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Risk of Ruin Calculator
Estimate how often a trading system could cross a ruin threshold from its win rate, payoff ratio and risk per trade.
Strategy inputs
Ruin estimate
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Risk of ruin estimates the chance that a sequence of wins and losses crosses a defined loss threshold. With win rate p, loss rate q, payoff ratio R and capital units U = ruin threshold / risk per trade, the closed-form estimate is ((1 - edge) / (1 + edge))^U, where edge = pR - q.
How it works
What risk of ruin means
Risk of ruin is a probability model for path risk. It asks: if this win rate, payoff ratio and fixed risk per trade repeated many times, how often would equity cross the loss threshold you call ruin? The threshold can be total loss, a 50% drawdown, or any other fractional line you choose.
The formula
q = 1 - p
capital units U = ruin threshold ÷ risk per trade
edge = p × R - q
risk of ruin = ((1 - edge) ÷ (1 + edge)) ^ U, clamped to 100% when needed.
In the symmetric Balsara case where R = 1, this reduces to (q / p)^U when p > q. The clean-room oracle example is p = 0.55, risk = 10%, so U = 10 and (0.45 / 0.55)^10 = 13.4%.
Closed form versus Monte Carlo
The closed form is strict for R = 1. When R is not 1, the edge-normalized closed form is an approximation. Monte Carlo is the better fit for asymmetric payoff paths because it samples each trade directly: wins add risk × R, losses subtract risk, and a path is counted as ruined once it crosses the threshold.
How to use this calculator
- Enter the strategy win rate as a percentage.
- Enter the payoff ratio, where 1 means average win equals average loss.
- Enter the fixed fraction of equity risked per trade.
- Set the ruin threshold, such as 100% for total loss or 50% for a half-account drawdown.
- Use closed form for the simple R=1 case, or Monte Carlo when the payoff is asymmetric.
Worked example - 55% wins, 1R payoff
A system wins 55% and loses 45%, with average win and average loss both equal to 1R. Risking 10% per trade against a 100% ruin threshold gives U = 1 / 0.10 = 10. The R=1 closed form is (0.45 / 0.55)^10, or about 13.4%.
Common mistakes
- Using a non-positive edge. If
edge <= 0, the closed-form ruin estimate is 100% because the system does not have a positive expectancy under the inputs. - Applying the closed form to every payoff shape. The strict closed-form result is for
R = 1. For unequal average wins and losses, run the Monte Carlo branch and treat it as a model estimate. - Forgetting the path. Two systems can have similar average expectancy but very different losing-streak behavior. Risk of ruin is about the sequence, not just the average trade.
Frequently asked questions
What is risk of ruin in trading?
Why does the calculator show 100% when edge is not positive?
edge = pR - q, a non-positive edge means the inputs do not produce positive expectancy. The closed-form ruin estimate is therefore clamped to 100%.Is the closed-form risk of ruin exact?
R = 1 case used in the classic Balsara form. When R is not 1, this tool labels the closed form as an approximation and provides Monte Carlo for direct path sampling.