Arbitrage betting means backing every possible outcome of an event, each at a different bookmaker, when their prices disagree by enough that the return is the same whichever outcome happens and larger than the total you staked. Bettors call one of these an arb. On paper the result of the match no longer matters.
In practice an arb swaps one risk for several others. The edge is usually small, often a percent or two of the money staked, and it depends on every bet standing exactly as placed, at the price you saw, under rules that treat the event the same way. This guide shows how to spot an arb from the odds, the stake formula for two-way and three-way markets with numbers that add up to the penny, and the things that turn a small profit into a loss. It assumes you are comfortable converting odds to implied probability.
How an arbitrage works
Every bookmaker builds a margin into its prices, so the implied probabilities of all outcomes in one market add up to more than 100%. An arb appears when you take the best price for each outcome from different bookmakers and the combined total drops below 100%.
Take a tennis match. Bookmaker A offers Player 1 at 2.10 (11/10, +110). Bookmaker B offers Player 2 at 2.00 (evens, +100). On their own, each bookmaker's market is overround as usual, but the two best prices imply 1 ÷ 2.10 = 47.62% and 1 ÷ 2.00 = 50.00%, a total of 97.62%. Because that is below 100%, a stake split between the two can return more than it costs whoever wins.
The size of the edge is 1 ÷ total - 1, so 1 ÷ 0.9762 - 1 = 2.44% of the money staked. If the total had come to 100.5%, there would be no arb, only two bets that together lose half a percent on average. The odds calculator converts fractional and American prices to decimal if you need to check a line quickly.
The stake split formula
There are two ways to size the stakes, and they give the same answer.
The first starts from the total you want to stake. Call the total T and the sum of the implied probabilities S. Then:
- Stake on each outcome = T × (1 ÷ that outcome's odds) ÷ S
- Return, whichever outcome wins = T ÷ S
- Profit = T ÷ S - T
The second starts from the return you want. Pick a target return R and stake R ÷ odds on each outcome. The total stake is whatever those add up to. This version is easier to do in your head and makes the numbers come out cleanly, which is why the examples below use it first.
Two-way example: a tennis match
Using the 2.10 and 2.00 prices, aim for a return of £210. Stake £210 ÷ 2.10 = £100 on Player 1 at Bookmaker A and £210 ÷ 2.00 = £105 on Player 2 at Bookmaker B. You have staked £205.
If Player 1 wins, Bookmaker A pays £100 × 2.10 = £210 and the £105 at Bookmaker B is lost. If Player 2 wins, Bookmaker B pays £105 × 2.00 = £210 and the £100 at Bookmaker A is lost. Either way you get back £210 for £205, a profit of £5, which is 2.44% of the total stake.
The first formula gives the same split. With T = £500 and S = 0.97619, the Player 1 stake is £500 × 0.47619 ÷ 0.97619 = £243.90 and the Player 2 stake is £256.10. A Player 1 win returns £243.90 × 2.10 = £512.19. A Player 2 win returns £256.10 × 2.00 = £512.20. The penny difference is rounding, and the profit is about £12.20 on £500, again 2.44%.
Three-way example: a football match
Football (soccer) match result markets have three outcomes, so you need three bets. Suppose the best prices are home 2.50 (6/4, +150) at Bookmaker A, draw 3.50 (5/2, +250) at Bookmaker B and away 3.40 (12/5, +240) at Bookmaker C. The implied probabilities are 40.00% + 28.57% + 29.41% = 97.98%, so there is an arb worth 1 ÷ 0.9798 - 1 = 2.06%.
Aim for a return of £350. The stakes are £350 ÷ 2.50 = £140.00 on the home side, £350 ÷ 3.50 = £100.00 on the draw and £350 ÷ 3.40 = £102.94 on the away side, a total of £342.94.
A home win pays £140 × 2.50 = £350.00. A draw pays £100 × 3.50 = £350.00. An away win pays £102.94 × 3.40 = £349.996, which rounds to £350.00. Every outcome returns £350 for £342.94 staked, a profit of £7.06, or 2.06%.
Three-way arbs need all three bets to stand. One void or rejected bet leaves you holding two thirds of a position on an outcome you never meant to back on its own.
Why arbs exist
Bookmakers do not share one price. Each one sets odds from its own model, its own customers and its own exposure, and they update at different speeds. A few common causes of gaps:
- A bookmaker is slow to react to team news, a weather change or a big move elsewhere. The line movement guide explains how prices move as information arrives.
- A bookmaker deliberately shades a price because too much money has come in on one side.
- A price boost or special offer temporarily lifts one selection above the market.
- An exchange price reflects what other bettors will accept, which can differ from a bookmaker's line.
- Someone makes a mistake when entering a price.
The last two are where many of the biggest-looking arbs come from, and they are also the ones most likely to be cancelled, which leads straight into the risks.
Commission and costs
If one leg is on a betting exchange, commission comes off net winnings on that leg. Its effective price is 1 + (odds - 1) × (1 - commission). At 2% commission, 2.10 becomes 1 + 1.10 × 0.98 = 2.078. The two-way arb now implies 48.12% + 50.00% = 98.12%, and the edge shrinks from 2.44% to 1.91%. With the same £205 total, the stakes become £100.54 on the exchange and £104.46 at Bookmaker B, and both outcomes return £208.92, a profit of £3.92 instead of £5. At 5% commission the effective price is 2.045 and the edge falls to 1.11%.
Payment fees, currency conversion and the cost of keeping money spread across several accounts all come off the same thin margin. Our guide to matched betting covers exchange commission in more depth.
The risks that turn an arb into a loss
None of these risks appear in the formula, and every regular arb bettor runs into them.
Prices move before the second bet goes on. You place £100 on Player 1 at 2.10, and by the time you reach Bookmaker B, Player 2 has dropped from 2.00 to 1.90. The total is now 47.62% + 52.63% = 100.25%, so there is no arb left. To return £210 on Player 2 you need £210 ÷ 1.90 = £110.53, a total stake of £210.53 for a £210 return. You lose about £0.53 whichever player wins, and that is the good outcome. If you leave the second bet unplaced, you simply hold a £100 bet on Player 1.
Bets are voided for a palpable error. Most bookmaker terms allow an obvious pricing mistake (a palp) to be voided or resettled at the correct price. If the £100 at 2.10 is voided, you get it back, but the £105 on Player 2 at 2.00 is now an ordinary bet that either wins £105 or loses £105.
Rules differ between bookmakers. Tennis is the classic case. One bookmaker voids all bets if a player retires, another settles in favour of the player who goes through. Put the Player 1 bet with the first and the Player 2 bet with the second. If Player 2 retires injured, the Player 1 bet is void (£100 back) and the Player 2 bet loses (£105 gone), a net loss of £105 on a position that looked locked in. Football has its own version: one bookmaker may settle on 90 minutes, another on the result including extra time.
Stakes are limited. A bookmaker may accept only part of your stake at the price, leaving the legs out of balance.
Accounts get restricted. Bookmaker terms generally let them limit stakes or close accounts, and an account that only ever bets at the highest price in the market, on obscure lines, in odd amounts such as £102.94, is easy to spot. Most people who arb regularly find their accounts limited sooner or later, and a limited account cannot be used for arbs or anything else at a useful size.
Pros
- When every bet stands, the return is the same whatever happens in the event
- Builds a sound habit of comparing prices across bookmakers
- The arithmetic is simple and checkable before you stake
Things to consider
- Edges are small, often a percent or two of the total staked
- Odds can move between the first and last bet
- Palpable errors can be voided, leaving one side exposed
- Different settlement rules can make both bets lose
- Bookmakers commonly limit or close accounts that bet this way
- Large amounts of money are tied up across several accounts
Before you place an arb
Arbitrage is a different activity from value betting, which accepts losing bets in exchange for long-run edge, and from hedging, which locks in a result after a bet has already moved in your favour. If you still want to try it, check the following before the first stake goes on.
- Recalculate the total implied probability yourself and confirm it is below 100%.
- Read the settlement rules on every leg for retirements, extra time, abandonment and void selections.
- Confirm each bookmaker will accept the full stake before placing the first leg.
- Place the leg most likely to move or be limited first.
- Include commission and any fees in the calculation, not after it.
- Keep a record of every leg so a void or resettlement is easy to trace.
Betting laws differ by country and, in the US, by state, and arbitrage betting is not a way around any of them. Only use operators licensed where you live, and read their terms. If betting starts to feel like work you cannot step away from, or the money involved is more than you can afford to lose, our responsible gambling page explains the tools and support available.
Frequently asked questions
Is arbitrage betting illegal?
In places where sports betting is legal, placing bets at prices that bookmakers offer is generally not a crime, but many bookmakers' terms allow them to limit or close accounts they believe are arbing. Laws vary by country and US state, so check the rules where you live. This is not legal advice.
How do I know if odds are an arb?
Convert the best price on each outcome to implied probability (1 ÷ decimal odds) and add them up. If the total is below 100%, the prices form an arb before costs. 2.10 and 2.00 give 47.62% + 50.00% = 97.62%.
How do I split my stakes on an arb?
Choose a target return and divide it by each price. For a £210 return at 2.10 and 2.00, stake £100 and £105. Every outcome then returns £210 for £205 staked.
What happens if one side of an arb is voided?
You get that stake back, and the other bet becomes an ordinary bet that can win or lose. On a three-way arb, a single void leaves you exposed on two outcomes.
Why do bookmakers restrict arbitrage bettors?
An arbitrage bettor takes the bookmaker's weakest prices and rarely bets anywhere else, so the bookmaker expects to lose money on that account. Most bookmaker terms allow them to limit stakes or close the account.