Why a 10% Loss Needs an 11.1% Gain (Not 10%)
Lose 10% on a trade, make 10% back, and you're even again. Right? No. You need 11.1%. And the deeper the loss, the worse the gap gets.
Say you put $100 into a trade and it drops 10%. You're left with $90. To get back to $100, you need to earn $10.
But $10 on a $90 base isn't 10%. It's 11.1%.
$10 / $90 = 11.1%
The gain is measured on the smaller, post-loss base.
That's the whole thing. A loss shrinks the number your next gain is measured against. So every recovery has to work harder than the loss that caused it.
The formula
One line covers every case:
Recovery gain = loss / (1 − loss)
Loss as a decimal — a 20% loss = 0.20
A 20% loss needs 0.20 / 0.80 = 25% back. A 40% loss needs 0.40 / 0.60 = 66.7%. The denominator keeps shrinking, so the required gain doesn't rise in a straight line — it accelerates.
The table worth knowing
| Loss | Capital left (from $100) | Gain to break even |
|---|---|---|
| 5% | $95 | 5.3% |
| 10% | $90 | 11.1% |
| 20% | $80 | 25% |
| 30% | $70 | 42.9% |
| 40% | $60 | 66.7% |
| 50% | $50 | 100% |
| 70% | $30 | 233% |
| 90% | $10 | 900% |
A 90% loss doesn't need a 90% gain back. It needs 900% — a tenfold return — just to break even.
Why it matters
Look at the gaps. A 5% loss vs a 10% loss: barely different, 5.3% against 11.1%. But a 40% loss vs a 50% loss? That jumps from 66.7% to 100%.
Losses don't cost you evenly. The deeper they go, the more each one costs — and past a point, recovery stops being realistic. That's the math reason good traders cut losers fast and never let one trade blow up the account.
Buffett's Rule No. 1, "Never lose money," isn't a slogan. It's this table. Staying out of the bottom rows is worth more than any winning streak — because the bottom rows are where you don't come back.
It's also why "cut losses short, let winners run" works. Keep every loss small — 1 to 2% of the account — and you stay in the top of the table, where recovery is easy. Let a loss run to 40 or 50% and you're fighting arithmetic that won't bend.
The catch
Reading this table isn't the same as feeling it. The moment that counts isn't now — it's when you're staring at a red position deciding whether to cut. That's when knowing it in your gut beats having read about it once.
The fix is simple: run the numbers yourself. Change the loss, watch the recovery climb.
Work the drawdown curve yourself
Sheet 1 of the TradingMath Excel workbook lets you change any loss figure and watch the required recovery accelerate, cell by cell. Ten sheets cover the math survivors burn into instinct — drawdown, expected value, risk-reward, Kelly, Bayesian, and more.
See the workbook — $29 →