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MMA and Gambling - The Art of the Arb

This diary entry was promoted to the front page by Luke Thomas.

An important aspect of betting MMA (and one that I am terrible at) long term is the ability to line-shop well.  The very obvious key involves having access to place bets at numerous books.  As most of us on Bloody Elbow probably don't live in Las Vegas, this means we need to have money online with the off-shore bookies.  For that reason, I think it's important for everyone to check out Sports Book Review.  Having money held by off-shore books can be a pretty scary enterprise, but if you're diligent about finding information about the history and reputations of the bookies, you can be at greater ease about the situation.

If you have access to multiple books and are diligent about checking the lines fairly often, one useful tool you can use is the arb (short for arbitrage).  An arb can simply be described as a situation that allows a bettor to back all outcomes and still make a profit.  People who jumped on Chael Sonnen at +400 have this ability now.  To show it mathematically, let's assume we have $100 on Sonnen at +400, and the current line for Paulo Filho is -200.  You can place a bet on Filho at any amount between $200 and $400 and show a profit.  So, let's say we put $300 on Filho.

Star-divide

If Sonnen wins, we win $400 and lose $300 for a profit of $100.
If Filho wins, we win $150 and lose $100 for a profit of $50.

I'm too lazy to figure out the exacts, but if you want to make the same amount regardless of the outcome, I think the correct amount is something close to $330 on Filho.

Even with the ability to arb, you might not want to.  Let's say we think (hypothetically) that Sonnen wins the fight 50% of the time.  In the example I used above, our EV for the fight would be $75.  Doing a quick calculation,

EV = ($400 * .5) - ($100 *.5)
EV = $200 - $50
EV = $150

we find that our EV on our original bet on Sonnen is $150.  So while we are guaranteed to make money by arbing, we still have a higher EV by letting our bet ride.  

But you shouldn't necessarily let EV dictate your decisions.  The closer the EV of arbing and letting it ride, your general level of risk aversion, the percentage of your bankroll in play, and so on should all be factos that help decide whether to take the guaranteed money or GAMBOOL.

The majority of arb opportunities you find are going to be similar to the Sonnen/Filho example.  You'll have a bad line that opens up, and the sharps come in and hammer it down a lot.  From time to time, you can find opportunities where, say, Bodog has Fedor Emelianenko at -250 and 5dimes has Randy couture at +260.  There's actually small arb opportunities on Franklin/Lutter and Danzig/Bocek if you have accounts at Sportsbook.com and Pinnacle.  Unfortunately, Pinnacle isn't open to U.S. players.

Best Fight Odds and Zewkey's MMA Betting Super Page are two quality resources to quickly compare lines across different sites.  BFO has a better layout and more books listed, but Zewkey's is the only page I've found that has a catalog of older fight lines (they have UFC lines back to UFC 56).

I'm running thin on topics that apply to MMA betting, so if there are things people would like to have explained, I'd love to hear some suggestions.

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