Guide · Risk of ruin
The short answer
Ruin is a function of risk per trade, win rate and payoff. At 2% per trade a normal losing run is survivable; at 10% it is not.
Risk of ruin is the probability that an account falls to a chosen floor — zero, or more usefully some level at which you would stop — before it grows. It combines win rate, payoff and position size into a single probability.
For fixed-fraction sizing with equal win and loss magnitudes, the classical form is:
with edge `e = 2p − 1` for win probability `p`, and `u` the account divided by the amount risked per trade.
A strategy winning 55% of the time with 1:1 payoff, risking 2% per trade, so 50 units of capital:
Effectively zero. Now hold the strategy constant and raise the risk to 10% per trade, which is 10 units:
The strategy did not change. The edge did not change. Position size moved risk of ruin from negligible to better than one in eight.
Where this goes wrong
Because every assumption fails in the same direction, the computed figure is a floor. A model saying 0.005% is telling you the risk is small under ideal conditions, not that it is small.
Do not use risk of ruin to reassure yourself about a number. Use it comparatively: hold the strategy fixed, vary the position size, and read off how fast the probability moves. That slope is the real output, and it is what makes the case for the 1–2% band better than any rule of thumb does.
The risk of ruin calculator shows the sensitivity directly.
Total ruin is the wrong threshold for most people, because almost nobody trades an account to zero — they stop somewhere well above it, usually at the point where continuing stops feeling rational.
Substituting that level for zero gives a far more useful number. If you would stop at a 30% drawdown, then your effective capital is 30% of the account, not 100% of it, and the exponent in the formula falls accordingly:
Four percent, against the 0.005% that assumed you would trade to zero. The second number is the honest one, because it is measured against the level at which you would actually stop.
The closed-form formula needs equal win and loss sizes and independent trades. Real records have neither. Resampling your own trades sidesteps both assumptions and takes about ten lines of code.
The result is usually worse than the formula suggests, because real trade distributions have fatter tails than the model assumes.
Ruin depends on the order of results, not only on their mix. A set of trades that is comfortably profitable overall can end an account if the losses cluster early, while the identical set in another order never threatens it.
This is why expectancy alone does not tell you whether a strategy is survivable, and it is the strongest argument for position sizes that look too small in a good month.
A single risk-of-ruin figure is close to useless in isolation, because every input is estimated and the model is optimistic. It becomes useful when it is used comparatively.