  We consider two players, starting with $m$ and $n$ units, respectively. In
each round, the winner is decided with probability proportional to each
player's fortune, and the opponent loses one unit. We prove an explicit formula
for the probability $p(m,n)$ that the first player wins. When $m\sim Nx_{0}$,
$n\sim N y_{0}$, we prove the fluid limit as $N\to \infty$. When $x_{0}=y_{0}$,
then $z\to p(N,N+z\sqrt{N})$ converges to the standard normal CDF and the
difference in fortunes scales diffusively. The exact limit of the time of ruin
$\tau_{N}$ is established as $(T-\tau_N) \sim N^{-\beta}W^{\frac{1}{\beta}}$,
$\beta=\frac{1}{4}$, $T=x_{0}+y_{0}$. Modulo a constant, $W \sim
\chi^{2}_{1}(z_{0}^{2}/T^{2})$.
