Bias Detection in Mechanical Roulette Wheels: A Statistical Framework

Claims of biased wheels are common in both folklore and published literature. We propose a rigorous statistical framework for detecting bias in mechanical wheels and apply it to a publicly available data set of 500,000 spins. Under our framework, none of the widely circulated 'biased wheel' claims survive a multiple-testing correction. We argue for stricter methodological standards in this area.

Mechanical bias has a romantic history in the roulette literature. Every decade produces a fresh story of a compromised wheel and the player who spotted it first. Most such stories crumble under scrutiny.

Our statistical framework uses a hierarchical chi-square test over pocket frequencies, with a pre-registered alternative hypothesis and a Bonferroni correction for the number of pockets. We apply it to the largest publicly available spin dataset.

Under our framework, zero pockets exceed the significance threshold. The appearance of clustering in raw data is fully consistent with uniform sampling.

We hope this framework is adopted by future authors. Bias is a meaningful, measurable property; sloppy claims about it do the field a disservice.