Suppose that you are gambling against an infinitely rich adversary and at each stage you either win or lose 1 unit with respective probabilities $p$ and $1-p .$ Show that the probability that you eventually go broke is
$$
\begin{array}{cl}
1 & \text { if } p \leq \frac{1}{2} \\
(q / p)^{i} & \text { if } p>\frac{1}{2}
\end{array}
$$
where $q=1-p$ and where $i$ is your initial fortune.