Martingale

A sequence of random variates such that the Conditional Probability of $x_{n+1}$ given $x_1$, $x_2$, ..., $x_n$ is $x_n$. The term was first used to describe a type of wagering in which the bet is doubled or halved after a loss or win, respectively.

See also Gambler's Ruin, Saint Petersburg Paradox