Arbitrage Calculator for Two or Three Outcomes
Type two or three prices from the same result, add an exchange commission if one leg needs it, and see whether the combined probability leaves a margin to split, or none at all.
Type the legs
Two legs for a head-to-head match. Three for anything with a draw. Odds are decimal; add an exchange commission rate only for a leg you would place on an exchange.
An arbitrage calculator checks whether two or three prices on the same result, added up as implied probability (1 ÷ the odds), come to under 100%. Type each leg's decimal odds above, and for any leg placed on an exchange, its exchange commission rate; a bookmaker leg stays at the 0 default. Two prices at 2.05 and 2.15 come to 95.29%, so splitting a £1,000 stake as £511.90 and £488.10 returns about 4.94% whichever leg wins, once both bets are matched at those prices. If the total reaches 100% or more, there is nothing to split: the tool says so plainly and points to the margin calculator instead. Pushes, voids and half-wins are out of scope, and no leg here comes without its own execution risk.
Reading the result
The tool adds the implied probability of every leg, 1 ÷ the effective odds, into one combined probability, S; effective odds only move away from the odds you typed once a leg carries an exchange commission rate above zero: 1 + (odds − 1) × (1 − commission). Leave a leg's exchange commission box at its 0 default and its effective odds equal its own odds. That default is not a claim about your own account, so type your own rate before trusting the split for an exchange leg.
Under 100%, the return on the whole stake is 1 ÷ S, minus 1. At S = 95.29% that is 4.94%, not the 4.71% you get from 1 − S, a different quantity this page never calls a return. Each leg's stake is total stake × (1 ÷ its effective odds) ÷ S, rounded to the penny, independently, rather than forced to add up exactly: the result says when the rounded stakes sit a penny or two from the total you typed, and when one leg's payout differs from another's by the same margin.
Two worked examples, run through the same formulas
Both use invented prices. Type them into the calculator above and it prints exactly these figures.
Example 1: two bookmaker prices, no exchange commission
| Leg | Odds | Stake | Payout if it wins | Profit |
|---|---|---|---|---|
| 1 | 2.05 | 511.90 | 1,049.40 | 49.40 |
| 2 | 2.15 | 488.10 | 1,049.42 | 49.42 |
| Combined probability (S) | 95.29% | 1,000.00 total | Return: 4.94% | |
Leg 2's 1,049.42 sits two pence above leg 1's 1,049.40: rounding 488.0952... up to 488.10 before multiplying it back out is the reason, not an error in the maths.
Example 2: two bookmaker legs and one exchange leg, three outcomes
| Leg | Odds | Exchange commission | Effective odds | Stake | Payout | Profit |
|---|---|---|---|---|---|---|
| 1 | 2.00 | 0% | 2.000 | 521.41 | 1,042.82 | 42.82 |
| 2 | 4.20 | 0% | 4.200 | 248.29 | 1,042.82 | 42.82 |
| 3 | 4.60 | 2% (example rate) | 4.528 | 230.30 | 1,042.80 | 42.80 |
| Combined probability (S) | 95.89% | 1,000.00 total | Return: 4.28% | |||
Leave that exchange commission field at 0, as if leg 3 carried none, and the combined probability flatters you: 95.55% instead of 95.89%, 0.34 of a point of margin that would not survive the exchange's own charge. That gap is what a per-leg commission field is for.
Under 100% is a number. Matched at those prices is a decision you still have to make.
Where the calculation stops
Read what a broker says about arbitrage, not only what the maths says. BetInAsia's marketing states plainly that "arbitrage and value bettors are not limited for their success"; its own archived terms, separately, reserve the right to "refuse, restrict, cancel or limit any wager at any time for whatever reason" (check the current version). AsianConnect's blog goes further, promising it will "never restrict accounts for using smart strategies like arbitrage"; its terms, elsewhere, cap use at a "personal non-professional capacity" and prohibit commercial use, a conflict this page does not resolve. Sbobet does not hedge: its help centre calls arbitrage a breach of its terms outright (see the sharp bookmakers list). Betfair's own terms say nothing about arbitrage specifically: read that silence as silence, not permission.
Some call a two-way arbitrage a "sure bet", but it only holds if every leg gets matched at the price you typed before the market moves.
A voided leg. A price that moved before the second bet landed. Either one breaks the sum above just as easily as a bad price would.
Three things this tool leaves alone entirely:
- A push, a void or a half-win on any leg, the kind of result the Asian handicap calculator settles rather than a straight arbitrage sum.
- Any deposit, withdrawal or currency-conversion charge: only the exchange commission you type sits inside the sum.
- Which countries or accounts can actually place these legs: that is a broker-by-broker question, not a maths one.
Seven ways the tidy number above can still turn into a smaller one once real bets replace typed prices:
- The price moves before your second leg is matched.
- A leg fills only in part on an exchange, or not at all, before the price disappears.
- A stake or liability limit takes less than the split asks for.
- A minimum-bet rule rounds your actual stake away from the figure above.
- The exchange commission you typed as an example may not be your own account's rate: check the current terms.
- A broker reviews the pattern of your betting, not one bet at a time: MadMarket's terms reserve the right to review "irregular playing patterns" and adjust limits at any time, without naming arbitrage as one of them.
- A bookmaker's own rules on arbitrage still apply to that leg, whatever a broker's marketing says elsewhere on the page.
Reaching a venue with a price worth checking is its own question: the broker comparison sets out what BetInAsia, AsianConnect, MadMarket and Sportmarket each charge and exclude, and opening a Betfair Exchange account directly covers the other route. For arbitrage betting itself, legality and account risk included, the guide on arbitrage betting goes beyond calculator mechanics, and the rest of this site's calculators covers the maths around it.
Questions people ask
How do I know an arbitrage actually exists from the numbers here?
Turn each leg's price into a share, 1 ÷ the effective odds, and add the shares up. Under 100%, there is a split that pays the same amount whichever leg wins. At or above 100%, there is not.
Does two-way arbitrage work differently from three-way?
The test is identical: sum 1 ÷ effective odds across every leg. A third leg adds a third share to that sum, which usually leaves less room under 100% than two legs alone, though it depends entirely on the prices in front of you, not a fixed rule.
Why does the calculator ask for an exchange commission rate?
Because a real exchange leg is rarely worth its face-value price once exchange commission comes off net winnings. The calculator turns it into an effective price first, using the exchange commission rate you type: 1 + (odds − 1) × (1 − commission). Leave the box at 0 for a bookmaker leg; type your own rate, not the default, for an exchange leg.
What happens if the combined probability comes to 100% or more?
A plain "no arbitrage at these prices" state, not a negative number. Try the margin calculator on the same prices instead.
Do the brokers on this site actually allow arbitrage betting?
Not consistently. BetInAsia and AsianConnect welcome arbitrage in their marketing while their own terms cap it at personal, non-commercial betting. MadMarket's terms do not name arbitrage but reserve a broad right to limit or review any account; Sportmarket states no arbitrage policy at all on the pages checked for this site. None of the four promises what its marketing page might suggest, so check the current terms yourself.