Calculators
Arbitrage calculator (2-way and 3-way markets)
Enter one price per outcome from different books. The calculator above shows whether the chances add up to less than one and how to split your stake.
Arbitrage +1.74%The prices add up to 98.29%, under 100%
| Outcome | Stake | Returns | Profit |
|---|---|---|---|
| Side Aat 2.05 | $250.00 | $512.50 | +$12.50 |
| Side Bat 2.02 | $250.00 | $505.00 | +$5.00 |
Split $500.00 as in the table and every outcome returns at least +$5.00 (+1.00%). Stakes are rounded to $5, so you stake $500.00 and the profit differs a little by outcome.
Risks: a book can cancel or limit a bet, or move a price before you place both. Then one side is left open and the maths no longer holds.
How it is calculated
Sum of implied chances = sum of 1 ÷ odds1 ÷ 2.05 + 1 ÷ 2.02 = 98.29%
Arbitrage if the sum is under 100%; return = 1 ÷ sum − 11 ÷ 98.29% − 1 = +1.74%
Stake on an outcome = total × (1 ÷ its odds) ÷ sum$248.16, $251.84 before rounding
Profit if it wins = stake × odds − total staked+$12.50, +$5.00
Arbitrage check: the sum of chances
Chance = 1 ÷ price. Add the chances of all outcomes (two or three). Total under one means arbitrage.
Example: For example, 2.05 at book A and 2.02 at book B: 1 ÷ 2.05 + 1 ÷ 2.02 = 98.3%. That is an arb of 1.74%.
Normal market vs arbitrage
Normal 2-way market
104.8%Both sides at −110: each side is 52.4%. The part above one is the margin.
Example 3-way market
102.5%This 60-minute 1X2 line has three prices that add up to 102.5%. That is more than one, so there is no arb.
Arbitrage
98.3%Prices from two different books add up to less than one. The gap is the arb.
Example: one game, two books
| Bet | Price | Stake | Return if it wins |
|---|---|---|---|
| Book A – home | +105 (2.05) | $49.63 | $101.74 |
| Book B – away | +102 (2.02) | $50.37 | $101.74 |
| Total | 98.3% | $100 | $1.74 profit |
The same return on either result if both bets stand at these prices. Stake per side = total × (1 ÷ price) ÷ sum of chances.
Arbitrage vs hedge
Arbitrage
- Both bets placed at about the same time
- Chances from different books add up to less than one
- Same return on either result if both bets stand
- Planned return is known before the game, if both bets stand at these prices
Hedge
- Second bet placed later, after prices move
- Covers a bet you already have open
- Fixes profit or loss on both results if bets stand, or cuts a possible loss
- Try the hedge calculator
Questions
What is arbitrage betting?
Betting every outcome of one event at different books when their chances (1 ÷ price) add up to less than one. If both bets stand, you get the same return on either result.
Is arbitrage betting legal in Canada?
The answer depends on the laws of your province and on each book's terms; this page is not legal advice. Check each book's terms on limits and voided bets. See is this sportsbook legal.
Can I use the arbitrage calculator for 3-way hockey markets?
Yes. For a 60-minute 1X2 line, enter all three prices: home, draw, away. The sum of 1 ÷ price must be under one for an arb.
Is a sure bet calculator the same thing?
Yes, it is another name for an arbitrage calculator. The name oversells it: prices move, stakes get limited and bets can be voided, so the planned return is not certain.
Is arbitrage the same as positive expected value?
No. Expected value compares one price with a fair chance – see the expected value calculator. An arb needs no fair-chance estimate, only chances that add up to less than one.