Drawdown & risk of ruin
How much do you need to make back — and how likely is the next big drawdown?
Lose 50% and you need +100% to get back to even. That asymmetry is the whole case for small position sizes. Put in your drawdown, then your win rate, reward-to-risk and risk per trade to see how many losses sit between you and your limit, and the odds of getting there before your edge plays out.
Drawdown versus the gain needed to recover it
| Drawdown | Gain to recover | Account goes from → to |
|---|
Next Set the risk per trade that keeps these odds low →
Reading the number honestly
- The formula: P(ruin) ≈ exp(−2μN ÷ σ²), where μ = pR − (1 − p) is the expectancy in R, σ² = pR² + (1 − p) − μ², and N = limit % ÷ risk % is the number of full-stop losses between you and the limit. Trades to recover = gain needed ÷ (μ × risk %).
- What it assumes: every loss is exactly one full stop, the edge holds, and the path is Gaussian. Against simulations it rounds the odds up slightly at small risk sizes; it stops meaning anything once fewer than five losses separate you from the limit, and it says 100% whenever one loss would breach it.
- Recovery arithmetic turns brutal above 30%. Most professional risk limits exist to make sure a trader never has to do the maths past that line.
- A rebate does not change these odds. It lowers cost per trade, which nudges expectancy; it does nothing for a method with no edge.
Questions
Why does recovery need more than the drawdown?
Because the gain is measured on a smaller base. Lose 20% of 1,000 and you have 800; to get back to 1,000 you need 200, which is 25% of 800. The deeper the hole, the steeper the wall: 50% needs 100%, 75% needs 300%.
How do I use this on a funded or prop-firm account?
Set the drawdown limit to the firm's maximum (often 10%) and the daily limit to its daily rule (often 5%). At 0.5% risk a trade that gives 20 full-stop losses to the maximum and 10 to the daily limit; the panel shows the odds of a streak long enough to end the day and the chance of reaching the maximum before the edge plays out.
Is 2% risk per trade safe?
It depends on the edge and the limit. With a genuine edge and a 50% limit, 2% keeps the odds low. Against a 10% limit it leaves five full stops, and the formula is already rough there. Without an edge, no percentage is safe — the calculator shows ≈100% whenever expectancy is zero or negative.
