Finding an arb is half the job. The other half is splitting your money correctly so the profit is actually locked in. Here is the math for two-way and three-way markets, plus the practical tweaks real arbers use. If you want the answer without the math, use the arbitrage calculator.
Step 1: Check that it is an arb
Convert each outcome's best price to decimal and add up 1 ÷ decimal:
If the sum is below 1, it is an arb. Return % = 1 ÷ sum − 1.
Step 2: Split the stake (equal profit)
To win the same amount whatever happens:
Two-way example
NFL total: Over 44.5 at +108 (2.08) at Book A, Under 44.5 at −102 (1.980) at Book B.
- 1/2.08 = 0.4808; 1/1.980 = 0.5050; sum = 0.9857
- Return = 1/0.9857 − 1 = +1.45%
With $1,000 total:
- Over: 1000 × 0.4808 / 0.9857 = $487.73 → returns $1,014.49
- Under: 1000 × 0.5050 / 0.9857 = $512.27 → returns $1,014.49
About $14.49 profit either way.
Three-way example (soccer)
Home 2.60 (Book A), Draw 3.70 (Book B), Away 3.30 (Book C).
- 0.3846 + 0.2703 + 0.3030 = 0.9579 → return +4.4%
With $600:
- Home: 600 × 0.3846 / 0.9579 = $240.91 → $626.36
- Draw: 600 × 0.2703 / 0.9579 = $169.29 → $626.36
- Away: 600 × 0.3030 / 0.9579 = $189.81 → $626.36
(Three-way arbitrage in soccer.)
Alternative split: free bet on one side
Instead of equal profit, you can stake so one outcome breaks even and the other wins everything. This is useful when you think one side is more likely than the market says, or for promo conversions.
Using the NFL example with $512.27 on the under: the under returns $1,014.49, so you can stake up to $502.22 on the over and still break even if the under wins. Then the under winning nets ~$0 and the over winning nets about $30. You have turned a locked-in $14.49 into a bet with no downside and a larger upside on the side you favor.
Rounding stakes
Stakes like $487.73 look automated and can draw attention. Round to natural amounts ($490 and $510) and recheck: you will usually keep most of the profit. Small arbs (under 1%) can disappear with rounding, so check the result.
Commission and fees
If one leg is on an exchange that charges commission on net winnings, reduce that leg's effective decimal odds: D_effective = 1 + (D − 1) × (1 − commission). Recalculate the sum with the effective price.
Common calculation mistakes
- Using American odds directly without converting
- Forgetting that a push on one leg (whole-number lines) breaks the arb math
- Mixing markets with different rules (overtime, player must play)
- Ignoring maximum stake limits on one leg
Frequently asked questions
How do you calculate arbitrage betting stakes?
Divide the total stake in proportion to each outcome's 1 ÷ decimal odds, then divide by the arb sum. Each outcome then returns the same amount.
What is the arbitrage formula?
An arb exists when the sum of 1 ÷ decimal odds across all outcomes is below 1. The locked-in return at those prices is 1 ÷ that sum minus 1.
Should I round my arbitrage stakes?
Rounding to normal-looking amounts is common to avoid attention. Recheck the profit afterwards, since small arbs can vanish with rounding.