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Arbitrage Calculator: Stakes and Theoretical Return
Compare prices for mutually exclusive, exhaustive results of ONE market. If the inverted-odds total is below 100%, the model shows an idealized arbitrage allocation, not a realizable guarantee.
How it works & examplesUnderstand the calculation
Arbitrage calculations require complete market coverage
The calculation begins with the sum of inverse decimal odds. When that sum is below one, the entered prices allow a positive theoretical return if every possible outcome is covered and the bets settle as assumed. With two exhaustive outcomes at 2.10 and a budget of 100, allocating 50 to each returns 105 whichever wins, a 5-unit model profit.
Binary YES/NO contracts have their own fee, order-book and settlement constraints; use the dedicated tools in Prediction Market Calculators.
That arithmetic does not verify availability, limits or matching settlement terms. A rejected bet, changed price, voided selection or fee can remove the modeled profit. Do not use two selections that can both lose as if they were a complete two-outcome market. For deliberately covering only selected outcomes, use Dutching and retain the uncovered-loss scenario.
Maths & verification
Test two-way or three-way decimal odds for mathematical arbitrage. Calculate proportional allocations, equal gross returns and theoretical profit.
Try the simulator below. Input values stay in your browser; no account or money is involved.
Model assumptions: No. Virtual games use declared teaching models. Verify any actual operator’s payout rules independently.
Arbitrage: positive maths is not a locked return
For exhaustive outcomes of one market, add 1 / decimal odds for each outcome. A total below 100% gives a theoretical positive equal-payout allocation before costs, not a guaranteed executable surebet.
How to interpret the result
The allocation divides a hypothetical budget across two or three outcomes. Gross return includes the stakes; the displayed profit and ROI subtract the total budget.
What this calculation cannot tell you: Different settlement rules, moving prices, fees, voids and betting limits can erase the mathematical result.
How to use the tool
Illustrate the mathematics of equal-payout allocation from quoted prices.
- Gather prices for every outcome of an identical two- or three-way market.
- Enter decimal odds and a single hypothetical total budget.
- Compare weighted allocation, common gross return and theoretical net result.
Understanding your result
The inverse odds are normalized to split the budget. Each outcome then yields the same gross return before fees. The theoretical ROI is (1 / sum of inverse odds − 1) × 100%.
Scope and limitations
Prices may move before both bets are accepted. Limits, partial fills, FX rates, tax, fees, different settlement rules and void bets can invalidate the scenario. A positive number is not a guarantee.
Before you rely on the result
- How the calculation works
Formulas, assumptions, rounding and model limits are documented on the methodology page.
- Check the current inputs
Use the odds, RTP, fees, bonus terms or other values currently shown by the operator or market.
Arbitrage betting maths: inverse odds, stake split and equal return
A mathematical arbitrage exists when mutually exclusive outcomes covering the same market have an inverse-odds sum below 1: Σ(1 / decimal odds) < 1.
For a total budget B, equal-return stake on outcome i is B × (1/odds_i) / Σ(1/odds). Each winning outcome then produces approximately the same gross return before limits, fees and rounding.
Two-outcome example
Odds 2.10 and 2.05 give an inverse sum of about 0.963995, which is below 1. With a 100-unit budget, the theoretical common gross return is about 103.74 and profit about 3.74.
| Outcome | Decimal odds | Approx. allocation | Gross return if wins |
|---|---|---|---|
| A | 2.10 | 49.40 | 103.74 |
| B | 2.05 | 50.60 | 103.74 |
Arbitrage percentage and theoretical ROI
If S = Σ(1/odds), theoretical return multiplier is 1/S and theoretical ROI is 1/S − 1. When S = 1 there is no edge; when S > 1 the equal-return allocation locks a theoretical loss instead.
Execution risk is separate from the formula
Different settlement rules, voids, maximum stakes, account limits, quote movement, exchange commission, FX conversion and rounding can destroy an apparent arbitrage. The calculator checks arithmetic, not whether the prices can actually be executed together.
Check whether quoted prices form an arbitrage
Use this when
You have best available odds for every outcome and want to know whether reciprocal probabilities total below 100%.
Read the result like this
Below 100% indicates theoretical arbitrage before limits, void rules, price movement and execution friction.
Common mistake
A calculator cannot guarantee simultaneous fills or identical settlement rules.
Worked example
With decimal odds of 2.20 and 2.10, the inverse-odds sum is about 93.07%. On a budget of 100, splitting approximately 48.84 and 51.16 gives the same gross payout near 107.44.
Why might the actual result differ?
Quote timing, stake limits, fees, void bets and mismatched settlement can remove or reverse the theoretical gain.
Questions about this calculation
Why does the calculator show a loss?
When the inverse-odds sum is 100% or greater, no strictly positive arbitrage exists in the simplified model.
Can I mix odds from two different matches?
No. The entered outcomes must belong to the same complete market with matching settlement rules.
When is Arbitrage Calculator: Stakes and Theoretical Return the right tool?
Illustrate the mathematics of equal-payout allocation from quoted prices.
How should I read the result from Arbitrage Calculator: Stakes and Theoretical Return?
The inverse odds are normalized to split the budget. Each outcome then yields the same gross return before fees. The theoretical ROI is (1 / sum of inverse odds − 1) × 100%.
What can Arbitrage Calculator: Stakes and Theoretical Return not tell me?
Prices may move before both bets are accepted. Limits, partial fills, FX rates, tax, fees, different settlement rules and void bets can invalidate the scenario. A positive number is not a guarantee.