Check prices and allocate a stake
A theoretical betting arbitrage exists when the sum of the inverse decimal odds for every mutually exclusive outcome is below 100%. This tool allocates stake in proportion to those inverse odds.
Formula and worked example
Inverse sum = Sum of (1 / Decimal odds)
Outcome stake = Total stake x (1 / Outcome odds) / Inverse sum
Equalised return = Total stake / Inverse sum
Two opposing outcomes at 2.10 each have an inverse sum of 95.24%. A total stake of 100 allocates 50 to each side, giving an equalised theoretical return of 105 and a theoretical ROI of 5%.
Execution risk matters
The calculation assumes every displayed price is available, accepted and settled under compatible rules. Price movement, stake limits, rounding, account restrictions, delays and void rules can remove a narrow theoretical margin before all bets are placed.
UK-licensed operators must publish rules covering voids, errors, withdrawals, maximum payouts and settlement. See Gambling Commission LCCP 4.2.6. Check the rules and final prices for every leg.
Limits and responsible use
Theoretical arbitrage is a mathematical condition, not guaranteed profit. The tool does not place bets or verify price availability. Set a spending limit before gambling and do not chase losses. Read GambleAware's advice and our responsible gambling guidance.
Related tools and guides
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Frequently asked questions
How do you calculate an arbitrage bet?
Add up 1 / decimal odds for the best price on each outcome, converting any moneyline prices first. If the total is below 1, an arbitrage exists. Stake share for each outcome is (1 / its odds) divided by that total, and the profit margin is 1 minus the total.
Is arbitrage betting legal?
It is not a criminal offence in the UK or the United States. It does breach the terms of many bookmakers, though, and accounts that do it are commonly limited or closed. Legal is not the same as permitted by the operator.
What is a typical arbitrage margin?
Usually under 2%, and often below 1%. Margins that look far larger normally mean a price has already moved, a market is about to be voided, or the two markets are not settling on the same thing.
Why did my arbitrage lose money?
Most often because one leg was not matched before the price moved, the two books settled on different rules, or one bet was voided and left the other side unhedged. Arbitrage is only riskless if every leg actually stands.
Sources
- Gambling Commission, LCCP condition 4.2.6. Current code accessed 30 July 2026.
- GambleAware, Advice to consider if you're gambling. Accessed 30 July 2026.