Can you win the lottery too many times?

Last year I posted on The Fabled 25 Sigma Event, referring to a quote from David Viniar, then CFO of Goldman Sachs, who was attempting to describe the magnitude of the movements in the financial markets. Mr. Viniar probably did not fully understand the implications of what he was saying, since a 25 sigma event translates into a phenomenon occurring once every 10^{135} years - a period of time that we have yet to see even a fraction of. Several researchers at the business school of the University College Dublin gave another interpretation of how unlikely this event was by stating that it equates to winning the UK lottery more than 20 times in a row.

Winning the lottery 20 times does seem very unlikely. Recently a woman won the Texas lottery for the fourth time in the last 10 years or so, accumulating prize money of  just over 20 million USD, and is being scrutinized by the press for potential fraud. There is a lot of suspicion about the luck of Joan Ginther (pictured below) and her winning streak. Googling on “4 time lottery winner” produces pages of articles on Ginther’s supposed luck.

Nathaniel Rich ran an interesting 4-page story in the August issue of Harper’s magazine, where he visits the small Texas town of Bishop to look at the lone town store where three of the winning tickets were purchased. Rich spoke to enough mathematics professors beforehand to determine that the odds of an individual winning four times by pure luck are extremely low indeed, about 10^{-24}, or a practical impossibility (still “far more likely” than a 25 sigma event though). The alternate scenarios are (1) an inside job potentially amongst the state lotteries and their suppliers (2) cracking the parameters of the psuedo-random number generator for selecting the winners, and (3) dumb luck, or increasing your odds of winning by buying many tickets. The most likely answer seems to be a combination of (2) and (3).

The local town people are going with scenario 3 or just ascribing it to pure luck outright, as there is a strong (American) belief that everyone can be a winner. Getting back to those 25 sigma events, it seems then that no one would actually be able to win the UK lottery over 20 times as they would be suspected of foul play, and likely to find themselves arrested way before that many wins. Perhaps Mr. Viniar should have been arrested for his remarks.