Arbitrage Calculator

How to use this calculator

Enter the best odds you can find for every outcome of one market, one leg per outcome: two for a tennis match, three for soccer (home, draw, away). Each leg can come from a different bookmaker or exchange and can carry its own commission.

• Back means betting on an outcome. Lay means betting against it on an exchange; the calculator converts a lay into the equivalent back bet and stakes it with your liability.
• Total stake splits a budget so every outcome pays the same profit. Fixed leg locks a stake you have already placed and sizes the others around it. Rounding rounds every stake to a whole increment and shows the profit range that leaves.
• The outcome table lists, for every result, which legs pay, the gross return, the commission and the net profit.

The arbitrage formula

Convert every price to decimal odds and add up their implied probabilities, 1 / odds. One bookmaker's market sums to more than 100% because the margin is in the prices. If the best prices across several venues sum to less than 100%, backing every outcome in proportion locks in a profit whatever happens. The return on the total stake is 1 / sum − 1, and each stake is the total times that leg's share of the sum: stake_i = total × (1 / odds_i) / sum.

Two-way odds of 2.10 and 2.10 sum to 95.24%, so 100 split 50 / 50 returns 105 on either side, a 5.00% profit. Real markets are rarely that generous.

Splitting the stakes for equal profit

One bookmaker offers 1.95 on one side of a two-way market and another offers 2.15 on the other. The implied probabilities are 51.28% and 46.51%, a sum of 97.79%. Staking 100 in total, the calculator puts 52.44 on the 1.95 side and 47.56 on the 2.15 side; either outcome returns 102.26, a profit of 2.26%. Open this example and change either price to watch the stakes rebalance. The shorter price always takes the larger stake, because stakes are proportional to implied probability; that is what makes the profit equal.

A three-way example

Soccer needs three legs, and the best price on each result usually sits at a different bookmaker: say 2.30 on the home win, 3.60 on the draw and 3.90 on the away win. The implied probabilities sum to 96.90%. On a total stake of 300 the calculator stakes 134.61, 86.00 and 79.39; every result returns 309.61, a profit of 9.61 or 3.20%. The pre-filled three-way calculator shows the full outcome table.

Back at a bookmaker, lay on an exchange

The most common two-way arbitrage is a hedge: back an outcome at a bookmaker and lay the same outcome on an exchange. A lay at 2.10 is the same as backing "not this outcome" at 2.10 / (2.10 − 1) = 1.909, with the liability as the stake, and the exchange takes commission from the profit when the lay wins.

Back 2.20 at a bookmaker and lay 2.10 on an exchange charging 5% commission, with 100 to stake in total. The calculator backs 45.86 at the bookmaker and lays with a liability of 54.14, matching a backer's stake of 49.22. If the outcome happens the bookmaker pays 100.89; if not, the exchange pays 103.36 less 2.46 commission. Both roads lead to a profit of 0.89%. The margin is thin because commission eats most of the gap between 2.20 and 2.10.

If you have already placed the back bet, switch to fixed leg and enter the stake. With 100 on at 2.20, the lay needs a backer's stake of 107.32 and a liability of 118.05, locking in 1.95. The commission calculator shows what each exchange's rate does to a lay on its own.

Why most arbitrages are small, and what kills them

Across sharp markets the best available prices usually sum to a fraction of a percent below 100, if they get there at all. Anything above 2% deserves a second look: it often means a bookmaker has mispriced a line (a "palp", short for palpable error) and will void the bet, or that the venues settle on different rules. What turns a paper arbitrage into a loss:

• Line moves between the first leg and the last. Place the leg most likely to move first, usually at the sharper venue.
• Stake limits. A bookmaker may accept only part of the stake. Fixed-leg mode re-sizes the other legs around what was accepted.
• Voids and palps. A cancelled leg leaves an ordinary bet on the other side. Check both venues' rules on postponements, retirements and dead heats.
• Rounding. Stakes rounded to whole units shift profit between outcomes; rounding mode shows the worst case.
• Commission and fees on the exchange or prediction-market leg. Make sure the rate matches your account.

Frequently asked questions

Why is a small margin flagged?

Below 0.5% the profit is usually smaller than the cost of rounding stakes to what a bookmaker accepts, and it disappears if any price moves before you place the last leg.

Do I lay the same selection I backed?

In a two-way market, yes: backing a team at a bookmaker and laying the same team on an exchange is the classic hedge. Set the second leg to lay and the calculator treats the market as "team wins" versus "team does not win".

Can I use this for three-way and larger markets?

Yes, up to 20 legs, as long as exactly one outcome can win. For prediction-market groups the Polymarket arbitrage calculator takes prices in cents directly.

What does a negative stake mean?

It means no combination of real bets gives equal profit, so there is no arbitrage. With lay bets or turnover commission the closed form does not apply; the calculator solves the equal-profit equations directly and reports the solution with a warning rather than hiding it.

The odds converter helps when venues quote in different formats, and the arbitrage betting guide covers finding and placing arbitrages.