Arbitrage Calculator
An arbitrage, or arb, exists when the best prices available on every outcome of an event, taken from different bookmakers, add up to less than 100% implied probability. Enter the best price on each outcome: the calculator tells you whether the arb is real, how to split the stake and what you get back on each result, with exact and rounded stakes.
The test: 1 ÷ odds A + 1 ÷ odds B (+ 1 ÷ odds C) must be below 1. With 2.10 at one bookmaker and 2.02 at another: 0.4762 + 0.4950 = 0.9712, so £100 split £49.03 / £50.97 returns £102.96 whatever happens, a profit of 2.96%.
Decimal odds. Each price can come from a different bookmaker; what matters is the best price on each outcome. To convert fractional or American prices use the odds converter.
Result
Rounded to whole pounds (£100.00 staked):
How an Arbitrage Is Worked Out
Every decimal price carries an implied probability of 1 ÷ odds. At a single bookmaker the implied probabilities of all outcomes add up to more than 100%: the excess is the bookmaker's margin, and the margin calculator measures it. Two evens prices on a tennis match are 2.00 and 2.00 (100%); a bookmaker offers 1.90 and 1.90, which adds up to 105.3%. An arb appears only when different bookmakers disagree enough that the best price on each side, taken together, falls below 100%.
When it does, each outcome gets a share of the total stake equal to its implied probability divided by the sum. That split makes every outcome return the same amount: total stake ÷ sum.
Two worked examples
| Market | Best prices | Sum | Stakes on £100 | Return |
|---|---|---|---|---|
| Tennis match, 2-way | 2.10 / 2.02 | 97.12% | £49.03 / £50.97 | £102.96 (+2.96%) |
| Football 1X2, 3-way | 2.60 / 3.60 / 3.40 | 95.65% | £40.21 / £29.04 / £30.75 | £104.55 (+4.55%) |
| One bookmaker, 2-way | 1.90 / 1.90 | 105.26% | £50.00 / £50.00 | £95.00 (−5.00%) |
Rounding the tennis stakes to £49 and £51 leaves £2.90 if the first player wins and £3.02 if the second does. On an arb of 1% or less, rounding can turn one side into a small loss, so the calculator shows both versions.
Why the profit is not risk-free
The arithmetic is exact; the bets around it are not. Four things break arbs in practice:
- Different settlement rules. Bookmakers do not settle every event the same way. In tennis, one operator voids a match when a player retires and another settles it on the player who goes through: our tennis betting rules guide compares them line by line. Arb one against the other and a retirement can leave you with one void bet and one loser.
- Price moves. If the second price shortens before you place it, the first bet is left uncovered. Placing the larger or more volatile side first limits the damage.
- Palpable errors.Bookmakers' terms let them void or resettle a bet struck at a price that was obviously wrong. A 20% arb is more likely to be an error than an opportunity.
- Account limits. Licensed bookmakers can restrict stakes or close accounts at their discretion, and accounts that only take prices above the market are a common target.
If one side of the arb is on a betting exchange, lay the selection instead of backing every other outcome: the back lay calculator includes the commission. To split a stake across several outcomes at one bookmaker, when the prices do not form an arb, use the dutching calculator.
Frequently Asked Questions
How do you calculate an arbitrage bet?
Add up 1 ÷ odds for the best price on every outcome. If the total is below 1, an arbitrage exists and the profit is 1 ÷ total − 1. Each outcome's stake is the total stake × (1 ÷ its odds) ÷ the sum. With 2.10 and 2.02 on a two-way market the sum is 0.9712, so £100 split £49.03 and £50.97 returns £102.96 whichever side wins: 2.96% profit.
Is arbitrage betting legal in the UK?
Yes. Placing bets with different bookmakers so that every outcome is covered is not against the law. Bookmakers' terms let them limit or close accounts at their discretion, though, and accounts that only take prices well above the market are often restricted. The risk is to your accounts, not a legal one.
What is a good arbitrage percentage?
Most real arbs found by comparing bookmakers are between 1% and 3%. Anything far above that is usually a pricing error, a market about to be suspended, or two bookmakers settling the event under different rules, and a bookmaker can void a bet struck at an obvious error under its terms.
Why should I round arbitrage stakes?
Stakes of £49.03 and £50.97 look automated and can draw attention. Rounding to £49 and £51 changes the result only slightly: £2.90 profit if the first side wins and £3.02 if the second does, against £2.96 on both with exact stakes. Check the rounded figures before placing: on a thin arb, rounding can push one side below zero.
What can go wrong with an arbitrage bet?
The second price can move before you place it, leaving one bet unhedged. Bookmakers can settle the same event differently, for example a tennis retirement or an abandoned match, so one bet is void and the other loses. Stake limits can cut the bet you need, and palpable error rules can void a bet placed at a mistaken price.
An arbitrage ties up the whole stake for a small margin, and a void or a moved price can turn it into an ordinary losing bet. Only use money you can afford to lose. 18+. If gambling stops being fun, see our responsible gambling resources.