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Losing streak calculator
A losing streak calculator gives the probability of consecutive losses over a run of trades: the chance of at least one streak of a given length, the longest streak to expect and the longest streak in 95% of cases. The calculation is exact, not a simulation.
Losing streak probability table: 100 trades
| Win rate | 4+ losses in a row | 6+ in a row | 8+ in a row | 10+ in a row | 12+ in a row | Expected longest streak |
|---|---|---|---|---|---|---|
| 30% | >99.9% | 99.0% | 85.8% | 58.0% | 32.9% | 10.7 |
| 40% | >99.9% | 87.3% | 49.0% | 20.5% | 7.7% | 7.9 |
| 50% | 97.3% | 54.6% | 17.0% | 4.4% | 1.1% | 6.0 |
| 60% | 80.1% | 21.2% | 3.6% | 0.6% | <0.1% | 4.6 |
| 70% | 43.3% | 4.8% | 0.4% | <0.1% | <0.1% | 3.5 |
How to use it
The formula
Chance that k given trades all lose = (1 − win rate)^k. That is the chance of one specific run, not the chance of a streak somewhere in N trades, which is much higher.
s(n) = s(n − 1) − win rate × (1 − win rate)^k × s(n − k − 1), with s(n) = 1 for n below k and s(k) = 1 − (1 − win rate)^k, is the exact chance of no streak of k or more losses in n trades. The calculator shows 1 − s(N).
Expected longest streak = the sum over k ≥ 1 of the chance of a streak of at least k. The longest streak in 95% of cases is the smallest length m for which the chance of no streak longer than m is at least 95%.
The model assumes independent trades with a constant win rate. Real results can cluster, for example when market conditions turn against a strategy, so treat these figures as a lower bound on the streaks to prepare for.
Worked example
Illustrative numbers: at a 40% win rate, the chance that the next 8 trades all lose is 0.6^8, about 1.7%. Over 100 trades, the chance of at least one streak of 8 or more losses is about 49.0%.
Over those 100 trades the expected longest losing streak is about 7.9, and in 95% of cases the longest streak is 12 or fewer. At 1% risk per trade, 12 losses in a row cost about 11.4% of the account; at 2%, about 21.5%.
Questions
What are the odds of 10 losses in a row at a 50% win rate?
Over 100 trades the chance of at least one streak of 10 or more losses is about 4.4%; at a 40% win rate it rises to about 20.5%. The chance that ten specific trades all lose at 50% is far lower, about 0.1%, but a long series offers many places for a streak to start.
How long a losing streak should I expect over 100 trades?
At a 50% win rate the expected longest streak is about 6 losses and 95% of cases stay within 9; at 40% about 7.9 and 12; at 30% about 10.7 and 17. More trades lengthen it: at a 40% win rate the expected longest streak over 250 trades is about 9.7.
Why is the chance of a streak so much higher than (1 − win rate)^k?
That formula covers one specific run of k trades. Over 100 trades a streak can start at almost any point, so the chances add up: at a 40% win rate, 8 losses in a row has a 1.7% chance at any given point but about a 49% chance of happening at least once.
How much should I risk per trade to survive a losing streak?
It depends on the drawdown you are prepared to accept rather than on a fixed rule. Take the longest streak in 95% of cases and work out its cost: 12 losses in a row cost about 11.4% at 1% risk per trade and about 21.5% at 2%. Real streaks can be longer than this model suggests.
Are trades really independent?
Not always. Losses can cluster when market conditions stop suiting a strategy, which makes long streaks more likely than this calculation shows. Treat its figures as a minimum to prepare for.
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