How many spins does wheel-bias detection need?
Power calculations for detecting a roulette pocket that lands 0.25 to 2 percentage points more often than the fair 1/37 baseline.
A “hot” pocket is easy to spot after the fact and hard to establish before the fact. This study calculates the observation count needed to detect one pocket whose true probability exceeds 1/37, first when that pocket was named in advance and then when all 37 pockets were searched.
Method
The calculation uses a one-sided normal approximation to a binomial test. The null isp₀ = 1/37; the alternatives add 0.25, 0.5, 1, or 2 percentage points. We solve for 80% power at a 5% false-positive rate. The scan-all column applies a Bonferroni correction of 0.05 / 37 because checking every pocket creates 37 chances to find an impressive fluctuation.
- Seed
- None — this is an analytic power calculation
- Null probability
1/37- Power / α
- 80% / 5% one-sided
- Multiple testing
- Bonferroni correction across 37 pockets
| True excess | True pocket rate | Named in advance | Scan all 37 |
|---|---|---|---|
| +0.25 points | 2.953% | 26,792 spins | 63,283 spins |
| +0.5 points | 3.203% | 6,887 spins | 16,110 spins |
| +1 points | 3.703% | 1,812 spins | 4,165 spins |
| +2 points | 4.703% | 495 spins | 1,105 spins |
Why casual spin logs mislead
A full one-percentage-point excess is large in roulette terms: the pocket rises from 2.703% to 3.703%. Even then, naming the pocket before observation requires about 1,812spins. Searching the whole wheel raises that to 4,165. A subtler quarter-point bias pushes the scan-all requirement beyond 63,283 spins. A few hundred observations can suggest a hypothesis; they usually cannot carry the proof.
Limitations
These are planning numbers, not guarantees. The normal approximation is less exact than a discrete binomial power calculation, wheel conditions may drift during collection, and spins from a physical wheel may not be identically distributed. Bonferroni control is conservative. A real protocol should pre-register the wheel, pocket, collection rules, and stopping rule before looking at results.