The name given to one of the classical topics in probability theory. A game of chance can be related to a series of Bernoulli trials at which a gambler wins a certain predetermined sum of money for every success and loses a second sum of money for every failure. The play may proceed until his initial capital is exhausted and he is ruined. The statistical problems involved are concerned with the probability of the ruin of a player, given the stakes, initial capital and chances of success, and with such matters as the distribution of the length of play. There are many variations to this classical problem, which is closely associated with problems of the random walk and in the limiting case, Brownian motion, in particular, of sequential sampling.