# The Gambler's Ruin

The Gambler's Ruin

The gambler starts with an unit stake and the casino or house starts with units. They repeatedly play a game for which the gambler has a fixed probability of winning and the winner gets 1 unit from the loser. Play continues until the gambler "succeeds" by acquiring units or is "ruined" by dropping to 0 units. This Demonstration computes the probability that the gambler will succeed by breaking the bank. Subtracting this probability from 1 gives the gambler's ruin probability. The theoretical expected number of plays of the game until success or ruin is also computed and a simulation gives empirical results for the various parameter values. In the example shown in the thumbnail we use , the player's probability of winning an "even money" bet in American roulette.

i

c

p

i+c

p=0.474