Topics: Random Walk - Stochastic Process

Say we’re studying a game between two players A and B. In it, there’s a probability of winning and of losing; there can’t be a draw.

The two players agree on giving each other a monetary unit upon losing. Player A starts with units, while B starts with , adding up to a total of .


Let be the stochastic process that represents the wealth of player A at the time .

This stochastic process is a random walk that starts at and finishes either at (player A is ruined) or at (player B is ruined). Hence, and are both absorbing states.

We can obtain the probability of ruin of a given player, as well as the expected amount of bets before a given player gets ruined.