  Xavier and Yushi run a ``random race'' as follows. A continuous probability
distribution $\mu$ on the real line is chosen. The runners begin at zero. At
time $i$ Xavier draws $\mathbf{X}_i$ from $\mu$ and advances that distance,
while Yushi advances by an independent drawing $\mathbf{Y}_i$. After $n$ such
moves, Xavier wins a valuable prize provided he not only wins the race but
leads after every step; that is, $\sum_{i=1}^k \mathbf{X}_i > \sum_{i=1}^k
\mathbf{Y}_i$ for all $k = 1,2, \dots, n$. What distribution is best for
Xavier, and what then is his probability of getting the prize?
