How to calculate arbitrage bets, with formulas and an example
Convert each side's odds to implied probability and add the two together. If the total is under 100%, you have an arbitrage. Then split your stake so both outcomes pay back the same amount. Arbocado's Arbitrage Finder does this math for you and shows the stake for each leg.
- An arbitrage exists when the implied probabilities of both sides of a two-way market add up to less than 100%.
- Implied probability is 1 divided by the decimal odds. The arbitrage percentage is the sum of both sides.
- Each side's stake is your total stake times its implied probability, divided by the arbitrage percentage.
- Your guaranteed return is your total stake divided by the arbitrage percentage.
- Most edges are 1% to 3%, so a rounding mistake can erase the profit. A calculator or scanner prevents that.
The short answer
Convert each side's odds to an implied probability, add the two together, and check that the total is under 100%. Anything under 100% is a guaranteed edge. Then split your stake between the two sides so either result pays back the same amount.
The math takes a minute. The hard part is doing it accurately while the odds are live. Most edges are 1% to 3%, so a small rounding mistake can turn a sure profit into a loss.
Step 1: Convert odds to implied probability
Implied probability is the chance of an outcome that a price represents. It's easiest to calculate from decimal odds.
Implied probability (from decimal odds)
implied probability = 1 ÷ decimal odds
Decimal odds of 2.10 imply 1 ÷ 2.10 = 0.476, or 47.6%. To convert American odds, divide a positive price by 100 and add 1 (+110 becomes 2.10). For a negative price, divide 100 by the price and add 1 (−120 becomes 1.833).
Step 2: Add them up
Take one side of a two-way market at one book and the opposite side at another. Add their implied probabilities to get the arbitrage percentage.
Arbitrage percentage
arb % = (1 ÷ decimal odds A) + (1 ÷ decimal odds B)
- Under 100%: an arbitrage exists.
- Exactly 100%: break-even. No profit either way.
- Over 100%: the normal case at a single book. The extra is the house edge, which is why betting both sides at one book loses money.
Step 3: Split your stake
The profit only locks in if both outcomes return the same amount. To get there, give each side a share of your stake equal to its implied probability divided by the arbitrage percentage.
Stake on each side
stake A = total stake × (implied prob A ÷ arb %)
Guaranteed return
return = total stake ÷ arb %
Profit
profit = return − total stake
A worked example on $100
FanDuel has one side at +112 (2.12 in decimal) and DraftKings has the other at +108 (2.08). Here's the full calculation on a $100 total stake.
| Step | FanDuel at 2.12 | DraftKings at 2.08 |
|---|---|---|
| Implied probability | 1 ÷ 2.12 = 47.2% | 1 ÷ 2.08 = 48.1% |
| Arbitrage % | 47.2% + 48.1% = 95.3% | Under 100%, so it's an arb |
| Stake | $100 × (47.2 ÷ 95.3) = $49.52 | $100 × (48.1 ÷ 95.3) = $50.48 |
| Return if this side wins | $49.52 × 2.12 = $104.98 | $50.48 × 2.08 = $105.00 |
For the intuition behind this and a side-by-side of both outcomes, see how arbitrage betting works.
Try it with your own odds
The calculator below starts with the same FanDuel and DraftKings prices. Change the odds or the stake and the split updates as you type. It also handles 3-way markets, other odds formats, commission, and rounding. The full version lives at the arbitrage calculator page.
Arbitrage calculator
Lakers +112 at FanDuel vs. Celtics +108 at DraftKings, $100 total.
Outcomes (2-way)
- Outcome 1SelectionSportsbook
OddsStake$2.12 · 28/25 · 47.17% · Returns $104.98
- Outcome 2SelectionSportsbook
OddsStake$2.08 · 27/25 · 48.08% · Returns $105.00
Result
Guaranteed profit $4.98
4.98% return on $100.00. You get this back whichever outcome wins.
- Total stake
- $100.00
- Profit
- $4.98
- ROI
- 4.98%
- Market total
- 95.25%
| If this wins | Bet | Profit |
|---|---|---|
| LakersFanDuel | $49.52 | +$4.98 |
| CelticsDraftKings | $50.48 | +$5.00 |
Break-even odds
How far each price can move, with the others unchanged, before the edge is gone.
- Lakers≥ -108
- Celtics≥ -112
Doing the math automatically
Arbitrage gaps often close within minutes, and stakes like $49.52 are easy to mistype. That's why most arbitrage bettors let software do the conversion and the split, and spend their time placing bets.
- 1
Scan for price gaps
A scanner checks the same market across many books and flags any pair that adds up to under 100%. - 2
Size each leg
It applies the stake formula to your total, so both outcomes pay the same. - 3
Re-size on line moves
If a price changes while you're placing the bets, it recalculates the stakes so the edge holds.
Let the Arbitrage Finder do the math
Arbocado's Arbitrage Finder converts the odds, finds sure bets across every major book, and shows the stake for each side in real time.
Open the Arbitrage FinderOnce you can calculate an arb, read whether it's legal and profitable and which sportsbooks to use.
Frequently asked questions
What is the arbitrage betting formula?
Add 1 divided by the decimal odds of each side. If the sum is below 1 (100%), an arbitrage exists. Your guaranteed return is your total stake divided by that sum, and your profit is the return minus your stake.
How do I split my stake between the two bets?
Give each side a share of your total equal to its implied probability divided by the arbitrage percentage. For example, a side with 47.2% implied probability in a 95.3% market gets 49.5% of your stake. Sized this way, both outcomes pay back the same amount.
Do I need to calculate arbitrage bets by hand?
No. The math is simple, but you have to do it quickly and exactly while the odds are live, and a rounding slip can wipe out a 1% to 2% edge. Arbocado's free arbitrage calculator sizes every leg for odds you enter, and the Arbitrage Finder finds arbitrages across every major book and sizes them in real time.