How to Use an Arbitrage Betting Calculator

An arbitrage betting calculator splits a total stake across opposing outcomes and helps you check the net profit for each one. Open the standalone arbitrage calculator, enter the odds for a complete outcome set, and check the result after commission and rounding. A positive calculation is a conditional model result—not a promise of payment.

The outcomes must be mutually exclusive and cover the same event, period, line, and settlement rules. Every example below is synthetic: these are not current sportsbook odds, placed bets, or typical market returns.

How to identify arbitrage and calculate stakes

Theoretical arbitrage exists when the sum of implied probabilities, S, is below 1 and the selected outcomes cover every possible winning result under matching rules. Convert all odds to decimal format before applying the formula.

Implied probability, 1/O, comes from the betting price. It is not a measured chance of winning.

Odds formats are display conventions, not predictions. Use the odds converter for other prices. Do not round American odds of −105.263… to −105 and expect to reproduce decimal odds of 1.95 exactly.

For a total budget B and decimal odds Oᵢ:

• Sum of implied probabilities: S = Σ(1/Oᵢ).
• Stake on each outcome: stakeᵢ = B × (1/Oᵢ) / S.
• Equal gross return before rounding: R = B/S.
• Net profit: P = R − B.
• Theoretical ROI on total stakes: (1/S − 1) × 100%.
• Probability gap below 100%: (1 − S) × 100 percentage points.

Use dimensionless S in the formulas—for example, 0.97793679, not the displayed percentage number 97.793679. Gross return R includes the winning stake. Net profit subtracts all stakes, including the losing ones.

At S = 1, a balanced split breaks even before costs. At S > 1, it produces a loss. After rounding, calculate again:

worst-case net profit = min(stakeᵢ × effectiveOddsᵢ) − actual total stakes

ROI after rounding is this worst-case net profit divided by the actual total stakes, multiplied by 100%.

Cropped ROI equation: net profit divided by total stakes, multiplied by 100%

Ashlin Darius Govindasamy, “Arbitrage Betting,” October 26, 2022, p. 6, equation 1.4. Original English image cropped to the formula only, excluding the equation number; source, licensed under CC BY 4.0. Here ROI is net profit divided by total stakes, multiplied by 100%, not the probability gap. Only this verified formula is adopted, not the paper’s other examples.

Two-way example: odds of 2.15 and 1.95

With a $1000 total stake, odds of 2.15 and 1.95, and no commission, theoretical ROI is 2.26%. After rounding stakes to the nearest $1, the minimum net profit is $21.80 and ROI is 2.18%.

All amounts below are in USD. This example assumes fixed prices, a complete mutually exclusive outcome set, matching settlement rules, and no additional taxes, currency conversion, subscription, or withdrawal costs.

Do not calculate the profit of accepted bets from display-only cents: those figures may conceal more precise underlying amounts. To make this example reproducible, use stakes rounded to the nearest $1.

The actual total stake is $1000. The worst-case net profit is $21.80, which gives ROI of 2.18%. The probability gap of 2.21 percentage points is neither this profit nor ROI.

How to repeat the calculation in the standalone tool

Select a fixed total, decimal odds, and $1 rounding, then enter 1000, 2.15, and 1.95. Results update automatically; there is no Calculate button.

1. Open the arbitrage calculator.
2. Select Decimal odds.
3. Under “Stake mode,” choose “Fixed total.”
4. Enter 1000 in “Total stake.”
5. Under “Currency,” choose “USD $.”
6. Under “Round stakes to,” choose “$1.”
7. Enter 2.15 and 1.95 in the two odds rows, with 0 in each “comm” field. You can keep the existing outcome names or rename them Outcome A and Outcome B.

The currency selector changes the currency symbol; it does not convert amounts using an exchange rate.

Local English calculator interface with a 1000 USD budget, odds of 2.15 and 1.95, zero commission, and rounded stakes of 476 and 524

Local interface capture showing the inputs and rounded stakes. This is not a production bet-placement test.

Check “Stake plan” for stakes of 476 and 524. The result should show minimum net profit of 21.80, “Return on stake” of 2.18%, “Total staked” of 1000, and “Combined implied prob.” of 97.79%.

The headline hint may show 2.26% while “Return on stake” shows 2.18%. The first is the ideal ROI before rounding; the second uses worst-case net profit after rounding and the actual total stake.

The “Guaranteed profit” label describes only the conditional model. It does not confirm that bets were accepted, rules match, or payment will be collected.

Local English results showing net profit of 21.80, return on stake of 2.18%, total staked of 1000, and combined implied probability of 97.79%

Local interface capture: the 2.26% hint refers to the ideal calculation, while 2.18% reflects rounded stakes. Actual bet placement was not tested.

“Copy stake plan” and “Copy link” let you save or share the calculation. Neither places a bet.

Three-way example: home win, draw, and away win

A soccer 1X2 market for regulation time requires all three outcomes: home win, draw, and away win. With odds of 2.70 / 3.80 / 3.90, a $1000 budget, no commission, and nearest-$1 rounding, this teaching model produces minimum net profit of $123.20.

Click “+ Add outcome” to create a third row. Enter 2.70, 3.80, and 3.90, keeping the total stake at 1000, commission at 0, and rounding at “$1.”

The sum of implied probabilities is 88.993852%, displayed as 88.99%. Actual total stakes are $1000, and ROI after rounding is 12.32%. This unusually high synthetic result was chosen to illustrate the mechanics, not typical market opportunities.

Local English three-way calculator with odds of 2.70, 3.80, and 3.90 and stakes of 416, 296, and 288

Synthetic 1X2 calculation in the local interface: 1000 USD budget, zero commission, and nearest-dollar rounding.

Do not replace the draw with a bet on a team to qualify. Betfair’s match-result rules use 90 minutes plus stoppage time, excluding extra time; qualification markets include extra time and penalties. If the score is 1–1 after 90 minutes and Team A wins 2–1 after extra time, the draw wins in that 1X2 market. This is an operator-specific example, not a universal rule for every market.

What changes with four or five outcomes?

The formula stays the same: add another 1/Oᵢ term for each outcome, but the set must still be complete and mutually exclusive. Adding rows does not create coverage by itself.

For a $1000 budget with no commission:

Four or five arbitrary correct scores are not a complete set because other scores remain possible. Check whether an “other” outcome exists and whether the selected outcomes together cover every result.

How commission and rounding change profit

Commission reduces effective odds, while rounding changes the stake split. Check gross return and net profit for every outcome rather than relying only on S < 1.

Suppose only the second arb leg—an ordinary back bet at 1.95—has a hypothetical 5% commission on net winnings, excluding the returned stake:

effective odds = 1 + (1.95 − 1) × (1 − 0.05) = 1.9025

Enter the raw odds 1.95 and commission 5 in that calculator row. Do not enter 1.9025 and also apply 5% commission, which would count the fee twice.

With a $1000 budget and nearest-$1 rounding:

Actual total stakes are $1000, minimum net profit is $8.35, and ROI is 0.835%, displayed as 0.84%. The 5% rate is an illustration, not a universal tariff.

When several bets are in the same exchange market, a per-leg fee calculation may not match the actual commission. Betfair describes commission on net market winnings, not universally on each bet’s winnings. Losing markets are not charged, and the applicable rate varies.

For comparison, odds of 1.90 / 1.90 produce stakes of $500 / $500, gross return of $950 for either outcome, and net loss of $50.

Hypothetical calculations with a 1000 USD budget and nearest-dollar rounding. A negative value is a loss. These are not market data or typical earnings; the chart shows net cash results, not the sum of implied probabilities or the probability gap.

Rounding each stake independently can also change the total. For example, a $50 budget, odds of 2.02 / 2.02, and nearest-$10 rounding produce stakes of $30 + $30 = $60. Gross return for either outcome is $60.60, so net profit is $0.60. Subtract the actual $60, not the original $50 budget.

If the minimum gross return after rounding does not exceed actual total stakes, the positive profit disappears. Check both figures before using the plan.

How to account for an accepted bet or a profit target

If one bet has already been accepted, use its actual stake and accepted odds as the calculation anchor. Target-profit mode instead estimates the required stakes at the entered prices; it does not guarantee that the target will be reached.

Under “Stake mode,” choose “One bet placed.” Select the accepted leg and enter a stake of 476 at odds of 2.15. Enter 1.95 for the opposing outcome and keep “$1” rounding.

This differs from splitting a fixed $1000 budget. Do not replace an already accepted bet with a new figure from another mode. Rounding can change the anchored stake too: select “Exact” or a compatible rounding increment and verify that the accepted amount remains unchanged.

If the second leg’s price changes, recalculate using the first leg’s accepted odds and the current remaining odds. If a bet was only partially accepted, use the actual accepted amount and account for the open position.

For “Target profit,” enter 50. With odds of 2.15 / 1.95, no commission, and nearest-$1 rounding, the calculation gives stakes of $1054 / $1162, total stakes of $2216, and minimum net profit of $49.90. This illustrates capital requirements and rounding—not an earnings plan. Check available balances and stake limits before acting.

What the inline calculator can and cannot do

The inline calculator provides a quick calculation for 2–5 outcomes without commission or rounding controls. To reproduce the main example, select Decimal, enter 2.15 and 1.95, and set the amount to 1000. The result is approximately $22.56 before fees and rounding.

Its initial American odds of +220 / −160 belong to a different example. Displayed cents use underlying exact mathematics. Any assertive verdict inside the widget should be read only as a conditional model result.

A positive result above does not verify outcome coverage, matching rules, or accepted bets. When S ≥ 1, the inline calculator returns a zero summary rather than the actual loss. Use the standalone calculator or check every outcome manually for negative cases. Invalid inline inputs fall back to 2.00, so inspect every entry.

The standalone calculator ignores invalid odds rows. Check that every intended outcome is present and valid: a result based on the remaining rows does not prove complete coverage.

The standalone tool is not a scanner, live odds feed, or bet-placement service. It does not validate rules or calculate taxes, currency conversion, free bets, or lay liability.

The preset button is labeled “Back vs lay (comm)”; “Exchange lay” is the name of a row it populates, not the button label. The preset does not change the engine: both rows use ordinary back-bet returns, with no lay-liability calculation. Do not enter lay odds as an opposing back price. As Betfair’s definition explains, a lay bet is against a particular selection and requires a liability calculation. Use the separate lay bet calculator for that model.

What to check before using a stake plan

Verify complete outcome coverage, matching rules, and actual accepted amounts before treating the calculation as a fully covered model rather than an open position. The calculator does not perform these checks for you.

1. Event and market conditions. Match the event, selection, period, line, and settlement rules. A market mismatch can leave a scenario uncovered.
2. Complete outcome set. Do not omit a draw, “other” result, or another possible outcome. Each modeled winning result must correspond to one arb leg.
3. Voids, pushes, and early endings. Compare cancellation, push, and retirement rules; do not assume exactly one winner in these states. For example, Pinnacle’s tennis match-winner retirement rules let bets stand if a full set has been completed; otherwise they are void. Other markets have different rules.
4. Balances and limits. Check whether every required stake can be accepted. Capital may remain locked until settlement.
5. Commission, rounding, and other costs. Use the actual applicable fee and final stakes. Taxes, currency conversion, subscriptions, and withdrawal costs are not included in these examples and reduce actual net profit.
6. Accepted odds and amounts. Compare actual bet confirmations with the plan. If the second leg has not been accepted and its price changes, you have an unhedged position, not completed arbitrage.
7. Acceptance status. An unmatched offer is not an accepted bet. Betfair distinguishes unmatched, partially matched, and fully matched bets. Do not automatically submit a duplicate bet after a delay; first verify the actual tickets and accepted amounts.
8. Every outcome’s net result. Subtract all final stakes from each gross return and check minimum net profit, not just the arbitrage hint.

For the broader method, see the arbitrage betting guide. This article focuses on reproducing the calculation and recognizing what the tool does not verify. For checks on live execution and accepted bets, continue with the live arbitrage betting guide.

Participate only if you meet the legal age requirement and only with licensed operators where permitted. Set affordable limits, do not borrow to gamble, and do not chase losses.