Arbitrage Betting Calculator

How arbitrage betting works

Bookmakers price the same event differently. Occasionally the best odds on every outcome, taken from different bookmakers, add up to an implied probability below 100%. Back every outcome in the right proportions and you are paid more than you staked no matter who wins. That gap is your arb margin, typically 1% to 5%.

The maths

Implied probability = 1 ÷ decimal odds. Add them up for every outcome. If the total is under 1.00 an arb exists.
Stake on outcome = total stake × (1 ÷ odds) ÷ sum of implied probabilities.
Profit = total stake ÷ sum of implied probabilities − total stake.

Things to watch

Odds move fast, so place the exchange or sharper leg first and the softer bookmaker leg immediately after. Check both bookmakers settle the market under the same rules (for example, tennis retirement rules differ). Keep stakes rounded and varied, as bookmakers restrict accounts that only ever bet on arbs. Many people combine arbing with matched betting offers, which is far friendlier on account longevity.

How to use the arbitrage betting calculator

Enter the best available price for each outcome, from whichever bookmaker is offering it, plus the total you want to stake. The calculator sizes each stake so the return is identical whichever result lands, and tells you whether the combined prices actually leave a profit.

The test is one number. Add up 1 divided by each decimal price. Below 100% is an arb; at or above 100% there is nothing there. Everything else the calculator does is dividing your stake up in the right proportions.

A worked two-way example

A tennis match. One bookmaker has the favourite at 2.10; a second has the underdog at 2.05. You have £200 to place.

Selection	Odds	Stake	Return if it wins
Favourite (bookmaker A)	2.10	£98.80	£207.47
Underdog (bookmaker B)	2.05	£101.20	£207.47

The two implied probabilities total 96.40%, so the market is 3.6% underpriced across the two books. £200 out, £207.47 back either way: £7.47 profit, or 3.73%, locked before the match starts.

A three-way market works the same way. At 2.80 the home win, 3.60 the draw and 3.10 the away win, the implied total is 95.75% and £300 returns £313.32 whichever way it goes — £13.32 profit.

Illustrative prices, not live odds. Arbs of this size are uncommon and rarely last long.

Arbitrage betting in the UK: the honest position

Arbing is legal. It breaks no law, the profit is not taxed as income, and nobody is going to come after you for it. It does breach most bookmakers’ terms, which is a commercial matter rather than a legal one — the same position we set out on whether matched betting is legal.

The real problem is shorter-term than any of that. Arbing is the single fastest way to get your bookmaker accounts restricted. The pattern is unmistakable: a bet placed at the exact moment a price moves out of line, for an odd amount, on a market you have never touched before, with no losing bets around it. Trading teams look for precisely this, and the reaction is usually stake limits within weeks rather than months.

That is the trade-off worth understanding before you start. An account that would have produced offers for two years can be reduced to £2 stakes in a fortnight, and the few percent you took from a handful of arbs rarely covers what those offers were worth. Account longevity is the constraint that matters, and matched betting versus arbitrage sets out the comparison properly.

What goes wrong in practice

• The second leg moves before you place it. You have the first bet on and the price you needed is gone. Now you are holding an open position, not an arb — and that is the most common way arbing loses money.
• The bet is voided on one side only. A palpable error or a rule-4 deduction can settle one leg and not the other, leaving you exposed. See what happens when a bet is voided.
• The stake gets limited mid-arb. You are offered £12 instead of £100 on the second leg, and the arb becomes a partial position.
• The margin is thinner than it looks. Withdrawal fees, currency conversion and the cash tied up across a dozen accounts all come out of a 2% edge.

Frequently asked questions

What counts as a good arb percentage?

Most genuine arbs sit between 1% and 3%. Anything above about 5% is worth a second look before you commit — it usually means a price has been entered wrongly and will be voided, or you have misread which market you are in.

Can I arb between a bookmaker and an exchange?

Yes, and it is often easier, because the exchange prices one side for you. Remember to account for commission on the exchange leg — the matched betting calculator handles that pairing directly.

Is arbitrage betting worth it?

It depends what you are spending. The profit per bet is small and the cost is account life. For most people the same accounts produce far more from promotions over a couple of years than from arbing them for a few weeks. If you are going to arb, it is worth doing on accounts you have already exhausted.

How is this different from dutching?

Dutching spreads a stake across selections so the return is equal — the maths is the same, but at a single bookmaker the total is always above 100%, so you lose the margin. Arbitrage is what you call it when prices from different bookmakers bring that total below 100% and the equal return becomes a profit.

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