The math of ruin
Lesson 1 · about 8 min
You finished Trading 101, so you know how orders fill, what a spread costs you and why the person on the other side of your trade is not doing you a favour. This course is about the one skill that decides whether you are still trading in three years: controlling how much you lose when you are wrong.
Start with the ugliest fact in trading. Losses compound against you, and the compounding is not linear.
Ten losses in a row
Every trader, no matter how good, will eventually take ten losses in a row. The only open question is how much of the account each loss removes.
Suppose you risk the same percentage of your account on every trade and the stop gets hit every time. After each loss the account is smaller, so the next loss is taken on a smaller balance.
Risk 1% per trade. After one loss you hold 99% of the account. After two, 0.99 × 0.99 = 98.01%. After ten:
0.99^10 = 0.904, so 90.4% of the account remains. That is a 9.6% drawdown.
Now risk 10% per trade:
0.90^10 = 0.349, so 34.9% remains. That is a 65.1% drawdown.
| Risk per trade | Account left after 10 straight losses | Drawdown |
|---|---|---|
| 0.5% | 95.1% | 4.9% |
| 1% | 90.4% | 9.6% |
| 2% | 81.7% | 18.3% |
| 5% | 59.9% | 40.1% |
| 10% | 34.9% | 65.1% |
| 25% | 5.6% | 94.4% |
At 1% per trade, ten losses is an annoying fortnight. At 10% per trade, the same ten trades end the account, because (as the next lesson shows) a 65% hole needs a 186% gain just to get back to even: 1 / 0.349 = 2.865, and 2.865 minus 1 is 1.865.
Key idea: The size of each loss, not the number of losses, is what decides whether a losing streak is a bad month or the end of your trading.
How likely is a streak of ten?
Streaks feel rare because any single one is rare. With a 50% win rate the chance that a specific run of ten trades all lose is 0.5^10 = 1 in 1,024, roughly 0.1%.
But you do not take ten trades. You take hundreds. A useful rule of thumb for the longest losing streak you should expect over N trades is:
expected longest losing streak ≈ ln(N) ÷ ln(1 ÷ loss rate)
For 1,000 trades at a 50% win rate: ln(1000) ÷ ln(2) = 6.91 ÷ 0.693 ≈ 10.
For 1,000 trades at a 40% win rate (so 60% of trades lose): 6.91 ÷ ln(1 ÷ 0.6) = 6.91 ÷ 0.511 ≈ 13.5, so a streak of 13 or 14.
| Win rate | Loss rate | Expected longest losing streak in 1,000 trades |
|---|---|---|
| 60% | 40% | 7 to 8 |
| 50% | 50% | 10 |
| 40% | 60% | 13 to 14 |
| 30% | 70% | 19 to 20 |
A thousand trades is two or three years for an active swing trader and a few months for a day trader. The ten-loss streak is not a tail risk. It is a scheduled event.
So the plan is never "avoid a ten-loss streak". The plan is "be sized so that a ten-loss streak is survivable and a fifteen-loss streak is unpleasant but not fatal".
Risk of ruin
Mathematicians call this the gambler's ruin problem. A player with a finite bankroll who keeps betting against an opponent with a much larger bankroll (the market) will eventually go broke if the game has no edge, and will go broke quickly if the bets are large.
Three things drive the probability of ruin:
- Your edge per trade (how much you expect to make on average).
- Your size per trade (how much of the account each bet puts at stake).
- The number of trades you take.
You do not control your edge on any given day; the market decides whether your setup works this week. You control your size completely, on every single trade, before you click. That asymmetry is the whole reason this course exists.
"Ruin" does not have to mean a zero balance. For a prop-firm trader it is the drawdown limit. For most people it is the point where the loss is so painful they quit, or start taking desperate trades to get it back. That point usually arrives somewhere between a 30% and 50% drawdown. Plan for your ruin line to be far above zero.
Try it: Take the percentage you currently risk per trade (if you have never measured it, estimate it from your biggest recent loss divided by your account size). Multiply (1 − risk) by itself ten times, then fifteen times. Write both numbers down. That is your account after the streak that is coming.
Recap
- Losses compound: ten straight 1% losses cost 9.6%, ten straight 10% losses cost 65%.
- Over 1,000 trades, a losing streak of 10 to 14 is expected, not unlucky.
- Risk of ruin depends on edge, size and number of trades; size is the only one you fully control.
- Ruin is wherever you stop trading or lose the account, usually well above a zero balance.
- Size for the streak that is certain to come, not for the trade in front of you.
See it drawn
Original diagrams for the ideas on this page. Illustrative, not real market data.