How it works
An arbitrage exists when the best prices for every outcome of a market, taken from different bookmakers, imply chances that add up to less than 100%. Stake each outcome in proportion to its implied chance and every result returns the same amount, more than the total staked.
Rounding a stake to a figure a bookmaker will take moves the returns apart, so the calculator shows each outcome’s return with the rounded stakes and reports the worst one.
The formula
- Book sum = 1 ÷ odds A + 1 ÷ odds B (+ 1 ÷ odds C)
- There is an arbitrage when the book sum is under 1
- Stake on an outcome = total stake × (1 ÷ its odds) ÷ book sum
- Return = total stake ÷ book sum
A worked football example
Over 2.5 goals is 2.10 at one bookmaker and under is 2.05 at another. The book sums to 96.40%, under 100%. With 100.00 in total, stake 49.40 on over and 50.60 on under: either result returns 103.73, a profit of 3.73 (3.73%).
What it does not tell you
The maths holds only while both bets stand at those prices. Prices move between placing the first bet and the second, bookmakers can void a bet struck at an obvious error, and accounts that take many arbitrages are often limited. Every outcome has to be covered: a draw left out is a loss.
Common questions
How do I know if there is an arbitrage?
Add up 1 divided by the best odds for every outcome. If the total is under 1, under 100%, backing every outcome in proportion returns more than you stake whichever wins.
How do I calculate arbitrage stakes?
Divide your total stake by the book sum to get the return, then stake the return divided by the odds on each outcome. At 2.10 and 2.05 with 100, the return is 103.73, so stake 49.40 and 50.60.
Is arbitrage betting allowed?
Placing bets at different bookmakers is allowed wherever betting is, but bookmakers’ terms let them limit or close accounts, and many do so to accounts that arbitrage.
Why does rounding change the profit?
Exact stakes like 49.398 return the same either way. Rounded to 49 and 51, one outcome returns 102.90 and the other 104.55, so the profit you can count on is the smaller one.
Can I arbitrage a three-way football market?
Yes, with the home, draw and away prices from wherever each is best. Three outcomes rarely add up to under 100%, and each extra bet is another price that can move before you place it.