the Gambler's Ruin Problem

The Gambler’s Ruin problem describes a scenario where a gambler has a certain amount of money and makes repeated bets. Each bet has a chance to win or lose a fixed amount, with probabilities that favor neither side. The question is whether the gambler will eventually lose everything (ruin) or potentially achieve a large fortune. The problem analyzes the likelihood of these outcomes over time, considering factors like initial capital, betting odds, and house edge. It helps understand risks and the inevitable decline or growth of a gambler’s funds under repeated betting conditions.