Arbitrage Calculator
When two bookmakers disagree enough about a market, backing both outcomes at the right stakes returns the same amount whichever result lands. This calculator sizes the second bet and tells you whether the prices are good enough to bother.
Calculator
How to use the arbitrage calculator
Enter the best price you can find on each outcome, at whichever books offer them, then the stake you want on the first. The calculator sizes the second bet so both results pay the same, and shows the profit that leaves.
The number to watch is the market percentage. Add the two implied probabilities together: under 100% and the position is profitable whichever way it lands, over 100% and you're paying the bookmakers' margin for the privilege of covering both sides.
The formula
For a stake S₁ at odds d₁, the stake that equalises the outcomes at odds d₂ is:
S₂ = S₁ × d₁ ÷ d₂
The return either way is S₁ × d₁, so profit is that less the total staked. An arbitrage exists when:
1/d₁ + 1/d₂ < 1
A worked example
One book has the home side at $2.10; another has the away side at $2.05. Together that's 47.6% + 48.8% = 96.4%, so there's 3.6% in it.
Stake $100 on the home side and the equalising away stake is $100 × 2.10 ÷ 2.05 = $102.44. Total outlay $202.44, return $210 whichever result lands, profit $7.56 — 3.7% on the money.
