Category:Gambler's Ruin

This category contains results about Gambler's Ruin.
Definitions specific to this category can be found in Definitions/Gambler's Ruin.

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 $N > C$.