Let two players each have a finite number of pennies (say, for player one and for player two). Now, flip one of
the pennies (from either player), with each player having 50% probability of winning, and give the penny to the winner. If
the process is repeated indefinitely, the probability that one or the other player will *eventually* lose all his pennies
is unity. However, the chances that the individual players will be rendered penniless are

**References**

Cover, T. M. ``Gambler's Ruin: A Random Walk on the Simplex.'' §5.4 in
*Open Problems in Communications and Computation.* (Ed. T. M. Cover and B. Gopinath).
New York: Springer-Verlag, p. 155, 1987.

Hajek, B. ``Gambler's Ruin: A Random Walk on the Simplex.'' §6.3 in
*Open Problems in Communications and Computation.* (Ed. T. M. Cover and B. Gopinath).
New York: Springer-Verlag, pp. 204-207, 1987.

Kraitchik, M. ``The Gambler's Ruin.'' §6.20 in *Mathematical Recreations.* New York: W. W. Norton,
p. 140, 1942.

© 1996-9

1999-05-25