Why a 50% loss needs a 100% gain
Because the gain is measured on what is left, not on what you started with.
required gain % = drawdown ÷ (100 − drawdown) × 100
Start with $10,000 and lose 50%. You now have $5,000. To get back to $10,000 you need to make $5,000 — which is 100% of your current balance. The loss was measured against the larger number; the recovery is measured against the smaller one.
This is also why "I lost 10% then made 10% back" leaves you down. $10,000 → $9,000 → $9,900. The 10% gain was worth $900, but the 10% loss was worth $1,000. You are at 99%, not 100%.
The full curve
| Drawdown | Gain needed to break even |
|---|---|
| −5% | +5.3% |
| −10% | +11.1% |
| −20% | +25% |
| −30% | +42.9% |
| −40% | +66.7% |
| −50% | +100% |
| −60% | +150% |
| −70% | +233% |
| −80% | +400% |
| −90% | +900% |
Read down the column and notice where it turns. Up to about 20% the recovery is a normal stretch of trading. Past 30% it needs a better run than the one that lost the money. Past 50% you are not recovering an account, you are building a new one out of the remainder.
What this changes about position sizing
The asymmetry is the argument for small per-trade risk, and it is a stronger argument than "be careful".
A trader risking 2% per trade who hits ten losses in a row is down about 18% — a 22% gain gets it back, which is a good quarter. A trader risking 10% per trade with the same ten losses is down about 65%, and needs +186%. Same losing streak, same skill, entirely different futures — decided before either trade was placed, by the size that was chosen.
The second cost, which the percentage hides
There is a behavioural half to this that no calculator prints. Deep drawdowns change how people trade: position sizes go up to "make it back faster", stops widen, and rules that held for months stop holding. The mathematical hole is 100%; the behavioural hole is usually what finishes the account.
The practical defence is a number decided in advance — a drawdown level at which you stop and review instead of continue. Chosen while the account is fine, it is arithmetic. Chosen at 40% down, it is negotiation.