THE MATHS, MADE CLEAR
How it works
The calculator converts each price to a reciprocal probability. A total below 100% identifies a theoretical arbitrage and the budget is divided to target similar returns for every listed outcome.
Arbitrage exists when Σ(1 ÷ oddsᵢ) < 1. Stakeᵢ = budget × (1 ÷ oddsᵢ) ÷ Σ(1 ÷ odds).
Worked examples
Two-way arbitrage
Two outcomes at 2.10 create a 95.24% implied total. A 100-unit budget splits 50/50 and returns 105 units either way before costs.
No arbitrage
Two outcomes at 1.90 total 105.26%. Equal-return allocation produces a theoretical loss rather than a risk-free profit.
Limitations and interpretation
The calculation assumes every price remains available and every market settles identically. Limits, fees, stake rounding, timing, void rules and account restrictions can remove the theoretical profit.