Model │ Math · Free tool
Arbitrage Calculator
Two books, opposite sides, prices that disagree. Enter both prices and a total stake. See whether the gap is real, the split that captures it, and the dollar profit either way.
A dollar amount greater than zero.
A price in any format, +110, 2.10 or 11/10.
A price in any format, +105, 2.05 or 21/20.
An arbitrage exists when the implied probabilities of the two prices sum to less than 100%, the market sum below.
- Stake on Side A ,
- Stake on Side B ,
- Return on stake ,
- Market sum (implied probabilities) ,
Where arbs come from, where they go
An arbitrage is a structural disagreement between two books, one has Side A too cheap, the other has Side B too cheap, and a bettor split across both wins money regardless of outcome. The math is fixed; the opportunity is fleeting.
- The market sum
- Add the implied probabilities of both prices. A sum below 100% is an arbitrage; the gap is the dollar edge per unit staked. A sum above 100% is the bookmakers' margin, the vig, and is what makes most markets unprofitable to play both sides of.
- The split
- Stakes are sized in inverse proportion to the prices, more on the shorter side so the payouts match. Get the split wrong and the "arbitrage" can pay one way and lose the other.
- Why these are rare
- Books move prices in seconds when they see one another. The window is usually thin and the limits are usually small; executing both sides before they move is its own skill.
Two-way arbitrage is the form most people meet first. Three-way and moneyline-versus-spread arbs follow the same logic with more bookkeeping. The principle is unchanged. When the implied total drops below one, the market has left a coin on the table.