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 ~ Nx0, n ~ Ny0, we prove the fluid limit as N → ∞. When x0 = y0, z → p(N, N + z√N) converges to the standard normal cumulative distribution function and the difference in fortunes scales diffusively. The exact limit of the time of ruin τN is established as (T - τN) ~ N-βW1/β, β = ¼, T = x0 + y0. Modulo a constant, W ~ χ21(z02 / T2).
