Arbitrage calculator: stakes for a sure bet
Enter the best price for each outcome, taken from different bookmakers, and the total you want to stake. The calculator says whether the prices form an arbitrage and how to split the money.
How the total stake is split
| Outcome | Price | Stake | Return if it wins |
|---|---|---|---|
| Outcome 1 | 2.10 | 493.98 | 1,037.35 |
| Outcome 2 | 2.05 | 506.02 | 1,037.35 |
How an arbitrage is spotted and staked
Add up one divided by each price. If the sum is under 100%, the prices leave room for a profit when every outcome is covered. The share of the total stake that goes on an outcome is its own one-over-price divided by that sum. Then each outcome returns the same amount, which is the total stake divided by the sum.
Worked example
One bookmaker offers 2.10 on the first outcome and another offers 2.05 on the second. The book is 96.40%, under 100.00%. From a total of 1,000, 493.98 goes on the first and 506.02 on the second. Either way the return is 1,037.35, a profit of 37.35 or 3.73%.
Within a single bookmaker the same sum shows the margin, set out in the calculator for margin and fair prices. Prices quoted as fractions or in American form can be changed in the converter between odds formats. For bets where you only hold an edge, not a sure profit, the Kelly calculator sizes the stake.
What the arithmetic of a sure bet hides
- Prices move. If one side changes before both bets are placed, the profit can turn into a loss.
- Bookmakers limit or close accounts that bet this way, and they can void a bet placed at a price posted in error.
- The calculator ignores stake limits, fees and the rules each bookmaker uses to settle a market.
Questions about arbitrage betting
When do two prices form an arbitrage?
When one divided by each price adds up to less than 100.00%. Prices of 2.10 and 2.05 give 96.40%, which leaves a profit of 3.73%.
Why is there no arbitrage inside one bookmaker?
Because the margin pushes the sum above 100.00%. Two sides at 1.91 add up to 104.71%, and covering both from 1,000 loses 45.
Is an arbitrage really free of risk?
The arithmetic is, the practice is not. A price can change between the two bets, a bet can be voided or limited, and the two bookmakers may settle the same event by different rules.
Can the same be done with casino games?
No. In a game every outcome is priced by the same operator with the house edge inside, so the outcomes can never be covered at a profit.