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Arbitrage calculator

Enter the best line available for each outcome (from different sportsbooks) and your total stake. The calculator tells you whether there is an arbitrage, how much to put on each outcome and the profit left whatever happens.

Arbitrage found: profit is locked in whatever the result.

StakeReturn
Outcome 1$49.40$103.73
Outcome 2$50.60$103.73
Total probability
96.40%
Guaranteed profit
$3.73
Profit on stake
3.73%

How it works

An arbitrage exists when the implied probabilities (1 ÷ odds) of all outcomes, using the best price for each, add up to less than 100%. It happens when books disagree on the price.

The stake is split in proportion to each outcome’s implied probability. That makes the return identical whoever wins, and the profit is the gap between that return and your total stake.

The outcomes must cover the whole market: home, draw and away in a 1X2, or both sides of the same line in a 2-way market.

Real risks: a price can move before you place the second bet, books can limit accounts or void bets on obvious price errors under their terms, and settlement rules (tennis retirements, overtime) can differ between books.

Formulas

  • Total = 1 ÷ o₁ + 1 ÷ o₂ (+ 1 ÷ o₃); arbitrage if total < 1
  • Stake on each outcome = total stake × (1 ÷ oᵢ) ÷ total
  • Return = total stake ÷ total
  • Profit = return − total stake; as % = 1 ÷ total − 1

Worked example

With +110 and +105 at two different books, total probability is 96.40%: there is an arbitrage. Staking $100.00 in total, you put $49.40 on the first and $50.60 on the second. Whoever wins, you collect $103.73, a profit of $3.73 (3.73%). At +110 on both sides the profit would be 5.00%.

FAQ

Is arbitrage betting legal?

Betting with licensed sportsbooks at different operators is legal. What books can do, under their terms, is limit the stakes on an account.

Why is the profit usually small?

Price differences between books on the same outcome tend to be small and short-lived. That is why splitting the stake precisely matters.

Can I round my stakes?

Yes, to meet minimums or to look less obvious. Once rounded, the profit is no longer identical on every outcome, so recalculate with the final amounts.

What if the odds move before my second bet?

Recalculate. If the new price pushes total probability above 100%, the arbitrage is gone and the first bet is exposed.

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