How the arbitrage calculator works
An arb (or sure bet) is a set of prices, usually from different bookmakers, where backing every outcome of an event costs less than it pays back. Type your total stake and the odds for each outcome, adding rows for a three-way market or a race. The arbitrage calculator shows the stake and return for each outcome, the guaranteed profit (or the worst case if there is no arb), the profit as a percentage of what you staked, and the combined book.
The combined book is the sum of 1 / decimal odds across every outcome. Under 100% the prices form an arb. Each stake is the total stake x (1 / its odds) / the combined book, so every outcome returns the same.
Two outcomes both at 2.10 with £100: the book is 95.24%, so you stake £50 on each and get £105 back either way, a 5% profit. Three outcomes at 3.0, 3.6 and 4.0 with £100: stake £38.71, £32.26 and £29.03, and £116.13 comes back whatever wins. That one is a teaching example; real arbs are usually far thinner.
Why round your stakes
Exact arb stakes come out as odd amounts like £48.24, and a bookmaker can notice a customer who always bets to the penny. The Round stakes to box rounds each stake to 10p, 50p or £1, and the calculator then shows what the rounding costs.
At 2.20 and 2.05 with £100, exact stakes of £48.24 and £51.76 return £106.12 either way. Rounded to £1, the stakes are £48 and £52: one outcome returns £105.60 and the other £106.60, so the guaranteed profit drops from £6.12 to £5.60. On the three-way example above, £1 rounding cuts it from £16.13 to £15.20. If rounding pushes one outcome into a loss, the calculator says so; try a finer rounding.
Arbitrage, dutching and matched betting
The maths is the same as the dutching calculator: split a stake in proportion to 1 / odds. The difference is purpose. Dutching backs some of the runners because you think one of them will win, so you can still lose. An arb covers every outcome at prices that add up to less than 100%, so the result doesn't depend on who wins. Matched betting is different again: it backs with a bookmaker and lays on an exchange to extract the value of free bets and offers, usually at a small loss on the qualifying bet. For that, use the matched betting calculator.
The risks of arbitrage betting
A guaranteed profit is only guaranteed if every bet stands at the price you took. The usual ways it goes wrong:
- Price moves: one price shortens before you place the second bet, and the arb disappears.
- Obvious error rules: bookmakers' terms typically let them void or resettle a bet struck at a clearly wrong price (a "palp"), which can leave the other side uncovered.
- Voids on one side: different rules on non-runners, abandonments or settlement can void one bet and leave the other running.
- Limits: a stake can be cut to a fraction of what you asked for, so the stakes no longer balance.
Bookmakers also restrict accounts for commercial reasons. In the Gambling Commission's figures for 2024, 4.31% of active betting accounts had some commercial restriction and 2.23% had been closed for commercial reasons. The Commission says operators are entitled to act in their commercial interests, but should be transparent about how, when and why an account might be restricted.