In a gambling context the term originally referred to a system for recouping losses by doubling the stake after each loss. The modern mathematical concept can also be viewed in such terms as a mathematical formalization of the concept of a ‘fair’ game defined as one in which the expected size of the gambler’s bank after the nth game given the results of all previous games is unchanged from the size after the (n 1)th game, i.e. the gambler’s average gain or loss after each game, given the previous history of the games is zero.