How the arbitrage calculator works
An arbitrage calculator splits one total stake across every outcome of an event, priced at different bookmakers, so that the return is the same whichever outcome lands. It tells you whether the prices in front of you add up to a profit at all, and if so how to divide the money.
- Convert each price to an implied probability: 1 divided by the decimal odds.
- Add the implied probabilities. Under 100% means the prices leave a margin for you; over 100% means the bookmakers keep it.
- Each stake is the total stake multiplied by that outcome's implied probability, divided by the sum. Every outcome then returns the same amount.
- Profit is the total stake divided by the sum of implied probabilities, minus the total stake.
Worked example
Two-way market, £100 in total. Bookmaker A has 2.10 on one side, bookmaker B has 1.95 on the other.
- Implied: 47.6% and 51.3%, total 98.9%.
- Stake £48.15 at 2.10 and £51.85 at 1.95.
- Either way the return is £101.12, a profit of £1.12, 1.1% of the outlay.
The arithmetic holds only if both legs are placed at those prices for those stakes. Prices move, stakes get limited and bets get voided, so treat the figure as the best case, not a certainty.
Questions
- What is an arbitrage opportunity?
- A set of prices across bookmakers whose implied probabilities add up to less than 100%. Covering every outcome at those prices returns more than the total stake, whichever outcome happens.
- Why does a small percentage matter?
- Because the same margin can be repeated across many events. A 1% edge on £100 is £1; on a season of opportunities it compounds, which is why bookmakers limit accounts that only take these prices.
- Can bookmakers restrict me for this?
- Yes. Accounts that consistently take only the prices that are wrong get their stakes limited or closed. That is the practical risk this calculator cannot show.
