How do I know it is really an arbitrage?

Add 1 divided by each side's decimal odds. If the total is below 1, every outcome can be covered for less than the guaranteed return, so it is an arb. At or above 1, there is no arbitrage.

Why are the stakes uneven?

The stakes are set so both sides pay out the same amount. The side with the shorter price needs more money staked to match the return of the longer price, so the split is rarely 50/50.

Why is the profit so small?

Arbitrage margins are usually a fraction of a percent to a few percent, because books price closely to each other. The profit is guaranteed but modest, and it shrinks if a price moves before you place both sides.

What are the practical risks?

Prices can move between placing the two bets, a book can void a bet on an obvious error, and books may limit accounts that arb often. The math is certain; getting both bets down at the shown prices is not.

Free calculator

Arbitrage calculator

Enter two opposing prices and your total stake to see whether they make an arbitrage. If they do, you get the stake for each side, the guaranteed payout, and the locked-in profit.

Side A price

Side B price

Total stake

Arbitrage, 2.21% margin

Back both sides with the split below to lock in the profit.

Side A · +120

$464.60

Side B · -110

$535.40

Guaranteed payout

$1,022.12

Profit

$22.12

Return on stake

2.21%

For information only. Not betting advice.

How it works

An arbitrage, or arb, exists when two books price the opposite sides of a market generously enough that you can back both and come out ahead whichever way it lands. The test is the implied probabilities: add 1 divided by each side's decimal odds. If the total is under 1, an arb exists.

To lock it in, split the stake so both sides return the same amount. Each side's stake is the total stake times its share of the combined inverse odds. The guaranteed payout is that return, and the profit is the payout minus the total staked.

The margin is how far the total implied probability falls short of 100%, read as a return on the total stake. Real arbs are usually small, and they close quickly.

Worked example

Back one side at +120 (decimal 2.20) and the other at -110 (decimal 1.9091). The inverses are 0.4545 and 0.5238, which sum to 0.9784, under 1, so it is an arb worth about 2.21%. On a $1,000 total stake, that is $464.60 on the +120 side and $535.40 on the -110 side. Either result pays about $1,022.12, a guaranteed profit of about $22.12.

Questions

How do I know it is really an arbitrage?: Add 1 divided by each side's decimal odds. If the total is below 1, every outcome can be covered for less than the guaranteed return, so it is an arb. At or above 1, there is no arbitrage.
Why are the stakes uneven?: The stakes are set so both sides pay out the same amount. The side with the shorter price needs more money staked to match the return of the longer price, so the split is rarely 50/50.
Why is the profit so small?: Arbitrage margins are usually a fraction of a percent to a few percent, because books price closely to each other. The profit is guaranteed but modest, and it shrinks if a price moves before you place both sides.
What are the practical risks?: Prices can move between placing the two bets, a book can void a bet on an obvious error, and books may limit accounts that arb often. The math is certain; getting both bets down at the shown prices is not.

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