Powerball and the Kelly criterion
A popular decision rule for investment and other forms of gambling is the Kelly criterion, named after mathematician (and successful investor) John Kelly. In the long run, following this rule will maximise long-run expected wealth.
If we assume that the story in Stuff about Wairarapa bettors having had a 2:1 return in the past year can be applied to tomorrow’s Powerball (which it can’t), we can look at what that would imply about rational betting.
The Kelly criterion specifies what fraction of your total wealth you should spend on an investment opportunity. The fraction is always less than your probability of winning. With 2:1 expected payoff and large odds, the recommended fraction is about half the probability of winning
The chance of the top Powerball prize (since this isn’t a ‘must win’ week) is 1 in 38 million for a $1 bet, so you should bet less than 1 dollar for each 76 million dollars of your current disposable wealth. For most of us, that’s less than one dollar.
It’s worth noting that while not everyone supports the Kelly criterion, most of the critics suggest that you should bet less than the criterion recommends, not more.
(via a commenter at Cornell physics blog The Virtuosi)
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »