Gambler's ruin: how win rate determines your fate

This computational essay looks at the classic Gambler’s Ruin problem. It studies the chance of going bankrupt and the expected length of the game for a gambler with a starting amount and a target amount. We use formulas and simulations together to check the results, and graphs show how the chance of ruin changes with the win probability. By exploring different starting and target amounts with interactive plots, we can see how the game settings affect the outcomes. This shows how theory, simulation, and visualization work together to help us understand random processes.

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