A trader runs a $50,000 account. Win rate: 55%. Average win equals average loss — a clean 1:1 system. Sounds profitable. They risk 20% per trade because they're "confident." After just 10 consecutive losses — which a 45% loss rate makes entirely possible — the account is gone. Not damaged. Gone. The maths didn't care about confidence.

Probability of ruin is the mathematical likelihood that a trading account reaches zero before reaching a target. It is not a feeling or an estimate. It is a formula with a definitive output. Most traders skip this calculation entirely, which is why most traders eventually hand their capital back to the market in one catastrophic sequence.

CONCEPTProbability of ruin drops exponentially as risk-per-trade decreases — even small reductions have outsized protective effects.
WARNINGRisking more than 2% per trade on a 55% win rate system gives a ruin probability exceeding 40% over 200 trades.
KEY IDEAA positive expected value system still ruins traders who size positions incorrectly — edge without sizing rules is not protection.

The simplified ruin formula for a fixed-fraction system is: R = ((1 - Edge) / (1 + Edge)) ^ (Capital Units). Edge here equals (Win Rate × Avg Win) minus (Loss Rate × Avg Loss), expressed as a fraction of risk. With a 55% win rate and 1:1 payoff, edge = (0.55 × 1) − (0.45 × 1) = 0.10. Risk 2% per trade, so capital units = 100/2 = 50. That gives R = (0.9/1.1)^50 = approximately 0.0076, or 0.76% ruin probability.

Probability of Ruin vs Risk % Per Trade0%25%50%75%1%5%10%15%20%25%Risk % Per Trade (55% Win Rate, 1:1 System)

Now change that single variable: risk 10% per trade instead of 2%. Capital units drop to 10. R = (0.9/1.1)^10 = approximately 0.389, or a 38.9% chance of ruin. Same edge, same system — completely different survival outcome. The Kelly Criterion, detailed on Wikipedia's Kelly criterion page, formalises optimal fraction sizing. The broader mechanics of ruin probability on Investopedia connect this to drawdown exposure. Practically, traders commonly apply position sizing frameworks to keep ruin probability below 1% — which generally means risking no more than 1-2% of capital per trade.

The formula is not pessimistic — it is structural. Build the inputs, calculate the output, then set your position size so ruin probability sits below 1% before placing a single trade.

Your edge means nothing if your sizing guarantees you won't survive long enough to collect it.

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