An arbitrage calculator takes the best price for each outcome at different bookmakers and adds up their implied probabilities. If the total comes in under 100%, it splits your outlay so every outcome returns the same amount. The formula is short: stake on an outcome = total outlay × (1 ÷ its price) ÷ the sum of (1 ÷ every price). You can run it by hand, or put the prices into BetBank's free arbitrage calculator, which needs no account.
The calculator only does arithmetic, though. It can't tell you whether the price is still there, whether the bookmaker will take your stake or whether both books settle the market the same way. Below is the maths for the cases most guides skip: three-way markets, a leg you've already placed, uneven stakes, and exchange commission. Every price in the examples is invented.
What an arbitrage calculator does
| You enter | It gives you |
|---|---|
| The decimal price for each outcome (2 or 3 of them) | The book percentage: the arb exists if it's under 100% |
| Your total outlay | The stake for each outcome |
| Commission on any exchange leg | The return and profit or loss on each outcome |
| A bet already placed (optional) | The stake still needed on the other side or sides |
The core formula is the standard one: convert each price to an implied probability (1 ÷ decimal odds), add them up, then share the outlay in proportion, as set out in Topendsports' arbitrage calculator guide. If prices are in fractional form, convert them first with our odds converter guide.
The arbitrage formula, step by step
Step 1: the book percentage
Add 1 ÷ price for the best price on each outcome. Bookmakers build their markets to total more than 100%: that excess is their margin. When two bookmakers disagree enough, the best prices across both can total less than 100%.
Step 2: the stake split
For each outcome: total outlay × (1 ÷ price) ÷ the book total from step 1.
Step 3: the return
Every outcome returns the outlay ÷ the book total. Profit is that return minus the outlay.
Worked example: a two-way NBA head to head
Bookmaker A has Team X at 2.12. Bookmaker B has Team Y at 2.02. You have $500 to spread across both.
| Team X at 2.12 | Team Y at 2.02 | Total | |
|---|---|---|---|
| 1 ÷ price | 0.4717 | 0.4950 | 0.9667 (96.67%) |
| Stake | $243.96 | $256.04 | $500.00 |
| Return if it wins | $517.20 | $517.20 | |
| Profit | $17.20 | $17.20 | 3.44% |
The book is 96.67%, so the gap below 100% shows up as a return of $500 ÷ 0.9667 = $517.20, whichever team wins. This is the case every calculator handles. The next four are where people get caught out.
Three-way markets: a Test match with a draw
A Test match has three results on most bookmakers' match markets: home, away or draw. The formula doesn't change. You just add a third leg. Here's $300 across three bookmakers:
| Home at 2.05 | Away at 4.40 | Draw at 3.60 | Total | |
|---|---|---|---|---|
| 1 ÷ price | 0.4878 | 0.2273 | 0.2778 | 0.9929 (99.29%) |
| Exact stake | $147.39 | $68.67 | $83.93 | $299.99 |
| Return | $302.16 | $302.16 | $302.16 |
That's a profit of $2.16, or 0.72%. Three-way arbs are usually thinner than this, and thin arbs don't survive rounding. Round those stakes to the nearest $5 ($145, $70, $85) and the returns become $297.25, $308.00 and $306.00. If the home side wins, you're $2.75 behind on a $300 outlay.
Before you treat a three-way market as an arb, check that all three bookmakers settle a tie, an abandonment or a washout the same way. If one voids the market and another doesn't, the maths above no longer applies.
When one leg is already placed
This is the most common real situation. You took one price, and by the time you get to the second bookmaker it has moved. You can't use the outlay formula any more, because one stake is fixed. Work backwards from the bet you hold:
- Target return = your placed stake × its price.
- Stake on each other outcome = target return ÷ that outcome's current price.
- Profit = target return minus everything you've staked.
Say you placed $200 on Team X at 2.12. The target return is $424. Now look at what Team Y's price does to the result:
| Team Y's price now | Stake on Team Y | Total staked | Profit either way |
|---|---|---|---|
| 1.98 | $214.14 | $414.14 | $9.86 |
| 1.90 | $223.16 | $423.16 | $0.84 |
| 1.85 | $229.19 | $429.19 | minus $5.19 |
A few cents of movement takes this from a profit to a loss. This is why the usual advice is to place the leg most likely to move or be refused first, as covered in our guide to how arbitrage betting works. BetBank's calculator has a placed-bet option that sizes the remaining side for you.
Uneven stakes: choosing where the profit lands
The standard split gives the same profit on every outcome. You can instead cover one side so it just returns your outlay, and put all the profit on the other. People call this a biased arb.
Using the NBA prices above with $500:
- Stake Team Y so it returns exactly $500: $500 ÷ 2.02 = $247.52.
- The rest goes on Team X: $252.48.
| Result | Return | Profit |
|---|---|---|
| Team X wins | $535.26 | $35.26 |
| Team Y wins | $500.00 | $0.00 |
The total profit isn't bigger. You've moved it so it all lands on one outcome. It's a choice about which result you'd rather have more on, and it's still an arb only if every bet stands.
Commission: when one leg is on an exchange
If a leg is a back bet on Betfair, the price on screen isn't what you get paid. Betfair charges commission on your net winnings in each market. Its market base rate for sport is 6%, and 10% for NRL. Sport went up from 5% in March 2025, according to The Straight.
Turn the exchange price into an effective price before you run the calculator:
Effective price = 1 + (exchange price minus 1) × (1 minus commission)
Say Team Y is 2.08 on the exchange. At 6% that's 1 + 1.08 × 0.94 = 2.0152. Paired with Team X at 2.12, the book is 96.79%, the stakes are $243.66 and $256.34, and the profit is about $16.57 on $500. At a 10% rate the effective price drops to 1.972 and the profit to about $10.83. Commission is the most common reason a "2% arb" on screen turns out to be close to nothing. Our Betfair commission guide has more on how it's charged.
What the calculator can't check
| Risk | What happens | What to do |
|---|---|---|
| Price moves | The second leg is shorter than when you started | Use the placed-bet maths above before staking |
| Stake limits | The bookmaker takes $40 of your $256 | Check the maximum before placing the first leg |
| Settlement rules | One book voids, the other settles | Read both books' rules for the market |
| In-play | Online in-play sports betting isn't allowed | Arbs are pre-match only online in Australia |
| Account restrictions | Books limit accounts that keep taking their outliers | Read why bookmakers limit winning punters |
The in-play point matters for Australians. The Interactive Gambling Act 2001 bans licensed sites from offering online in-play sports betting, with only limited exceptions. An arb you spot once a game has started isn't one you can place online.
Using BetBank's arbitrage calculator
- Open the arbitrage calculator and pick two or three outcomes.
- Enter the best decimal price for each outcome. Use the odds screen to see every bookmaker's price side by side.
- Enter your total outlay, or switch to the placed-bet option if one leg is already on.
- Add commission on any exchange leg.
- Choose rounding (cents or the nearest $5) and check the profit on every outcome after rounding, not just the headline figure.
The calculator is free, along with the rest of the betting calculators (no-vig, hold, hedge, Kelly and more). The live arbitrage finder, which scans bookmakers for these gaps, is part of the Gold plan on the pricing page.
Try the maths on a real board
Next time two prices on the odds screen look far apart, put them into the free arbitrage calculator before you stake anything, and check the result after commission and rounding.
18+ only. Arbitrage maths assumes every bet stands, and it doesn't always. Set a limit, bet only what you can afford to lose and gamble responsibly. If you want a break from betting, BetStop lets you exclude yourself from every licensed Australian bookmaker, and our responsible gambling page lists free support services.