Balance the outcomes
Arb calculator
Compare two, three or more outcomes, or calculate a back/lay balance with commission. See rounded stakes, liability and the result under each assumption.
Your result
$5.00
Net result before costs, either outcome
Enter valid inputs to calculate.
- Stake on outcome 1
- $50.00
- Stake on outcome 2
- $50.00
- Gross return
- $105.00
Illustrative inputs. Results depend on the assumptions shown.
Assumes every outcome is covered and all bets settle as entered. Prices, limits, commission and rounding can change the result.
Your result
$6.40
Net result before costs, any outcome
Enter valid inputs to calculate.
- Stake per outcome
- $32.00
- Gross return
- $102.40
- Book percentage
- 93.75%
- Outcome count
- 3
Illustrative inputs. Results depend on the assumptions shown.
Assumes every outcome is covered and all bets settle as entered. Prices, limits, commission and rounding can change the result.
Your result
−$5.88
Net result after commission, rounded
Enter valid inputs to calculate.
- Lay stake
- $98.04
- Lay liability
- $205.88
- If back bet wins
- −$5.88
- If back bet loses
- −$5.88
Illustrative inputs. Results depend on the assumptions shown.
Assumes both bets settle on the same event under the same rules, commission is charged only on a winning lay bet and you have no other bets in that exchange market.
Compare the full market
At 2.10 on each side of a two-outcome market, a $100 total splits into $50 per side. Either winning side returns $105 before costs. This is an arithmetic example using hypothetical prices, not a live opportunity.
An arb calculator, short for arbitrage calculator, works from decimal odds alone. Each price's reciprocal is the share of the total stake that outcome needs, and the reciprocals added together form the book percentage. Below 100%, the stake split returns more than the total stake whichever covered outcome wins, before costs. At 100% or more, no split of the same prices can produce a positive result.
Two-way, three-way and four-way markets
Use the 2-way tab when a market has exactly two possible results. Where a draw is possible the market has three results, so a three-way arb needs all three prices: choose 3+ outcomes and enter home, draw and away. The same tab works as a 4 way arb calculator and accepts up to 20 mutually exclusive outcomes. The sport does not change the arithmetic. What matters is that no two outcomes can both win and that together they cover everything that can happen.
| Outcomes | Decimal odds | Total stake | Stake per outcome | Return per outcome | Net result |
|---|---|---|---|---|---|
| 2 | 2.10 / 2.10 | $100.00 | $50.00 | $105.00 | $5.00 |
| 3 | 3.20 / 3.20 / 3.20 | $96.00 | $32.00 | $102.40 | $6.40 |
| 4 | 4.20 / 4.20 / 4.20 / 4.20 | $100.00 | $25.00 | $105.00 | $5.00 |
| 2 | 1.90 / 1.90 | $100.00 | $50.00 | $95.00 | −$5.00 |
Display currency
Choose USD, GBP or EUR to change the currency symbol in the labels and results, for example when you use the arb calculator in the UK with stakes in pounds. The tool does not convert between currencies, so enter every stake in the same currency.
Recalculate after rounding stakes
Actual stakes need currency precision. Rounding can make the returns differ, so the result must show each rounded stake and the lowest net result. A small apparent margin can disappear after costs.
This calculator rounds each stake down to whole cents, then gives the leftover cents to the outcomes with the largest rounding remainders. It recalculates every return from those rounded stakes and reports the lowest net result, so the headline figure reflects the stakes you would actually enter rather than an idealised split.
Matching settlement is essential
The calculation assumes every possible outcome is covered, all stakes are accepted and the bets settle under identical rules. Limits, price changes, voids and commissions can change the result. The tool does not monitor operators or place bets.
The formulas, rounding rules and test cases are set out in About our calculations.
Back/lay, commission and free bets
A lay stake is not its liability. At lay odds of 3.10, a $98.04 lay stake exposes about $205.88 if the backed outcome wins. A $100 cash back bet at 3.00 with 4% lay commission balances to about −$5.88 either way. A stake-not-returned free bet uses only the back profit as its available winning return; its nominal stake is not treated as cash invested. Check offer and exchange terms separately.
Cash stake or free bet
Choose Cash stake when your own money is on the back bet; the calculator balances both settlement outcomes after the lay commission you enter. Choose Free bet · stake not returned for a free or bonus bet whose stake is not paid back with winnings. Laying such a bet at an exchange is often called a free bet conversion, and the result shows how much of the nominal stake would be kept whichever way the event settles. The calculator does not check whether an offer applies to you.
| Back bet type | Lay stake | Lay liability | If back bet wins | If back bet loses |
|---|---|---|---|---|
| Cash stake | $98.04 | $205.88 | −$5.88 | −$5.88 |
| Free bet · stake not returned | $65.36 | $137.26 | $62.74 | $62.75 |
Arbitrage questions, answered
No. The result assumes every stake is accepted and every outcome settles under matching rules. Changed prices, void bets, fees and rounding can remove the margin.
Yes. Choose 3+ outcomes, then add each mutually exclusive outcome. Include every possible result for the market.
Lay stake is what you stand to win before commission. Liability is what you risk if the backed outcome wins: lay stake multiplied by lay odds minus one.
No. It only changes the symbol shown for USD, GBP or EUR. Enter all prices and stakes in the same currency.