
Kelly Criterion For Sport Betting - chegra84
http://chestergrant.posterous.com/kelly-criterion#
======
gwern
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.

~~~
btilly
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.

~~~
gwern
> 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.

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Dn_Ab
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...](http://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected_utility_theory).
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...](http://www.pitt.edu/~sorc/trade/files/RiskManagement/kelly.pdf)

[2]
[http://www.edwardothorp.com/sitebuildercontent/sitebuilderfi...](http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/Good_Bad_Paper.pdf)

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Read_the_Genes
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.

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jakewalker
If you find this interesting, I highly recommend the book Fortune's Formula by
William Poundstone.

[http://www.bookfinder.com/search/?author=&title=&lan...](http://www.bookfinder.com/search/?author=&title=&lang=en&isbn=0809046377&submit=Begin+search&new_used=*&destination=us&currency=USD&mode=basic&st=sr&ac=qr)

~~~
RockyMcNuts
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.

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btilly
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.

~~~
ssp
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)).

~~~
btilly
You're right. I'll fix later.

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TillE
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.

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

~~~
VB6_Foreverr
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

~~~
khafra
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.

~~~
VB6_Foreverr
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.

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VB6_Foreverr
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

~~~
rudiger
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).

