Definition
Risk of ruin
Risk of ruin is the probability a strategy reaches a failure threshold before its edge compounds. Definition, formula, and why it is a sizing problem, not an edge problem.
Risk of ruin is the probability that a sequence of trades drives an account down to a defined failure threshold before the strategy’s edge has time to compound. It depends on the win rate, the payoff ratio, the risk taken per trade, and how much drawdown counts as ruin — and it is dominated by the last two, which is why identical strategy statistics can be perfectly safe or nearly certain to fail.
- Also known as
- RoR · probability of ruin
How it is calculated
A = (p·R − q) ÷ (p·R + q) normalised edge
U = Ruin threshold % ÷ Risk per trade %
RoR = ((1 − A) ÷ (1 + A))^U when A > 0, otherwise 100 %
p = win rate q = 1 − p R = payoff ratio
Worked example: 45% win rate at 2:1 payoff, risking 1% per trade against a 40% ruin threshold → near-zero probability.
Sizing moves it by orders of magnitude
Halving the risk per trade doubles the number of consecutive losses an account can absorb, and ruin probability falls exponentially in that count. A strategy risking 1% per trade and the same strategy risking 5% are not variations on a theme — they are different propositions, and only one of them survives an ordinary losing streak.
Ruin is rarely zero
Most accounts are abandoned long before they are emptied, so the useful threshold is the drawdown at which you would genuinely stop, not 100%. A strategy abandoned at −40% has failed exactly as completely as one liquidated at −100%, and setting the threshold honestly is what makes the resulting probability worth anything.
How it gets misread
A low risk-of-ruin figure is often read as a safety guarantee. The formula assumes constant fractional risk, independent trades, and a stable edge — real strategies violate all three, since losses cluster in regime changes and correlated positions concentrate risk that looks diversified. Treat it as a lower bound on danger.
Sources
- Grinstead and Snell's Introduction to Probability — American Mathematical Society (CHANCE Project edition)
- Optimal Gambling Systems for Favorable Games — Proceedings of the Fourth Berkeley Symposium (UC Berkeley Digital Collections)
Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.
Definitions are the easy part
Knowing what drawdown means is not the same as having a system that halts on it. QANTERION applies these limits while a strategy runs.