DISCLAIMER: I’m aware of all of the provisos, addenda, and other errata regarding the perils of trying to beat the sports books via arbitrage bets. I hold no delusions that I can make consistent money at this, and mostly I’m just interested in the math of it all.
With that out of the way, the explanation AI gave me for how to spot an arbitrage bet made no sense. The sports books apps all express their odds like Team A +115 Team B -225. What calculations do I need to make, with the props expressed this way, to know if I’m looking at a possibility for an arb bet?
As in: GigaSports offers the odds above. What information would I need to look for on the MondoBets app to see an opportunity?
To facilitate your arithmetic, I’d convert the +/- odds into decimal factors. +115 means that if you bet $100 and win, you’ll make a profit of $115. You’ll also get your initial stake of $100 back, for a total payout of $215, so in decimal terms, +115 would be expressed as 2.15. -225 means you need to come up with a stake of $225 for a chance to win $100 if the team wins, plus repayment of your initial stake, so a stake of $225 results in a payout of $325, which is, in decimal terms, 1.44 (325/225).
Next, to offer a profitable opportunity for arbitrage, you need to find a situation where the inverses of the decimal odds of all possible outcomes add up to less than 1. Suppose you have two teams that are exactly equal, and suppose no draw is possible. In such a situation, a fair bet would offer you odds of 2.0 on both teams. Of course betting companies will always factor in an advantage for themselves and not offer you a fair bet, so they might offer you, say, 1.8 on either team. The inverse of 1.8 is 0.56, so the sum of the two inverses is 1.12, which is larger than 1, so this bet is disadvantageous to you.
But suppose you find two different betting companies, one offering you 1.9 on team A and the other 2.5 on team B. The inverses add up to 0.53 + 0.4 = 0.93, which is less than 1, so you have an arbitrage opportunity here. If you bet $100 on team A with the first company and $76 on team B with the second company, you stand to get back $190, for a net profit of $14 ($190 minus the $176 that you’ve spent on wagers) no matter how the game ends.
But don’t forget that (1) the betting companies monitor each other’s odds and (2) you really need to cover all possible outcomes for a sure-fire arbitrage opportunity to arise.
@Schnitte outlines the process well.
I’d add that you need to look in betting markets where this is (slightly) more likely.
In US professional sports the US market makers are drawing on the same win/loss performance stats, applying essentially the same algorithms and can validate their odds against their peers easily. Chances of an arbitrage split is lower and quickly corrected if it occurs.
However consider the football (soccer) World Cup. Say there is an England vs Argentina fixture. A bit of history and patriotic urges to tweak the odds off “true”. Limited comparative stats. It would not be unexpected that support for and the odds of an ENG win offered by an English bookie would be lower than the odds of an ENG win offered by an Argentinian bookie.
So consider backing an ARG win in England and an ENG win in Argentina. Patently it’s a more complicated operation with accounts, currency and timing, as befits searching for a free lunch.