Optimum Strategies in Red & Black

In a game called red and black, you can stake any amount is in your possession. Suppose your goal is 1 and your current fortune is $f$, with 0$p$ and lose your stake with probability, $q$=1-$p$. In this paper, we consider optimum strategies for this game with the value of $p$ less than $^1/_2$ where the house has the advantage over the player, and with the value of $p$ greater than $^1/_2$ where the player has the advantage over the house. The optimum strategy at any $f$ when $p$<$^1/_2$ is to play boldly, which is to bet as much as you can. The optimum strategy when $p$>$^1/_2$ is to bet $f\cdot\alpha$with $\alpha$, a sufficiently small number between 0 and 1.