Risk of ruin is the probability that a trader loses enough capital to be unable to keep trading — not necessarily to zero, but below the point where the strategy can operate.
It depends on three inputs: win rate, the ratio of average win to average loss, and how much of the account is risked per trade.
The simplest version
For even-money bets with win probability p and loss probability q, starting with N units and risking one unit per trade, risk of ruin against an unlimited opponent is (q ÷ p)^N when p > q.
A trader winning 55% of even-money trades with 20 units of capital has risk of ruin of (0.45 ÷ 0.55)^20 ≈ 1.8%. With 10 units, it’s about 13%. With 5 units, about 37%.
Same edge, same strategy. The only thing that changed was how much was risked per trade.
Why size dominates
An edge tells you the expected outcome over many trades. Risk of ruin tells you whether you’ll survive long enough for the expectation to matter. A strategy with a real edge and oversized positions will still go bust, because a run of losses arrives before the edge can express itself.
This is why every sizing rule — fixed fraction, Kelly, volatility targeting — is really a risk-of-ruin control.
In practice
Real trading has variable position sizes, correlated losses and fat tails, so the formula understates the true risk. Treat any calculated figure as a floor, not an estimate.