Risk of Ruin: The Math Behind Going Broke

You can be a profitable trader and still go broke — if you size your bets wrong.

Risk of ruin is the probability that a string of losses will reduce your account to zero (or to a point where you can no longer trade). It's the number that separates "profitable strategy" from "strategy I can actually trade."

The formula (simplified)

For a strategy with an edge, the approximate risk of ruin is:

Risk of ruin = ((1 − edge) / (1 + edge)) ^ units

Where edge is your per-trade advantage and units is your account expressed in risk units (account ÷ risk per trade).

Example: $10,000 account, 1% risk ($100) = 100 units. Edge = 0.05 (5% advantage).

RoR = ((1 − 0.05) / (1 + 0.05)) ^ 100 = (0.9524) ^ 100 ≈ 0.76%

That's a 0.76% chance of going broke — very low, but not zero.

What changes risk of ruin

Two takeaways:

1. Risk per trade is the dominant lever — doubling it doesn't double risk of ruin, it takes the square root (and since RoR is a fraction below 1, the square root is a much larger number)
2. Even a positive edge can ruin you if you size too aggressively

The 1%–2% rule explained

Most risk rules exist to drive risk of ruin toward zero, not to maximize returns. The 1%–2% rule works because:

• At 1% risk, you need ~100 consecutive losses to blow the account
• At 2%, ~50 losses
• At 10%, just 10 losses — and 10-trade losing streaks happen to every strategy

A 10-trade losing streak at 1% risk leaves you down 9.6%. The same streak at 10% risk leaves you down 65% — and that's without compounding psychology.

Why edges aren't guaranteed

Risk of ruin assumes your edge is real and stable. In practice:

• Edges decay as markets change
• Edges are estimated, not known
• Execution costs erode the real edge below the backtested one

If your true edge is half what you think, your risk of ruin can be 10× higher than calculated. Treat edge estimates with skepticism.

Practical rules

1. Cap risk at 1%–2% per trade — use the position size calculator
2. Track losing streaks in a journal — if your real streaks exceed backtested ones, your edge estimate is too optimistic
3. Reduce risk during drawdowns — many pros halve risk after a 10% drawdown
4. Diversify across uncorrelated setups — multiple independent edges cut risk of ruin multiplicatively
5. Never martingale — increasing size to recover a loss sends risk of ruin toward 100%

The honest truth

A strategy with a real edge and 1% risk per trade is, mathematically, almost impossible to blow up. The traders who go broke don't lack an edge — they lack discipline on size. Risk of ruin is the math that explains why position sizing is the most important skill in trading.