Losing streak calculator
Given a win rate and a number of bets, the exact chance of hitting a run of losses that long, the run you should actually plan for, and what it takes out of the account.
Worked example — Chance of a run of 7 losses somewhere in 500 trials: 64.4%. 55.00000000000001% win rate, 500 trials: the single-start shortcut says 0.37%
Good system, normal Tuesday: A good system, not a fantasy one, where a 7-loss run is still more likely than not
Completely normal: a run this long is more likely than not.
At a 55% win rate the longest run over 500 trials is as likely to be above 7 losses as below it, and 11 in a row is the first length that drops under a 1-in-20 chance.
Trials are treated as independent with a constant win rate, which is the assumption a streak calculation cannot do without and the one real records break first: losses cluster when the same regime hurts several positions at once, so the real probability of a long run is higher than this, not lower. Position sizing is treated as a fixed fraction of the current bankroll, so each loss is smaller than the last.
In plain English: the exact column checks every place the streak could begin, including overlapping streaks. Its recurrence is f(n) = Σ qi(1 − q)f(n − i − 1), with f(n) = 1 when fewer than k trials remain, and it is independently checked with a k-state transfer matrix. The two agree to 9.4e-15 here, which is the check being run rather than a claim being made. The shortcut column is qk: the chance of a run starting at one nominated trial. It misses all the other places the run could start.
Chance of a losing streak, by run length
At a 55.00000000000001% win rate over 500 trials, here is the exact chance of a losing run of each length somewhere in the record.
| Losses in a row | Exact probability | Bankroll cost at 2% risk |
|---|---|---|
| 3 | 100.00% | 5.9% |
| 4 | 100.00% | 7.8% |
| 5 | 99.52% | 9.6% |
| 6 | 90.31% | 11.4% |
| 7 | 64.40% | 13.2% |
| 8 | 36.89% | 14.9% |
| 9 | 18.61% | 16.6% |
| 10 | 8.82% | 18.3% |
| 11 | 4.06% | 19.9% |
| 12 | 1.84% | 21.5% |
| 13 | 0.83% | 23.1% |
| 14 | 0.37% | 24.6% |
| 15 | 0.17% | 26.1% |
| 16 | 0.08% | 27.6% |
| 17 | 0.03% | 29.1% |
Is a 7-game losing streak normal at a 55% win rate?
Yes. Over 500 bets at a 55.00000000000001% win rate, a run of 7 losses in a row hits 64.4% of the time, more likely than not. Most people running a system this good have not planned for seven, because seven feels like a broken strategy rather than a normal Tuesday. The arithmetic says otherwise, and it is not close.
Why the usual losing-streak shortcut is wrong
Search this and you will usually be handed the loss rate raised to the run length. At a 44.99999999999999% loss rate and a 9-loss run that is 0.08%, and it is not wrong so much as irrelevant: it is the probability that a run of nine begins at one nominated trial. Over 500 trials there are hundreds of places a run could start, they overlap, and the correct question is whether one occurs anywhere. The true answer is 18.6% , about 246 times the copied one. Both numbers are printed side by side in the calculator above for every run length, because seeing the ratio at your own inputs does more than being told the formula is wrong.
What this does not model
- Independence is the load-bearing assumption and the one most likely to be false. Real losses cluster: correlated positions lose together, a regime change turns a good edge bad for a month, and a tilted trader makes worse bets after four losses than after four wins.
- The win rate is treated as known; if it came from a short record, it is an estimate with a wide interval around it, and the run lengths implied by the pessimistic end of that interval are the ones worth planning against.
Undersized survival planning kills more sound systems than bad edges do. Take the run length that still has a one-in-twenty chance over your expected sample, assume it happens, and check that the drawdown leaves you solvent with the risk of ruin calculator. If it does not, the fix is the position size rather than the strategy, on the position size calculator. And if a losing run already happened and you are wondering whether the strategy is broken, run the record through the track record significance calculator: a run this page calls ordinary is not evidence of anything.
The next question after this one
Risk of ruin calculatorCalculatorThe streak length is only half of it. This turns a run of that length into the probability of losing a stated share of the bankroll.Open nextOther questions
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What Pro adds here
Streak analysis over an imported ledger, correlated-run modelling, and drawdown alerts are Pro features. The launch list sends one email at launch.