Betting mathematics
Arbitrage Calculator: Dutching Stakes & Returns
This arb calculator divides a total budget across mutually exclusive outcomes. Check whether the entered prices form a mathematical arbitrage and see each rounded stake.
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How dutching and arbitrage differ
Dutching divides a budget so the gross return is approximately equal whichever selected outcome wins. It does not by itself create a profit. Arbitrage requires the sum of the reciprocal decimal prices to be below one, and all possible outcomes must be covered. This single calculator handles both uses of the same stake-allocation method.
For decimal prices d₁ … dₙ, calculate Q = 1/d₁ + … + 1/dₙ. With budget B, stake on outcome i = B ÷ (dᵢ × Q). Before rounding, gross return = B ÷ Q and net result = B ÷ Q − B.
Two-way and three-way arbitrage examples
At 2.10 on both sides, Q = 0.952381. A $100 budget splits $50/$50, returning $105 and a $5 net result. At 1.90 on both sides, the same split returns $95: a $5 loss, not an arbitrage.
A three-way market needs home, draw and away prices. At 3.20 each, Q = 0.9375; the ideal $100 allocation is $33.333… each. The tool rounds each stake independently to cents and recalculates the total and outcome-specific net amounts, so the spent budget can differ by a few cents.
Why a “surebet” is only a mathematical model
An arbitrage betting calculator cannot verify that quotes are still available, stakes are accepted or the market rules match. Missing draws, different overtime rules, voids, commission, taxes, stake limits and changing prices can remove the modeled margin. A positive result is not a promise of risk-free execution.
Use the hedge calculator when one ticket is already placed and its stake is fixed. For a back bet paired with a lay bet and commission, use the matched betting calculator. The no-vig calculator estimates normalized probabilities rather than allocating money.