What are the odds of red 10 times in a row in roulette?
On a European wheel, red 10 times in a row has a probability of 0.074%, about 1 in 1,347. After those ten reds, the chance of red on the next spin is still 18/37, or 48.65%.
The odds of red n times in a row
18 of the 37 European pockets are red, so one red has probability 18/37 = 48.65%. Spins are independent, so n reds in a row is (18/37)n. On an American wheel it is (18/38)n. Black is identical.
| In a row | European | 1 in | American | 1 in |
|---|---|---|---|---|
| 2 | 23.6669% | 4.2 | 22.4377% | 4.5 |
| 3 | 11.5136% | 8.7 | 10.6284% | 9.4 |
| 4 | 5.6012% | 18 | 5.0345% | 20 |
| 5 | 2.7249% | 37 | 2.3848% | 42 |
| 6 | 1.3256% | 75 | 1.1296% | 89 |
| 7 | 0.6449% | 155 | 0.5351% | 187 |
| 8 | 0.3137% | 319 | 0.2535% | 395 |
| 9 | 0.1526% | 655 | 0.1201% | 833 |
| 10 | 0.0743% | 1,347 | 0.0569% | 1,758 |
| 12 | 0.0176% | 5,691 | 0.0128% | 7,837 |
| 15 | 0.0020% | 49,424 | 0.0014% | 73,734 |
| 20 | <0.0001% | 1,813,779 | <0.0001% | 3,091,874 |
| 26 | <0.0001% | 136,823,184 | <0.0001% | 273,708,560 |
The 26 row is not hypothetical. On 18 August 1913, black came up 26 times in a row at the Monte Carlo Casino, and gamblers lost heavily betting that red was due. It is the textbook case of the gambler’s fallacy.
Rare to call, common to see
Calling ten reds in advance is a 1-in-1,347 shot. Seeing a run of ten somewhere in a long session is not. The table counts sessions in which a run of at least n of the same colour appears anywhere, computed exactly by dynamic programming over the current run length rather than by simulation.
| Run of at least | Red, 100 spins | Red, 500 spins | Red, 1,000 spins | Either colour, 1,000 spins |
|---|---|---|---|---|
| 6 | 49.49% | 97.08% | 99.92% | >99.99% |
| 7 | 27.55% | 81.38% | 96.59% | 99.90% |
| 8 | 14.22% | 55.37% | 80.28% | 96.25% |
| 9 | 7.07% | 32.24% | 54.35% | 79.35% |
| 10 | 3.46% | 17.17% | 31.60% | 53.33% |
| 12 | 0.81% | 4.33% | 8.56% | 16.39% |
| 15 | 0.09% | 0.50% | 1.02% | 2.03% |
Why the next spin is still 48.65%
The wheel has no memory. In this simulator that is literal: each result is a hash of a seed, and nothing about the previous spin goes into the next one. On a fair physical wheel it is just as true, if less visible. The probability of eleven reds in a row is small, but by the time ten have already happened, ten of those eleven factors are paid. What remains is one spin at 18/37. Betting against a streak is tested directly on betting against a streak, and it loses the house edge like everything else.
Losing streaks on an even-money bet
For a bettor on red, a losing spin is anything else, black or zero: 19/37 = 51.35%. That is the number that breaks a Martingale. Doubling from $5, the eighth stake is $640, past a $500 table limit, so seven losses in a row ends the progression.
| Losses in a row | Next n spins | Somewhere in 100 | Somewhere in 1,000 |
|---|---|---|---|
| 5 | 3.571% | 84.58% | >99.99% |
| 6 | 1.834% | 59.73% | >99.99% |
| 7 | 0.942% | 36.27% | 99.11% |
| 8 | 0.484% | 20.20% | 90.80% |
| 10 | 0.128% | 5.58% | 46.17% |
Calculator
Any streak length, any session length, either wheel. Exact, computed in your browser.
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