Risk of ruin

Risk of ruin is the probability that a trading account is wiped out — or falls below a threshold from which recovery is psychologically or mathematically impractical — given a defined edge, win rate and risk-per-trade.

Two intuitions are worth internalising before any equation. First, recovery from a drawdown is non-linear: a 20% loss requires a 25% gain to break even, a 50% loss requires 100%, and a 90% loss requires 900%. Drawdowns compound against you. Second, even a positive-expectancy strategy has a non-trivial probability of long losing streaks, and those streaks happen far more often than people’s gut tells them.

A useful approximation: if your win rate is W and average win/loss ratio is R, your expectancy per trade is W·R − (1 − W). A profitable system needs expectancy above zero, but expectancy alone does not tell you survival probability. The standard risk-of-ruin formula combines expectancy with the fraction of equity risked per trade and the depth of drawdown you call “ruin.”

A practical rule of thumb falls out of the maths. Risking 1% of equity per trade with a positive-expectancy edge produces a vanishingly small probability of catastrophic ruin. Risking 5% per trade with the same edge raises the probability sharply. Risking 10% almost guarantees a terminal drawdown within a few hundred trades, regardless of how good the edge looks.

AI strategies do not change this maths — they only change the inputs. Treat any AI bot’s claimed win rate with scepticism, then run the risk-of-ruin numbers as if its true edge were half what it claims. If the strategy survives that stress test, it is robust enough to consider.