Bias inna di roulette wheel
A bias roulette wheel favour some pocket cause a one physical defect: a loose fret, a rotor weh nuh even, pocket weh wear out. Roulette wheel bias exist an people tek advantage a it. Di problem a dat a perfectly fair wheel mek “hot numba” all di time, suh di question neva a whether a numba hot, but whether di whole pattern more lopsided dan chance allow.
1. Tek a sample fram a fair wheel
Spin weh draw fram a simulated wheel wid no bias at all. Change di sample size an watch di hottest pocket.
2. Wah show up versus wah expected
Evry bar a one pocket inna wheel order. Di dash line a di expected count, n/37. Di shade band a ±2 standard deviation: pon a fair wheel, bout one pocket outta twenty wi poke outside it by chance alone.
3. Chi-square test
Di test add up ow far evry pocket deh fram di expectation, square an scale. Pon a fair wheel, di sum follow a chi-square distribution wid 36 degrees a freedom; people usually call a p-value unda 0.05 significant.
n = 370 · E = 10.00 · χ² = 32.80 · p = 0.622
4. Ow much spin yuh woulda need
Di spin yuh need fi detect one pocket weh hit more often dan 1/37, at a one-sided 5% level wid 80% power. A pocket weh hit 1 time inna 35 instead a 1 inna 37 woulda be a strong edge fi a playa, an it tek tens a thousands a spin weh write dung fi confirm it.
Methodology
Sumting fi laugh
A fair wheel mek hot numba evry night. Fi prove a bias, yuh need tens a thousands a spin.
Source dem
- Pearson, K. (1900). On the criterion that a given system of deviations… Philosophical Magazine, 50(302).
- Thorp, E. O. (1969). Optimal gambling systems for favorable games. Review of the International Statistical Institute, 37(3).
- Ethier, S. N. (2010). The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer. Ch. 13, Roulette.