Kelly Criterion For Sport Betting

I once used the Kelly Criterion to try to guide my wagering on the Intrade prediction markets: <a href="http://www.gwern.net/Prediction%20markets#how-much-to-bet" rel="nofollow">http://www.gwern.net/Prediction%20markets#how-much-to-bet</a><p>Holy cow was it tough; the warners aren't kidding that it requires a strong stomach. Even with small edges it asks you to bet what feels like an impossibly large fraction of your portfolio.

The Kelly criterion is essentially just optimizing the expected value of the log of your net worth. It was known in some form to Daniel Bernoulli in the late 1700s: <a href="http://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected_utility_theory" rel="nofollow">http://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected...</a>. Anyway knowing this will allow you to calculate it for more complex scenarios and even multiple simultaneous bets [1] simply enough with an optimization algorithm .<p>The problem with Kelly [2] and even fractional Kelly (unless the fraction is very small, then your problem is extremely slow growth) is that it is a long term strategy and it is very sensitive to your estimates. It can be dominated by other strategies in the short term or for those who seek different risk properties (prefer lots of small wins and want less volatility).<p>[1] page 19 of <a href="http://www.pitt.edu/~sorc/trade/files/RiskManagement/kelly.pdf" rel="nofollow">http://www.pitt.edu/~sorc/trade/files/RiskManagement/kelly.p...</a><p>[2] <a href="http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/Good_Bad_Paper.pdf" rel="nofollow">http://www.edwardothorp.com/sitebuildercontent/sitebuilderfi...</a>

This is a very well written blog, and the links to pdfs providing further detail are excellent.<p>As pointed out in jane.pdf, and also be Ed Thorp elsewhere, betting with the Kelly criterion requires large amounts of capital. The reason is simple; there is a real chance of going broke if you start out near 0. This can be countered by playing a fractional Kelly strategy, where you bet Kelly, but only on a fraction of your bankroll.

If you find this interesting, I highly recommend the book Fortune's Formula by William Poundstone.<p><a href="http://www.bookfinder.com/search/?author=&#38;title=&#38;lang=en&#38;isbn=0809046377&#38;submit=Begin+search&#38;new_used=*&#38;destination=us&#38;currency=USD&#38;mode=basic&#38;st=sr&#38;ac=qr" rel="nofollow">http://www.bookfinder.com/search/?author=&#38;title=&#38;lan...</a>

If anyone wants more detail on the Kelly Criterion, I wrote up an explanation at <a href="http://elem.com/~btilly/kelly_criterion/" rel="nofollow">http://elem.com/~btilly/kelly_criterion/</a> along with a calculator that can do things like estimate where you will be after a certain number of bets at various percentiles.

I've always thought that you could make a fair bit of money betting on football matches where one team is at least two goals up with only a few minutes to go. You still get a payout of 1%, and it's a near-certain bet. If you're willing to risk a decent chunk of money and add a few sanity checks (never bet on Arsenal if Manuel Almunia is in goal), it could be some nice income. One percent a couple times per week.<p>I have to actually figure out one of these betting site APIs and try to do it some day.

I wrote a program to calculate my kelly stakes based on supposed 'true' odds (ie no bookie overround) on English football matches. Maybe it would have worked out in the long run but I gave up owing to the effect it was having on my bank. I got my true odds from the Fink Tank column in the Saturday edition of The Times and bet on betfair for convenience and the ability to lay as well as back. I have no doubt that if your true odds are accruate it would maximise your returns. The hard part of course is estimating odds