Arbitrage Betting With Exchange Commission: Stakes, Margin and Risks
Prices that add up to under 100% leave room for a margin. Here is the arithmetic, and the legs that can break it.
Arbitrage betting means backing every outcome of one event at prices whose implied probabilities add up to less than 100%, with stakes split so that the result is the same on every outcome. Add 1 ÷ odds for each outcome; a total below 100% leaves room for a margin. A betting exchange changes the sums in one way: commission comes off the winnings of an exchange leg, so the margin shrinks. What stays open is each leg. A price can move, and a bet can be refused, cancelled or matched in part, and then the result is no longer the same on every outcome. Below: the calculator, the rule, the commission, and four situations for a pair of legs, in pounds.
Try two prices, then three
The two panels are worked out in your browser; nothing is sent anywhere.
Arbitrage calculator
Type the prices you see and the calculator splits one total stake across the outcomes of a market, then shows what each outcome returns once exchange commission is out. It is arithmetic on typed prices: it cannot tell whether a price is still on offer or will be accepted. Everything is worked out in your browser and nothing is sent anywhere.
Back every outcome
Pick two or three outcomes that cover one market, type the decimal odds for each and say where each price sits. The total stake is split so that every outcome returns the same amount.
At these prices the split returns more than the total stake on every outcome. That is arithmetic on quoted prices: it says nothing about whether each leg is matched, accepted or settled at the price you typed.
Commission is applied to each exchange leg's winnings on its own. Two legs in the same exchange market are charged on that market's net profit instead, which this panel does not model.
Example shown: outcome 1 at 2.09 with a bookmaker, outcome 2 at 2.03 on an exchange, commission 3%, total stake £800. Replace them with your own.
Back at a bookmaker, lay at an exchange
Back a selection at a bookmaker and lay the same selection at an exchange. The lay stake is sized so that the result is the same whether the selection wins or loses.
The commission is taken on the lay's winnings at the exchange; the bookmaker back bet carries none. A lay can stay partly matched and a bookmaker can cut a stake, so the figures are arithmetic on the prices you typed.
Example shown: back £140 at 2.34 with a bookmaker, lay at 2.26 on an exchange with 3% commission. Replace them with your own.
The rule: prices that add up to under 100%
£17.42. That is what £800 returns above its stake when two prices and a 3% example commission leave a 2.18% margin. It is also the first number to disappear.
Two prices that disagree are only half of it. What counts is whether the chances they imply, 1 ÷ odds, add up to less than 100%. Four lines carry the whole method.
Book = sum of 1 ÷ odds
Margin = 1 ÷ book - 1
Stake on an outcome = total stake ÷ (odds × book)
Every outcome then returns total stake ÷ book
For an exchange leg, "odds" means the price after commission, which the next section works out. Here is the calculator's opening pair, £800 across 2.09 with a bookmaker and 2.03 on an exchange at an example 3% (rounded to the penny):
- Book
- 97.87%
- Stake, outcome 1 (bookmaker, 2.09)
- £391.11
- Stake, outcome 2 (exchange, 2.03, 3%)
- £408.89
- Return on either outcome
- £817.42
- Result
- +£17.42
- Margin
- 2.18%
Three outcomes, no commission
Say a football match is priced 3.62 on Home, 3.46 on the Draw and 2.38 on Away, at three bookmakers, and the total stake is £750. The book is 98.54%. The stakes are £210.25, £219.97 and £319.79 (the pennies are rounding, so together they run a penny over £750). Each outcome returns about £761.09, a margin of 1.48%.
Some people call this a surebet. The name promises more than the arithmetic does. This is arithmetic on typed prices. It does not find prices, and it does not say whether any venue will take the stake. Where a price comes from is a separate question, the one the value betting guide asks. What each venue takes before any of this pays is on the page on break-even and costs.
The calculator takes decimal odds. A tool to turn any format into decimals does the conversion, and the same page runs a margin check on one set of prices.
What an exchange does to the margin
On Orbit Exchange, commission comes off the net profit of a market, not off a stake or a loss. Orbit's own betslip message reads "A commission is charged on net profit from each market". An exchange leg at odds O and commission rate c is therefore worth 1 + (O - 1) × (1 - c) in place of O. That holds for a leg that is your only bet in its market; two exchange legs in one market are charged on that market's net profit instead, which the calculator does not model.
At 2.03 and an example rate of 3%, taken as 0.03 in the formula (the calculator's own field takes 3), that is 1 + 1.03 × 0.97, or 1.9991. The leg that looked like 2.03 behaves like a price just under 2.00, and that is the number the calculator uses. The rate is yours to type: the calculator takes your own, the commission page lists what each broker quotes, and prices after commission sets one price against another.
Run the same two prices, 2.09 and 2.03, through a range of example rates. With no commission the margin is 2.98%. At 3% it is 2.18%. It is gone at 10.93% (a figure the arithmetic produces, not a rate this page attributes to anyone).
Prices 2.09 at a bookmaker and 2.03 on an exchange, any total stake. Example rates only. The margin is gone at 10.93%.
Show the data table
| Commission | Margin |
|---|---|
| 0% | +2.98% |
| 2% | +2.45% |
| 4% | +1.91% |
| 6% | +1.36% |
| 8% | +0.81% |
| 10% | +0.26% |
Now the other shape: back at a bookmaker, lay at an exchange. The lay stake is back stake × back odds ÷ (lay odds - commission), with the commission as a decimal, so 3% is 0.03. Say £140 is backed at 2.34 with a bookmaker and laid at 2.26 on an exchange at an example 3%. The lay stake is £146.91 and its liability £185.10. The result is +£2.50, or 1.78% of the back stake, on either outcome while both bets stand at those prices. Below lay odds of 2.2998 the result is positive, at 2.2998 it is zero and above it negative; the calculator shows 2.299, the highest price to three decimals that still leaves a positive result. How a lay works has the mechanics.
This variant suits a price you can lay at an exchange at a size the market holds. It is not ideal if the lay is likely to stay partly matched.
Where a leg goes wrong
Picture a bettor with stakes the prices can fill and both venues open to them. The question stops being whether a bookmaker will take the bet. It becomes whether both legs will stand at the prices typed. Getting two bets to sit still is the hard part, and the arithmetic stays silent on it.
Take the pair from the calculator and put it through four situations, all hypothetical. The stakes and prices are in the chart note.
£391.11 on outcome 1 at 2.09 with a bookmaker, £408.89 on outcome 2 at 2.03 on an exchange, an example 3% commission, worked from unrounded stakes. Hypothetical. "Half" is a leg matched for half its stake; "void" is a bet the bookmaker cancels.
Show the data table
| Situation | Result |
|---|---|
| Both legs, 1 wins | +£17.42 |
| Both legs, 2 wins | +£17.42 |
| Leg 1 only, 1 wins | +£426.31 |
| Leg 1 only, 2 wins | -£391.11 |
| Leg 2 half, 1 wins | +£221.86 |
| Leg 2 half, 2 wins | -£186.85 |
| Leg 1 void, 1 wins | -£408.89 |
| Leg 1 void, 2 wins | +£408.52 |
With leg 1 only, the bet is a plain one on outcome 1. With leg 2 half matched, the exchange leg is matched for £204.45 of £408.89. When leg 1 is voided, the bookmaker cancels it after leg 2 is matched, and the exchange leg is left as a bet on outcome 2.
Here is what the brokers and the exchange write about a price that moves or a bet that is cancelled. Sportmarket's article on its Arb Calculator says "Odds can change: The available price may move before the hedge is placed." and "Liquidity matters: Available stake at the displayed price may affect execution." AsianConnect's article on arbitrage says "By the time you log into each platform and place a bet, the odds may have shifted." Partial matching has its own page: how a stake gets matched in part.
Orbit's exchange rules cover the exchange leg. For related bets on a combination of its exchange products and/or the betting products of other third parties, they say "it is possible for bets on one product to be voided" in accordance with its terms, while "bets on another product may stand", and that the exchange will have no liability to you when it amends or voids a bet in accordance with its terms, "even if your other related bets stand".
The exchange "reserves the right at any time in its sole and absolute discretion to suspend an Exchange market", and, in the interests of integrity and fairness, "may also void certain bets in a market or void a whole market in its entirety", and "reserves the right to cancel unmatched bets to protect customers at any time". On soccer markets scheduled to turn in-play, except Australian soccer markets, if the exchange does not suspend a market on time for a goal being scored, a penalty being awarded or a player being sent off, it "reserves the right to void bets unfairly matched after the Material Event has occurred", and the voiding "may take place during the event or retrospectively once a game is completed".
Fine. Now the boring part. The same pair in whole pounds, £391 and £409, gives +£17.19 if outcome 1 wins and +£17.63 if outcome 2 does (the two outcomes no longer match: whole pounds tilt the result towards outcome 2). When a market is settled, Orbit's exchange rules round winnings, losses and commission to the nearest two decimal places.
Reality check
The same result on every outcome holds only while both legs stand at the prices you typed. A margin of 2.18% on £800 staked is a thin return for a lot of exposure, and in this example one failed leg can cost more than a long run of good pairs earns. Leg 1 alone loses £391.11 on the wrong outcome; a good pair leaves £17.42 on top.
Decide what one failed leg is allowed to cost before you size a pair, not after. The page on gambling responsibly goes further.
Four brokers, two kinds of sentence
Each broker says something about arbitrage on its pages and something about bets in its terms. The quotations are word for word.
AsianConnect
It writes: its article on arbitrage says "we welcome profitable players and never restrict accounts for using smart strategies like arbitrage." Its bet types FAQ lists "Arbitrage combinations (across platforms)".
Its terms: the terms say AsianConnect "reserves the right to refuse any bet or part of a bet without providing a reason at any time". For the one-time rollover before a withdrawal, "all draw, cancelled and bets made on both outcomes are not considered towards the calculation of the turnover".
Open the brokerBetInAsia
It writes: its arbitrage calculator page takes decimal, fractional or American odds and has an option labelled "Enable 3-Way Arbitrage".
Its terms: clause 9.2, on the turnover needed before a withdrawal, includes the words "If a Customer places bets on opposing side on the same market, only the lower stake will count toward turnover". Clause 12.6 reads "We also reserve the right to adjust limits on individual Accounts as well."
Open the brokerMadMarket
It writes: its FAQ reads "Value bettors and Arbitrage seekers are welcomed without restriction!" Its arbitrage calculator page says that Edge and several others "might need to approve this betting strategy".
Its terms: clause 6.5 includes the words "We reserve the right to refuse, restrict, cancel or limit any wager at any time for whatever reason".
Open the brokerSportmarket
It writes: its article on sports brokers says "The broker model suits arbitrage and value bettors, because brokers are built around winners rather than limiting them", and adds that "each bet is ultimately placed under the individual bookmaker's own betting rules, so those rules still govern how a bet is accepted and settled". Its article on the Arb Calculator says the tool "lets you enter the odds and stake of a bet placed on another bookmaker".
Its terms: "Bookmakers may accept or decline the whole or any part of your bet up until they issue their confirmation."
Open the brokerBetInAsia's own welcome sentence for winners is already printed on the page on stakes and caps, so it is not repeated here. Enough quoting.
Who this suits
Best for: a bettor who can place both legs within moments of each other and whose stake the prices can fill.
Not ideal if: a leg sits at a venue where your stake is capped, or your stake is bigger than what the price offers. How deep a market is and who caps a stake take those one at a time.
Questions about stakes, commission and failed legs
How do you split your stakes in an arbitrage bet?
Divide the total stake by odds × book, where the book is the sum of 1 ÷ odds with each exchange price taken after commission. Say a total of £800 is split between 2.09 with a bookmaker and 2.03 on an exchange at an example 3% rate: the stakes are £391.11 and £408.89, and either outcome returns £817.42.
How does exchange commission change an arbitrage?
It comes off the winnings of an exchange leg, so the price you are really backing is lower. The same two prices leave a 2.98% margin with no commission and 2.18% at an example 3%; the margin is gone at 10.93%. The commission page lists what each broker quotes.
What happens if one leg is cancelled or only partly matched?
The bet that stands is a plain bet. With leg 1 placed and leg 2 half matched, the result is +£221.86 or -£186.85; with leg 1 cancelled after leg 2 is matched, -£408.89 or +£408.52. For related bets across products, Orbit's exchange rules say a bet on one product can be voided under its terms while a bet on another may stand. All four situations are charted above.
Can a bookmaker limit or close an account that places arbitrage bets?
AsianConnect's article writes that most bookmakers "will limit or close accounts that consistently win or engage in arbitrage". MadMarket's guide, that bookmakers "may limit or ban accounts that engage in consistent Arbitrage betting". Sportmarket's article on brokers, that arbitrage and value betting "both tend to be restricted quickly at soft bookmakers". Each broker's terms are quoted above; how winners are treated says more.
Is arbitrage betting the same as matched betting?
No. Matched betting is its own subject; it also uses a back and a lay. This page is about something else: two or three prices that differ between places, worked out with the stakes and the commission above.
Can an arbitrage bet still lose money?
Yes, when a leg fails. With only leg 1 placed, the pair on this page loses £391.11 if outcome 1 does not win, where two legs that both stand leave £17.42 on top. The four situations are charted above.
Where the two legs can sit
Each of the four brokers opens Orbit Exchange and at least one Asian bookmaker, so a single account can hold both kinds of venue and both legs sit in one place. Which broker opens which venue lists them, the brokers that open Orbit Exchange compares the four, and the books behind the brokers covers the Asian side. Orbit Exchange itself sits behind a broker; the way in explains how.
More sums are on the other calculators, and the wider roadmap shows where this page fits.