Free calculator

Arbitrage Betting Calculator

Check whether 2 or 3 odds make a sure bet and split your stake so every outcome pays the same. Decimal, fractional or American odds, with optional stake rounding.

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Calculator

Exact stakes like £41.86 are a neat way to tell a bookmaker what you are up to.

How do you calculate an arbitrage bet?

Add up 1 ÷ decimal odds for every outcome. Below 1 is an arb, and profit % = 1 ÷ sum − 1. Stake on each outcome = total × (1 ÷ odds) ÷ sum.

What odds make a sure bet?

Any full set of outcomes whose implied probabilities add up to less than 100%. 2.10 and 2.10 add up to 95.2%, for about 5.0% profit. 1.90 and 1.90 add up to 105.3%, which is about 5.3% overround and no arb.

Do bookmakers limit arbitrage bettors?

They can limit anyone. The Gambling Commission says operators can manage liabilities by capping stakes, down to a stake factor of 0.00. It does not single out arbers, but taking the best price on the board every time is not a great way to stay anonymous.

Can a sure bet still lose money?

Yes. Odds can move before the second bet is on, a stake can be capped, and a voided bet leaves the other unhedged. Operators must publish their rules on voids and errors, so read them first.

Do you pay tax on arbitrage betting winnings in the UK?

The Gambling Commission says winnings from gambling for customers are tax-free in the UK, regardless of the amount. HMRC guidance says living off betting does not by itself make it a trade.

The formula

Arbitrage % = sum of (1 ÷ decimal odds) across every outcome
An arb exists when that sum is below 1 (100%)
Profit % = 1 ÷ sum − 1
Stake on outcome i = total stake × (1 ÷ odds i) ÷ sum
Return = stake i × odds i (the same for every outcome before rounding)
If the sum is above 1: overround = sum − 1

Worked example

Two bookmakers both offer 2.10 on opposite sides. Sum = 1/2.10 + 1/2.10 = 0.952.

Profit = 1/0.952 − 1 = 5.0%. On £100, stake £50 on each and either result returns £105.


Uneven prices: 2.50 and 1.80. Sum = 0.4 + 0.556 = 0.956, profit 4.65%.

Stakes on £100 are £41.86 and £58.14. Either way you get back £104.65.

Round to the nearest £1 and the stakes become £42 and £58. Returns are £105.00 and £104.40, so the worst case is £4.40 profit.


No arb: 1.90 and 1.90. Sum = 1.053, so the overround is about 5.3%. That is the bookmaker being paid, not you.

Methodology

How it calculates

  • Converts every price to decimal odds and adds up 1 ÷ odds across the outcomes.
  • If the sum is below 1, splits the total stake so every outcome returns the same amount.
  • With rounding on, rounds each stake, then reports worst-case profit as the lowest return minus the amount actually staked.
  • If the sum is 1 or above, shows the overround instead of stakes.

Formula

Arbitrage % = sum of (1 ÷ decimal odds) across every outcome
An arb exists when that sum is below 1 (100%)
Profit % = 1 ÷ sum − 1
Stake on outcome i = total stake × (1 ÷ odds i) ÷ sum
Return = stake i × odds i (the same for every outcome before rounding)
If the sum is above 1: overround = sum − 1

Assumptions

  • Assumes every bet is accepted at the odds and size entered, and that every bet stands. Bookmakers can cap stakes, odds can move, and published rules can void bets.
  • The outcomes must be mutually exclusive and cover every result. The tool cannot check that for you.
  • No commission, fees or currency costs. No live odds feed; you type the prices.
  • UK tax position per the Gambling Commission: customer gambling winnings are tax-free. Other countries can differ.

Edge cases

  • Blank fields are ignored (not treated as zero). No results show until every input is valid.
  • Odds of 1.0 or below are invalid. American odds below 100 in size are invalid.
  • A sum of exactly 1 is no arb, with 0% overround.
  • Rounding can push worst-case profit below zero, or round a stake to zero and leave an outcome uncovered. The tool flags both.

Sources

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FAQ

Is an arbitrage bet really risk free?

The maths is. The real world is not. Odds can move before your second bet goes on, stakes can be capped, and a voided bet leaves the other one unhedged.

Can bookmakers limit my account?

Yes. The Gambling Commission says operators can act in their commercial interests and manage liabilities, usually by cutting your maximum stake to a percentage of the normal one. A stake factor of 0.00 stops you betting altogether.

Can a bookmaker void a winning bet?

It depends on its rules. Licensed betting operators must publish when they will void a bet and how they treat errors, so a price that looks too good may not survive being a mistake (a palpable error, in the trade). Read the rules before you rely on one.

Are arbitrage winnings taxed in the UK?

The Gambling Commission says winnings from gambling for customers are tax-free in the UK, whatever the amount. HMRC guidance says being skilled or systematic enough to live off betting does not by itself make it a trade. Unusual setups or other countries can differ, so check yours.

Why does rounding change my profit?

Exact stakes make every return equal. Rounded stakes do not, so one outcome pays less than the others. The calculator shows that worst case, and on small stakes rounding can wipe out the arb.

Does this include exchange commission?

No. The calculator takes the odds as you enter them, so commission, fees and any currency costs still need to come off. On a thin arb that can be the whole profit.

Sources

Rates, rules or specs last checked 1 Nov 2026. Confirm on the official page before you act.

Not financial advice. This calculator is for education only. Double-check results before you make money decisions. Past moves do not predict future ones.