Some people have all the luck

TL;DR

This study analyzes Florida Lottery winners to distinguish between genuine luck and potential cheating by using optimization models and probability bounds, confirming illegal behavior among the most suspicious players.

Contribution

Introduces a novel method combining optimization and probability inequalities to identify implausibly lucky lottery winners and detect potential fraud.

Findings

Identified individuals with implausibly high winning frequencies

Law enforcement confirmed illegal behavior among suspicious winners

Developed a quantitative framework for lottery fraud detection

Abstract

We look at the Florida Lottery records of winners of prizes worth $600 or more. Some individuals claimed large numbers of prizes. Were they lucky, or up to something? We distinguish the "plausibly lucky" from the "implausibly lucky" by solving optimization problems that take into account the particular games each gambler won, where plausibility is determined by finding the minimum expenditure so that if every Florida resident spent that much, the chance that any of them would win as often as the gambler did would still be less than one in a million. Dealing with dependent bets relies on the BKR inequality; solving the optimization problem numerically relies on the log-concavity of the regularized Beta function. Subsequent investigation by law enforcement confirmed that the gamblers we identified as "implausibly lucky" were indeed behaving illegally.