Risk of ruin: the math behind blown accounts

Two traders. Both have a positive expectancy. Both win 55% of their trades and earn 1.2× their risk on winners. One trader risks 1% per position; the other risks 3%. After 500 trades, the first has roughly a 0.02% chance of going broke. The second has roughly an 18% chance.

Same edge. Same strategy. Different sizing. Different probability of being out of the game. This is risk of ruin — the maths behind why most strategies fail their traders before they fail on their own merits.

The intuition first

Risk of ruin is the probability that, over some sequence of trades, your equity touches zero (or some "blown" threshold like -50%) before you walk away. The formula has three inputs: win rate, win/loss ratio, and risk per trade. Everything else is consequence.

A simple closed-form approximation, attributed to Ralph Vince, looks like this:

ROR ≈ ((1 - edge) / (1 + edge)) ^ U

where:
  edge = 2 × winRate - 1              (for a 1:1 R/R strategy)
  U    = unitsOfRiskToZero
       = equity / (riskPerTradeFraction × startEquity)

The exact formula varies for non-1:1 R/R strategies, but the shape is the same: ROR shrinks exponentially as U (the number of risk-units before zero) grows, and U grows linearly as you cut risk per trade. Cutting risk in half does not halve your risk of ruin — it squares it in your favour.

A worked example

Consider a strategy with a 55% win rate and 1:1 R/R — a fairly typical retail-trader profile. Trader A risks 1% per trade. Trader B risks 3%.

Trader E flips a coin on whether they survive. Same strategy as Trader A. The maths is pitiless: ROR is set by sizing, and once you cross ~3% per trade you are gambling on the variance of the streak, not the edge of the strategy.

But I will not ride it to zero — I will stop at -50%

A common rebuttal. The maths still applies, just with a smaller threshold. Risk of 50% drawdown is much higher than risk of complete ruin, and 50% is effectively a blown account — psychologically, you are out, even if the broker statement is not zero. Recovering from -50% needs +100%; almost nobody does that with the same strategy.

A useful adaptation: compute risk of ruin to -50%, not zero. The numbers get scarier. A 55% / 1:1 / 3% trader is sitting on a ~22% chance of hitting -50% in 500 trades. That is one career in five wiped, on a strategy with a positive expectancy.

Edge is smaller than you think

Retail content promises 80% win rates and 3:1 R/R. The numbers that survive real trading are much more modest. A successful retail strategy typically lives somewhere around:

Anything claiming a Sharpe of 3 or an 80% win rate on a 1-year backtest is either overfit, scalping with structural costs the backtest is hiding, or simply not real. Plan your sizing around the modest end of the table above — and your ROR works out fine.

Variance is brutal — even at 60% win rate

A 60% win rate sounds robust. The probability of a 10-trade losing streak inside 500 trades is still ~33%. Inside 1,000 trades it is ~55%. If your account is sized so a 10-trade streak takes you down 40%, you will hit that drawdown more often than not — because of variance alone, on a strategy with a real edge.

This is why position sizing is not "the gentle precaution" — it is the primary defence against the maths of streaks. A strategy is only as good as the worst run it can survive without breaking the trader.

Monte Carlo — the practical tool

The closed-form formula is a single number. Monte Carlo simulation runs your strategy thousands of times with randomised trade ordering and produces a distribution: the 5th-percentile drawdown, the 50th-percentile drawdown, the 95th-percentile drawdown. The 95th-percentile is your honest "what could go wrong" number.

AlphaLab-AI EAs are stress-tested with Monte Carlo on every walk-forward window. The reported drawdown numbers in the methodology panel are the 95th-percentile of the simulation, not the in-sample minimum.

The 1% ROR rule

A practical rule from professional trading: size positions so your risk of 50% drawdown is under 1% over the next 1,000 trades. For most realistic strategies that means 0.5–1% per trade on personal capital, and 0.25–0.5% on prop accounts. The rule is conservative on purpose — your real edge is smaller than your backtest suggests, your variance is larger than you remember, and your tolerance is lower than you claimed.

The bottom line

You cannot eliminate risk of ruin. You can drive it arbitrarily small by sizing small. The traders who survive ten years are not the ones with the best entries — they are the ones who never let risk per trade creep above 1%, even when the edge looked enormous. Variance always shows up; the only question is whether you are still in the game when it does.