Roulette wheel statistics, with the ranges that count as normal
Roulette statistics are simple to compute and easy to misread. The computation gives you an average; the misreading comes from expecting any real sample to match it. This page gives the averages and, more usefully, the ranges a fair wheel wanders through by chance, so that you know what normal looks like before you decide something is not.
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Single numbers
| Spins | Expected hits per number | Normal range (±2 SD) |
|---|---|---|
| 37 | 1 | 0–3 |
| 100 | 2.7 | 0–6 |
| 500 | 13.5 | 6–21 |
| 1,000 | 27 | 17–37 |
| 10,000 | 270 | 238–302 |
Only at the bottom of the table does a wheel's record start to look like the average. Above it, individual numbers scatter widely by chance alone.
Colours and even-money bets
Red should be 18 of 37 spins, 48.65%. Over 100 spins expect 49, with a normal range of about 39 to 59. Over 1,000: 486, range roughly 455 to 518. A session where black came up 60 times in 100 is a 2-SD event, unusual but not remarkable, and tells you nothing about spin 101.
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Streaks
| Run | Chance of this run from a given spin |
|---|---|
| Same colour 5 in a row | 2.7% |
| Same colour 8 in a row | 0.31% |
| Same colour 10 in a row | 0.075% |
| Same number twice running | 2.70% |
| Same number three times running | 0.073% |
| Same dozen 6 in a row | 0.12% |
Over a long session, the chance of seeing a given run somewhere is much higher than the per-spin figure: a run of 8 of one colour appears in roughly 45% of 200-spin sessions.
Sectors
The three traditional sections cover 17, 12 and 8 numbers. Voisins du Zéro should hit 45.9% of spins, Tiers 32.4%, Orphelins 21.6%. Over 100 spins, Voisins expects 46 hits with a normal range of about 36 to 56. A sector that hits 60 times in 100 is a 3-SD event. It happens about once in 370 such samples somewhere on a fair wheel, which across every table in the world is constantly.
Zero
2.70% of spins, one in 37. Over 100 spins expect 2.7, range 0 to 6. A hundred spins with no zero is a 6.5% event. A hundred spins with six zeros is about 4%. Both are ordinary.
What would be unusual
A single number at 50 hits in 1,000 spins is more than 4 SD out and worth noticing. A sector at 60% over 1,000 spins would be extraordinary. Anything at the 100-spin scale is not evidence of anything; the ranges are simply too wide. If a result looks wrong, lengthen the sample before drawing a conclusion. On a licensed online table, the conclusion will be that the wheel is fair, because they are checked for exactly this.
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Quick answers
What is the probability of the same number twice in a row?
1 in 37, or 2.70%. The first spin can be anything; the second must match it. The same as the chance of any specific number on a single spin.
How often does red come up 10 times in a row?
About 0.075% of ten-spin sequences on a single-zero wheel. Over an evening of 300 spins the chance of seeing such a run of red somewhere is around 10%, and around 20% for either colour.