Quick answer: an arbitrage bet (an “arb” or “sure bet”) means backing every outcome of an event at different bookmakers whose odds disagree, so that if every bet stands, you get back more than you staked whatever happens. It works when 1 ÷ odds for each outcome adds up to less than 1. Enter the best odds for each outcome below and the calculator splits your stake, shows the return and tells you if the arb is real.
Stakes are split so every outcome returns about the same amount. Commission, if you enter it, is taken from that outcome’s winnings only. Rounded stakes change the profit slightly, and the calculator shows the result after rounding. Odds move and bookmakers can void or limit bets, so an arb is never a sure thing.
How to use the arbitrage calculator
- Pick 2-way or 3-way. Use 2-way for markets with two outcomes, such as a tennis match. Use 3-way for markets like a football match result (home, draw, away).
- Enter your total stake, the amount you want to spread across all the bets.
- Enter the best decimal odds for each outcome, each from a different bookmaker or exchange. To convert fractional or American odds, see the table below or use our odds calculator.
- If one leg is on a betting exchange, enter its commission and pick that outcome. The calculator lowers those odds to what you really get after commission.
- Choose how to round your stakes. The result shown is after rounding, so you can see whether round numbers still leave a profit.
- Check the odds again just before you place each bet, and place the bets as close together as you can.
What is arbitrage betting?
Each bookmaker sets its own odds and builds in a margin, so normally 1 ÷ odds for every outcome adds up to more than 1 (more than 100% when shown as implied probabilities). Sometimes two or three bookmakers disagree enough that, if you take the best price for each outcome from a different one, the total drops below 100%. That gap is the arb.
You then stake more on the shorter-priced outcome and less on the longer one, so the return is the same whichever outcome wins. Because it only uses price differences, arbing needs no free bets. That’s the difference from matched betting, which uses bookmaker promotions and lays them off on an exchange.
Arbitrage betting formulas
d is the decimal odds for each outcome, T your total stake and c the exchange commission as a decimal (5% = 0.05):
| What you want | Formula |
|---|---|
| Implied probability of one outcome | 1 ÷ d |
| Book total (S) | 1 ÷ d₁ + 1 ÷ d₂ (+ 1 ÷ d₃ for 3-way) |
| Is it an arb? | Yes if S is below 1 |
| Stake on each outcome | T × (1 ÷ d) ÷ S |
| Return if any outcome wins | T ÷ S |
| Profit | T ÷ S − T |
| Return on total stake (ROI) | 1 ÷ S − 1 |
| Odds after exchange commission | 1 + (d − 1) × (1 − c) |
Arb sites quote two different percentages. Some show the gap below 100% (1 − S), others the profit on your stake (1 ÷ S − 1). For odds of 2.10 and 2.05 the first is 3.60% and the second 3.73%. Our calculator shows the second, because that’s the money you make.
Arbitrage betting examples
Two-way (tennis). One bookmaker offers 2.10 on player A and another 2.05 on player B. S = 0.4762 + 0.4878 = 0.9640, so it’s an arb. With £100, you stake £49.40 on A and £50.60 on B. If A wins you get back £103.74; if B wins, £103.73. That’s a profit of £3.73, or 3.73% of your stake.
Three-way (football). The best prices are 2.60 home, 3.60 draw and 3.40 away. S = 0.3846 + 0.2778 + 0.2941 = 0.9565, so it’s an arb. With £100, you stake £40.21, £29.04 and £30.75. Each result returns £104.54 to £104.55, a profit of about £4.54 (4.55% before rounding to the penny).
These are made-up odds to show the maths. Real arbs are usually smaller, and you have to find them before the prices change.
How rounding stakes changes your profit
Round stakes look more natural, but each outcome then returns a different amount, and what you can count on is the lowest one. In the football example, rounding to £40, £29 and £31 gives returns of £104.00, £104.40 and £105.40, so the profit you can rely on drops from £4.54 to £4.00.
On a thin arb, rounding can wipe out the profit. Odds of 2.05 and 1.97 add up to 99.54%, a 0.46% arb: £49 and £51 return £100.45 or £100.47. Round both stakes to £50 and you get £102.50 if the first outcome wins, but only £98.50 if the second does, a £1.50 loss. Set the rounding in the calculator to check before you bet.
How exchange commission affects an arb
Betting exchanges charge commission on your net winnings, so a back bet at 2.05 with 5% commission really pays like odds of 1 + 1.05 × 0.95 = 1.9975. In the tennis example, if the 2.05 is on an exchange at 5%, the arb shrinks from 3.73% to 2.37%: £48.75 and £51.25 return £102.38 and £102.37.
It can also turn an arb into a loss. Odds of 2.02 on both sides look like a 1% arb, but with 5% commission on one of them you lose about £0.29 per £100. Always enter your exchange’s commission; our matched betting calculator page lists the main exchanges’ rates. Deposit fees or currency conversion work the same way: they reduce what you really get back.
How to convert odds to decimal
| Odds format | To decimal | Example |
|---|---|---|
| Fractional n/d | n ÷ d + 1 | 5/2 = 3.50; 1/4 = 1.25 |
| American, positive (+A) | A ÷ 100 + 1 | +150 = 2.50 |
| American, negative (−A) | 100 ÷ A + 1 | −200 = 1.50; −110 = 1.909 |
How big are arbs, and how long do they last?
Small, and not long. Guides often quote 1% to 5% per arb, but many are lower, and stake limits cap how much you can put on each one. Prices tend to correct within seconds or minutes. That’s why paid scanners such as OddsJam, RebelBetting and BetBurger exist: they compare prices across many bookmakers to spot arbs quickly. We don’t recommend any of them, and no tool can promise a profit.
What can go wrong?
- A bet is voided. Bookmakers can cancel bets struck at an obviously wrong price (a “palpable error”). If one leg is voided and the other stands, you are left with an ordinary bet that can lose.
- Bookmakers settle the same event differently. Tennis retirements are the classic case: some bookmakers void bets unless the match is completed, others settle them once the first set is finished. One leg can be paid while the other is voided. Read each bookmaker’s rules for that sport first.
- The odds move between placing your first and second bet, leaving you with a smaller arb, no arb or a loss.
- Your account gets limited. Bookmakers can cut your maximum stakes, remove offers or close accounts they think are arbing (often called being “gubbed”).
- Simple mistakes, such as backing the wrong selection, the wrong market or the wrong stake, turn an arb into a real gamble.
Is arbitrage betting legal?
In the UK, yes: arbing isn’t against the law. But many bookmakers’ terms let them restrict or close accounts they suspect of it, and some ban it outright, so it is a breach of contract risk rather than a legal one. Under HMRC guidance, betting winnings are not normally taxable for UK individuals, even when you bet in a systematic way. Rules differ in other countries and can change, so this isn’t tax advice.
Arbitrage betting vs matched betting
| Arbitrage betting | Matched betting | |
|---|---|---|
| Where the edge comes from | Bookmakers disagreeing on odds | Free bets and promotions |
| Bets you place | Back every outcome, at different bookmakers | Back at a bookmaker, lay on an exchange |
| Typical result | A small return on each arb, if every bet stands | A small loss on qualifying bets, most of each free bet’s value kept |
| Main risks | Voids, odds moving, account limits | Mistakes, offer terms, account limits |
| Our tool | This calculator | Matched betting calculator |
More tools: the no vig calculator shows a bookmaker’s margin in any market, the odds calculator converts odds formats, and the each way calculator and accumulator calculator work out returns on those bets. To size bets when you have an edge, try the Kelly criterion calculator.
How we checked this
We built the calculator ourselves and tested it in a browser against every example on this page, which match our own calculations to the penny. The formulas are standard maths; the effective odds after commission are our own working, based on exchanges charging commission on net winnings. Everything else is checked against at least two independent sources:
- Arb condition and stake formula: Wikipedia and TopEndSports.
- Commission on net winnings: Wikipedia and Sporting Life.
- Odds conversion: Covers and TopEndSports.
- Voids, settlement rules, odds moving and account limits: Soccerway, RG.org, Flashscore, Action Network and IDnow.
- Legality and bookmaker terms: LiveScore, Soccerway, RG.org and SEON.
- Tax: HMRC’s manual and Pulse Accountants.
- Arb sizes, how long they last and scanners: Soccerway, RG.org, SEON, TopEndSports and 11v11.
Last checked: 9 October 2026. Betting is for adults (18+) only. Arbitrage betting isn’t risk-free and it isn’t a way to earn a living: bets get voided, odds move and accounts get limited. If betting stops being fun, our responsible gambling guide lists ways to set limits, and our gambling budget calculator helps you plan.
Arbitrage betting calculator FAQs
How do you calculate arbitrage bets?
Add up 1 ÷ odds for every outcome. If the total is below 1, it’s an arb. Stake on each outcome = total stake × (1 ÷ its odds) ÷ that total. Odds of 2.10 and 2.05 give a total of 0.964, so £100 splits into £49.40 and £50.60.
Is arbitrage betting legal?
Yes, in the UK it isn’t illegal. But many bookmakers’ terms let them limit or close accounts they suspect of arbing.
Can bookmakers ban you for arbing?
Yes. Common responses are lower maximum stakes, no more offers, or closing the account.
How much can you make from arbitrage betting?
Usually a small percentage per arb, often quoted as 1% to 5% and many lower, and stake limits cap how much you can bet. No amount is guaranteed.
Is arbitrage betting risk-free?
No. A voided bet, different settlement rules, odds moving before you place the second bet, or a simple mistake can all leave you with a loss.
