Kelly Criterion For Sport Betting | Hacker News Reader

Kelly Criterion For Sport Betting

chestergrant.posterous.com

32 pointschegra8423 comments

I once used the Kelly Criterion to try to guide my wagering on the Intrade prediction markets: http://www.gwern.net/Prediction%20markets#how-much-to-bet

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.

Worse yet, if you consistently overestimate your edge, you'll bet too much and could eventually go broke. Furthermore the optimal long-term strategy can be negative for far longer than most would believe.

For instance with your President example where the true odds are 60% and you're being offered even odds, after 100 such bets, following Kelly, you've got over a 15% chance of being behind.

> Worse yet, if you consistently overestimate your edge, you'll bet too much and could eventually go broke.

Yes; I thought I had an edge because I had read a bunch of cognitive bias materials and I had calibrated myself with the usual quizzes and through things like registering hundreds of predictions on PredictionBook.com (http://predictionbook.com/users/gwern) and that sort of thing, but in all honesty, the overall number of independent discrete bets I made on the IEM and Intrade was low enough that I probably just got lucky.

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: http://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected.... 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 .

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).

[1] page 19 of http://www.pitt.edu/~sorc/trade/files/RiskManagement/kelly.p...

[2] http://www.edwardothorp.com/sitebuildercontent/sitebuilderfi...

This is a very well written blog, and the links to pdfs providing further detail are excellent.

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.

http://www.bookfinder.com/search/?author=&title=&lan...

Fortune's Formula is an amazing book. In line with this is also Jeff Ma's "The House Advantage", it's a solid read - http://www.amazon.com/House-Advantage-Playing-Odds-Business/...

Also strongly recommend! Amazing ramble through the weird intersection of information theory, financial markets, degenerate gamblers, and gangsters. Kelly, when he wrote his paper at Bell Labs, was three degrees or less of separation from Claude Shannon, who invented the 'bit', information theory, and what everything digital comes from; Ed Thorp, who wrote 'Beat The Dealer' and started one of the earliest and most successful successful hedge funds (until his firm was busted by Rudy Giuliani); and mobster Manny Kimmel, who won a garage on Kinney Street in Newark on a bet, which eventually grew into Time Warner. Shannon built a wearable computer in the early 60s to try to predict roulette, and they would go to Nevada casinos to test out the theory and practice.

The book's web site is here - http://home.williampoundstone.net/Kelly/Kelly.html

A simple explanation of the Kelly criterion is that if you have an edge (ie bet $5 and win $6 on a fair coin toss) you should bet edge / odds. The edge in this example is 0.1 (50% * -1 + 50% * 1.2), the odds are even money 1:1. The Kelly bet would be 10% (the edge) / 1 (the even money odds) = 10% of your bankroll. (corrected)

If you bet 0 each time, the expected growth rate is 0, if you bet 100% each time, the expected growth rate is 0, because eventually you will lose your whole bankroll.

10% is big enough to matter, but not so big that a losing streak will eventually decimate your bankroll.

If memory serves, when you bet the Kelly amount, you have a 1-p probability of eventually experiencing a p drawdown, ie if you have $10, you have a 10% chance of ever getting as low as $1 before resuming the expected long-run growth rate. (which would be the edge (10%) * the bet (10%) = 1% of your bankroll per betting round)

Been a while since I tried to understand this, if I screwed it up hopefully someone will correct me.

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

Looks good, but are all the $ signs around the variable names intentional? Makes it hard to read imo.

[edit] Actually, it looks like a borked latex doc, perhaps?

Do you have JavaScript turned off? I'm using JSMath, which should translate all of that to nice looking formulas. It works for me on Firefox and Chrome.

If not, you can just treat it as borked LaTeX, because that is what it is.

JS was turned off. Thanks.

Interesting, thanks.

I think there is a typo in the formula that follows "In this case our random variable is log(X). So we get:". On the third line, an n is missing after E(log(X)).

You're right. I'll fix later.

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.

I have to actually figure out one of these betting site APIs and try to do it some day.

Works fine until it doesn't. Therein lies the rub.

The best strategy for this is to only do it for a limited period at large stakes so that your actual outcome is more likely to deviate from the expected outcome

I don't think you can get around the nightingale-ish expected value of this strategy, no matter how you adjust the stakes and number of bets.

If the true odds are greater than 50% then you are more likely to win the bet than to lose it. So even if the odds given imply true odds far greater than 50% (ie poor odds) then you will still probably win money if you bet just 1 bet.

The minute in football where most goals are scored is the 90th (because it is often as long as 5 mins long). I remember where someone laid at huge odds (in running) a horse after Tony McCoy fell off only for McCoy to get back up and win the race http://www.youtube.com/watch?v=PcEjgnBXP40

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

ha! I can't tell if this is a joke. Maybe you didn't estimate your edge correctly, or didn't have one? Or is this really dry British humor, as your handle leads one to suspect?

Kelly criterion betting will always have huge swings, and there's a huge danger of over-betting if you don't precisely estimate your odds. For this reason, players will often bet an amount like "half Kelly" (simply half the bet given by the Kelly formula).

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