Definition:Gambler's Ruin

Definition

Gambler's ruin is the classic problem to determine the probability that a gambler $G$ with an initial capital of $C$ units becomes bankrupt in a sequence of games in which:

$G$ gains $1$ unit of capital with probability $p$

$G$ loses $1$ unit of capital with probability $q = 1 - p$.

$G$ is ruined if and only if he loses all $C$ units.

There is usually a condition that $G$ stops on attaining a total fortune of $N$ units, where $N > C$.

Also see

• Definition:Random Walk, of which gambler's ruin is an instance

• Solution to Gambler's Ruin

• Results about gambler's ruin can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): gambler's ruin
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): gambler's ruin