Gambler's Ruin Probability Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: July 27, 2026A classic problem with a sobering answer
Gambler's Ruin calculates the probability of losing an entire bankroll before reaching a target bankroll, given a fixed per-bet win probability - even a game close to even odds shows a surprisingly high ruin probability when the starting bankroll is small relative to the target.
Worked example
For a starting bankroll of 10 bet units, targeting 20 units, at 47.4% win probability per bet (close to a European roulette even-money bet):
Result = 73.903% chance of going broke before reaching target
This dramatic result - a nearly 74% chance of ruin despite a win probability close to 50% - illustrates why bankroll size relative to bet size and target matters enormously for extended play sessions, a foundational insight from classical probability theory dating back over a century.