
06513103
j
2016a.00889
Arratia, Richard
Garibaldi, Skip
Mower, Lawrence
Stark, Philip B.
Some people have all the luck.
Math. Mag. 88, No. 3, 196211 (2015).
2015
Mathematical Association of America (MAA), Washington, DC
EN
K60
gambling
optimization problem
doi:10.4169/math.mag.88.3.196
Summary: We looked 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 distinguished the ``plausibly lucky'' from the ``implausibly lucky'' by solving optimization problems that took into account the particular games each gambler won. Plausibility was 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 relied on the BKR inequality; solving the optimization problem numerically relied on the logconcavity of the regularized Beta function. Subsequent investigation by law enforcement confirmed that the gamblers we identified as ``implausibly lucky'' were indeed behaving illegally.