Arbitrage betting calculator: two-way and three-way stakes

A calculator allocates stakes at supplied prices; it cannot confirm acceptance, live availability or matching settlement rules.

What the calculator actually checks

An arbitrage betting calculator checks whether the prices for a complete set of mutually exclusive outcomes allow you to cover every result for less than the resulting payout. It then divides your budget across those outcomes. A calculator does not find current odds, confirm that a bookmaker will accept a stake, or reconcile different settlement rules. Those are separate checks.

Start with the sure-bet calculator if you already have prices. Use this guide to understand its arithmetic and decide whether the inputs describe the same bet. For finding prices rather than allocating stakes, read the arbitrage software comparison. Confusing those two jobs is how a mathematically correct calculation becomes a losing position.

Decimal odds include your returned stake. A winning 100-unit bet at 2.10 returns 210 units, not 310. Entering fractional odds directly into a decimal calculator changes the calculation completely. Convert fractional 11/10 to decimal 2.10; convert American prices before comparing them too. Keep the currency and payout convention consistent throughout the worksheet.

The formula, without confusing margin and return

For decimal prices O₁ through Oₙ, calculate the sum of their reciprocals:

S = 1/O₁ + 1/O₂ + ... + 1/Oₙ
Arbitrage condition, before costs: S < 1
Stake on outcome i = total budget × (1/Oᵢ) / S
Equal gross payout = total budget / S
Profit = total budget × (1/S − 1)
ROI on total stakes = (1/S − 1) × 100%

The probability gap, 1 − S, is not the same percentage as return on the money staked. When S is 0.96, the gap is 4%, but return on total stakes is approximately 4.167%. A scanner may display either convention. Check its definition before comparing opportunities or reconciling a spreadsheet with the app.

Smarkets' calculation guide explains the same underlying relationship: the combined implied probabilities must fall below 100%. Its worked examples are explanations, not evidence that those prices remain available. All numbers below are likewise hypothetical. They make the calculation reproducible without pretending to publish an executable opportunity.

Worked two-way example

Suppose a tennis match offers Player A at 2.10 and Player B at 2.10, with both operators applying equivalent retirement and settlement rules. The reciprocal sum is 1/2.10 + 1/2.10 = 0.952381. With 200 units, allocate 100 to each player. The winning leg returns 210 units; total stakes are 200; the net result is 10 units before fees.

That is a 5% return, although the implied-probability gap is about 4.762%. Equal prices make equal stakes appropriate. With unequal prices, equal stakes generally do not produce equal payouts. The stake formula matters because the lower-priced outcome requires a larger share of the budget.

Now change the second price to 1.90 before acceptance. A 100-unit stake on that side returns 190. If that player wins, the two original 100-unit stakes lose 10 overall. The earlier calculator output was not wrong; it described prices that you no longer hold. Recalculate whenever a price or accepted stake changes.

Worked three-way football example

A standard 1X2 market contains home win, draw, and away win. Covering only home and away leaves the draw uncovered. Suppose the best matching prices are 2.20, 3.80, and 4.10. Their reciprocal sum is approximately 0.961606.

With a 1,000-unit budget, the allocation shown to four decimal places is approximately:

Small differences in the displayed figures arise from rounding. The theoretical profit is about 39.93 units, or 3.993% of total stakes. Do not confuse the roughly 3.839% probability gap with that ROI. Confirm the exact accepted amounts in your own calculation rather than copying rounded numbers from a table.

This is also why a three-way calculator is not interchangeable with a two-way calculator. “Team to qualify” can have two outcomes; “match result after 90 minutes” normally has three. The labels may name the same teams, but the underlying events differ.

Rounding and minimum stakes

Bookmakers may accept only certain stake increments. If the calculated stake is 273.665 units but the operator accepts whole units, test both nearby feasible amounts. Calculate the net result for every outcome after rounding. You are looking for the lowest outcome profit, not merely a positive average.

A practical spreadsheet needs an outcome-by-outcome payoff matrix. Each row represents a possible settlement; each column represents one accepted bet. Add all returns in a row, subtract all stakes and costs, and inspect the minimum. This catches the uncovered draw, a misread handicap, and rounding that pushes one outcome below break-even.

Do not round stakes to make activity appear recreational or to evade account controls. Rounding is an arithmetic constraint, not a method of defeating bookmaker terms. If the minimum required stake or maximum accepted stake prevents a complete allocation, reduce the whole position or reject it.

Commission changes the usable odds

An exchange can deduct commission from net market winnings. In a simple isolated winning back bet, a commission rate c changes its effective decimal price to 1 + (O − 1) × (1 − c). This shortcut is not a universal model for several positions in the same market, because commission may depend on the market's net result.

At an illustrative 2% commission, decimal 2.10 becomes an effective 2.078 for that isolated calculation. Replacing the original price with the effective price can eliminate a narrow apparent arbitrage. Deposit costs, withdrawal charges, currency conversion, and software subscriptions are additional economic costs, even when they do not affect settlement.

For back-and-lay combinations, distinguish the lay stake from lay liability. At lay price L, liability is lay stake × (L − 1). An exchange balance must cover liability, not just the number typed into the lay-stake field. Use a calculator designed for that position and the actual commission convention.

A repeatable checking workflow

1. Identify the event, competition, participants, date, and start time.
2. Match the market period and settlement rule, including extra time and abandonment.
3. Check every price directly with the operator, not only in an alert.
4. Enter the full set of outcomes and the budget you can afford to lose.
5. Include relevant commission and currency assumptions.
6. Apply actual stake increments and maximum accepted amounts.
7. Calculate every possible net outcome using the rounded stakes.
8. Treat only accepted bets as positions; record their confirmation details.

If one leg is accepted and another fails, you no longer have the theoretical position. You have exposure that requires a fresh decision. There is no universally safe instruction to “just increase the other stake.” A new hedge might cost more than accepting the original risk, and either choice can lose.

Four-way markets and overlapping outcomes

The general reciprocal formula extends beyond three outcomes only when the selections are mutually exclusive and collectively exhaustive. Four arbitrary correct scores do not satisfy that condition: many other scores remain possible. Neither do two overlapping handicap selections automatically form a complete partition.

Asian lines can introduce half-wins, half-losses, and pushes. Dead heats can reduce returns. Instead of forcing such markets into a simple n-way calculator, build a payoff matrix covering the actual settlement states. The number of named selections is not enough to identify the correct calculation.

The expected-value guide explains a different concept: a single bet can have positive estimated EV while still losing in an individual outcome. An arbitrage calculation instead evaluates a complete payoff structure. Both require accurate prices, but they solve different problems.

Android apps, APKs, and browser calculators

A calculator does not need access to your bookmaker password, wallet seed phrase, or text messages to divide stakes. Treat unnecessary permissions as a reason to stop. Prefer a known provider's official website or a verified store listing reached from that provider. A search result containing “latest APK” is not verification.

A responsive browser calculator may be adequate on Android or iPhone without installing anything. Check that decimal separators, currency formatting, and keyboard entry work correctly. Test a simple known case, such as two outcomes at 2.10, before trusting complicated inputs.

“Lot size” usually belongs to leveraged trading, while “AP turnover” can mean accounts-payable turnover. Neither should be silently substituted for sports-betting stake allocation. If a promotion has turnover requirements, read that promotion's rules separately; a calculator cannot convert restricted bonus funds into freely withdrawable cash by assumption.