Gambler's Ruin

Gambler's Ruin describes a situation where, given enough time or repeated bets, a gambler with finite resources will almost certainly lose all their money if they continue playing against a system with a negative expected outcome. It models scenarios like a gambler tossing a fair coin, where each win or loss adjusts their capital slightly, but the chance of eventually losing everything increases over time. Despite occasional wins, persistent betting leads to eventual ruin, illustrating how finite resources combined with randomness ultimately result in total loss in the long run.