Arbitrage betting explained

Arbitrage betting ("arbing", or "sure betting") means backing every outcome of an event at different sportsbooks, at prices that together lock in the same return whatever happens. It works only when sportsbooks disagree enough that their prices, converted to probabilities, add up to less than 100%. In theory that's a risk-free profit. In practice the profit is small and the risks are about execution, not the game.

How it works

Every price implies a probability. For decimal odds, the implied probability is 1 ÷ odds, so 2.10 implies about 47.6%. A single sportsbook's prices for both sides of a market add up to more than 100%; the excess is its margin.

But different sportsbooks set prices independently. If one book is generous on Team A and another on Team B, the best price for each side, taken together, can add up to less than 100%. That gap is the arbitrage.

A worked example

Two sportsbooks price the same two-way market:

The total is 3.60 percentage points under 100%, so there's an arbitrage. To make every outcome pay the same, split your stake in proportion to each implied probability. With $100:

• Stake on Team A: $100 × 47.62% ÷ 96.40% = $49.40, returning $103.73 if A wins
• Stake on Team B: $100 × 48.78% ÷ 96.40% = $50.60, returning $103.73 if B wins

Either way you get back about $103.73: a return of roughly 3.7% on the $100 staked. The general formula is return = 1 ÷ (sum of implied probabilities) − 1.

You can try your own numbers, including three-way markets, with the arbitrage calculator.

Rounding changes the result

Sportsbooks don't always take odd amounts, and round stakes are less conspicuous. Round the example to $49 and $51 and the outcomes no longer match: Team A returns $102.90 (a $2.90 profit), Team B $104.55 ($4.55). Still profitable either way, but uneven. On thinner arbs, rounding can push one outcome into a loss, so check every leg.

Where arbitrage goes wrong

The math is certain. Getting both bets on at those prices isn't.

• Prices move. By the time you place the second bet, its price may have changed. If it no longer covers the first bet, you're holding an ordinary one-sided bet.
• Bets get rejected or cut. A sportsbook can refuse a stake, accept only part of it, or hold it for review while the price moves.
• Rules differ. Two books can settle the "same" market differently: overtime, abandoned matches, player withdrawals, or what counts as a push. If one leg is voided and the other isn't, the hedge is gone.
• Obvious errors get cancelled. Sportsbook house rules let the book void, or resettle at a "correct price," bets placed in obvious error. BetMGM's Massachusetts rules, for example, list wagers "at odds that are materially different from those available in the general betting market" as one kind of obvious error.^[2] An unusually large arb is that kind of price. In Massachusetts an operator may cancel an accepted wager for an obvious error only as defined in its internal controls, and BetMGM's rules say it won't void one without the Commission's prior approval.^[3][2]
• Accounts get limited. Arbitrage is one of the betting styles sportsbooks report limiting for.^[1] See Why sportsbooks limit winning bettors.
• Money is tied up. You need funded accounts at several sportsbooks, and withdrawals take time.

Is it worth it?

Typical arbs are a few percent at best, so the return depends on how much you can stake and how many you can actually place before limits arrive. Software helps you find more opportunities, but it doesn't remove any of the risks above. If you're considering paying for an arbitrage scanner, start with What to check before paying for an arbitrage scanner.