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## Kelly Criterion for Fun and Profit

Wed, Sep 9, 2015 | Greg Wagner

The Kelly criterion a betting optimization formula that tells you what percentage of your bankroll you should bet on a particular wager based on the odds and what probability you estimate you have of winning. The simple formula is

where f* is percent you should wager, b is the odds, p is the probability that the wager is correct and q is the probability the wager is wrong or 1-p.

For most American football and basketball bets for the spread or over/under the odds are 100/110.

For example you want to bet on college football game where you estimate that the probability of beating the spread is 60% (or .6), based on the Kelly criterion you should bet 16% of bankroll.

If the value of f* is less than 0.0 you should not take that bet. For example, you estimate you have a 52% percent change of getting the bet right the value of f* is -0.008. For football and basketball you need to have a probability of .525 or better in either direction to have a positive Kelly bet.

Despite my PhD (or because of it), I did most of my research for this topic on Wikipedia, but there is a good technical paper about it by Jane Hung at Washington U.

There are lots of articles for and against using the Kelly criterion, I have found it works quite well with my prediction algorithm where I modeled 9 college football seasons using Kelly bets with a few modifications (basically, I capped the percentage of bankroll at 30%) and my model compounding the winnings in 8 seasons my model would have won money with average increase over starting bankroll of 40,054.23% (sic). This increase is really high a small sample due to an exceptional year for 2013 model where the model had me winning 22,932.89% of my payroll. If you remove that year there was still a 2140.175% increase over the initial bankroll.

This post was originally posted on my my blog.