Let's say that I start with \$200 and need to obtain \$500 by betting on an unfair coin. I can bet \$X and will receive \$X more dollars with probability $p$ ($p$ < $\frac{1}{2}$) and will lose \$X dollars otherwise. What is the optimal strategy for achieving \$500? In other words, how would you maximize the probability of attaining \$500?
I'm really not even sure how to start for this question...