  We study the following game. Three players start with initial capitals of
$s_{1},s_{2},s_{3}$ dollars; in each round player $P_{m}$ is selected with
probability $\frac{1}{3}$; then \emph{he} selects player $P_{n}$ and they play
a game in which $P_{m}$ wins from (resp. loses to) $P_{n}$ one dollar with
probability $p_{mn}$ (resp. $p_{nm}=1-p_{mn}$). When a player loses all his
capital he drops out; the game continues until a single player wins by
collecting everybody's money.
  This is a "strategic" version of the classical Gambler's Ruin game. It seems
reasonable that a player may improve his winning probability by judicious
selection of which opponent to engage in each round. We formulate the situation
as a \emph{stochastic game} and prove that it has at least one Nash equilibrium
in deterministic stationary strategies.
