  We consider a large community of individuals who mix strongly and meet in
pairs to bet on a coin toss. We investigate the asset distribution of the
players involved in this zero-sum repeated game. Our main result is that the
asset distribution converges to the exponential distribution, irrespective of
the size of the bet, as long as players can never go bankrupt. Analytical
results suggests that the exponential distribution is a stable fixed point for
this zero-sum repreated game. This is confirmed in numerical experiments.
