Risk of Ruin Calculator

The formula assumes constant bet sizing — every bet is the same dollar amount, regardless of bankroll changes. It also assumes every bet has the same win probability and the same odds. Real betting is messier, but the simplification captures the essential dynamic: bigger bets relative to bankroll mean exponentially higher ruin risk.

If you size bets as a percentage of current bankroll (Kelly-style), the math is different — properly fractional sizing has zero theoretical risk of ruin since the bet shrinks as the bankroll shrinks. See what is Kelly staking? for that approach.

The math is exponential. A bettor with a 53% win rate at −110 has a tiny edge per bet, so the ratio r = q / (p·b) is close to 1. Raising a number near 1 to the power of "units in bankroll" gives a number that decays slowly — meaning you need a LOT of units to drive risk of ruin down.

Concretely: 53% at −110 with 50 units of bankroll has ~27% risk of ruin. With 100 units it drops to ~7%. With 200 units, ~0.5%. That's why "well-bankrolled" advice from sharp bettors usually means 100+ units, not 20.

The standard target is below 5%, with under 1% preferred for serious bettors. If the bankroll IS your income (you can't easily replenish it), aim lower. If you're a recreational bettor and the bankroll is discretionary money you wouldn't miss, somewhat higher risk is reasonable.

The two ways to lower risk of ruin: bet smaller (more units in your bankroll) or sharpen your edge (higher win probability). Most bettors over-focus on the second and under-focus on the first.