In one sentence
Arbitrage means combining prices from different places so that every possible result leaves you with the same profit, with no dependence on who wins.
How it works
Different bookmakers and the exchange do not always agree. If one firm's price on an outcome is higher than the price you can lay it at elsewhere, you can back at the high price and lay at the low one. Whatever happens, one side pays for the other and a little is left over.
The same idea works across all outcomes of a market. If the best back prices across firms add up to less than 100% implied probability, backing each outcome in the right proportions guarantees a profit.
The profit per arb is usually small, often 1% to 3% of the stake. The skill is in speed, accuracy and keeping your bookmaker accounts open.
The maths
- L: the lay stake needed on the exchange.
- S b: your back stake at the bookmaker.
- O b: the bookmaker's back odds.
- O l: the exchange lay odds.
- c: exchange commission rate on winnings.
- O i: the best back price for each outcome across firms (for the second condition).
In plain English: size the lay so that the lay side's net return matches the back side's return; or, across firms, if the best prices add up to under 100% implied, a sure profit exists.
Worked betting example
Football, Match Odds. A bookmaker offers the draw in Aston Villa v Everton at 3.20. On Betfair you can lay the draw at 3.05, with 2% commission.
- Back £100 at 3.20.
- Lay stake = (£100 × 3.20) ÷ (3.05 − 0.02) = £320 ÷ 3.03 = £105.61.
- Lay liability = £105.61 × (3.05 − 1) = £216.50.
If the match is a draw:
- Bookmaker pays £100 × 2.20 = £220 profit.
- Exchange loses the liability of £216.50.
- Net: +£3.50.
If either team wins:
- Bookmaker stake lost: −£100.
- Exchange lay wins £105.61, less 2% commission = £103.50.
- Net: +£3.50.
A £3.50 profit either way, a 3.5% return on the £100 bookmaker stake, but £316.50 of capital was tied up (£100 plus £216.50 liability).
Where it's good
- Using bookmaker offers and price boosts, where the back price beats the exchange.
- Slow-to-update bookmakers after team news or market moves.
- Checking market consistency across firms as a data-quality signal.
- Low-risk use of spare capital, provided accounts stay open.
- Understanding the floor price at which a trade becomes a sure thing.
Limitations and pitfalls
- Bookmakers restrict or close accounts that arb regularly. This is the main practical limit, and it tends to come quickly.
- Prices move while you place the second leg. If the lay price drops before you are matched, the arb can become a loss.
- Palpable error rules let bookmakers void bets at obvious mistakes, leaving you with an unhedged exchange position.
- Returns on capital are small and much capital is locked up in liabilities.
- Different settlement rules (abandoned matches, extra time, void rules) can break the hedge.
How to build it
- Python with the Betfair Exchange API (betfairlightweight) and an odds-comparison feed; pandas to scan for books under 100%.
- Data: live prices from several bookmakers plus exchange depth at each price.
- Practical tip: always place the harder-to-get leg first (usually the bookmaker bet), then lay on the exchange, and check settlement rules match before you start.
Related methods
- Overround: arbs exist when the combined best book falls under 100%.
- Dutching: the same staking maths for several back bets.
- Back-lay hedging: locking in profit on a trade, a close cousin.
- Commission-adjusted EV: why commission must be in the lay formula.
- Market efficiency: arbs are brief because markets correct.