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.