Free tool
Arbitrage calculator.
When two firms disagree enough, backing both sides in the right proportion returns the same whichever wins. This splits the stake and tells you honestly whether there's an arb — or whether you'd just be locking in a loss.
An arb is real only until the price moves. If the book is under 100% the profit is locked — but bookmakers limit and close arbing accounts, prices shift between your two clicks, and stake caps get in the way. The maths is honest; the practice is fragile. 18+ · information, not advice.
The worked example
£100 across two outcomes both priced 2.1. Implied probabilities: 1÷2.1 + 1÷2.1 = 0.952, a 95.2% book — so an arb exists. Split £50 / £50, and either winner returns £105: a £5 (5%) profit whichever lands. If both were priced 1.95, the book would be 102.6% and every split would lose — no arb.
Straight answers
How does an arbitrage bet work?
An arbitrage ('arb') exists when the prices on all outcomes of an event, across different bookmakers or exchanges, imply a total probability under 100%. You back every outcome in the right proportions so that whichever one lands, the return is the same and beats the total staked.
How do you calculate arbitrage stakes?
For a two-way market, work out each outcome's implied probability (1 ÷ its odds), add them, and split your total stake in proportion to those probabilities. The guaranteed return is total stake ÷ (sum of implied probabilities).
Is arbitrage betting legal?
Placing bets at published odds is legal, but bookmakers dislike arbing and routinely limit or close accounts that do it. The maths here is sound; the practical risk is account restriction, prices changing between placing the two bets, and stake limits.
Why is there no arbitrage most of the time?
Because bookmakers build a margin in — the implied probabilities usually add to more than 100%, which is their edge. An arb only appears when two firms disagree enough that the combined book drops below 100%, which is rare and short-lived.
Spotting the under-100% book is arithmetic. Getting both bets down before it closes is the game.
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18+ · Education, not betting advice · No tips, no picks · BeGambleAware.org
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