}$ where the player has the advantage over the house. The optimum strategy at any f when p>$frac{1}{2}$ is to play timidly, which is to bet 1 all the time. This is called as Timid1 strategy. In this paper, we perform the simulation study to show that the Timid1 strategy is optimum in discrete red and black when p＞frac{1}{2}.