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Arbitrage Calculator

Check whether two or more prices on the same event lock in a profit, and get the stake for each side.

This prices a set of bets that between them cover every outcome of the event, so the guarantee is only as good as that list: anything that can happen and is not priced here takes the whole outlay when it does.

Profit if that's the whole market

$5.00

5.00% on $100.00

only if there is no third outcome to this event

The book

Book %

95.24%

Margin

+4.76%

Your stake

Best odds on each outcome

  1. Out 1
    Stake
    $50.00
    Return
    $105.00
  2. Out 2
    Stake
    $50.00
    Return
    $105.00

Every odds field reads a decimal price (2.50). Switch the format above to enter prices the way your book quotes them, or open the odds converter to see one price in all of them.

Return any result$105.00Total stake$100.00Profit+$5.00

This only holds if these two outcomes are the whole market. A draw, or any other result the event can settle on, is not covered here, and it takes the whole outlay if it lands. Add it as a third outcome if the market has one, place every leg before any price moves, and stake what you can get matched on the shortest price first.

Written and reviewed by Alexander Korsager · last reviewed October 8, 2026 · corrections

The idea

What this tool shows

An arbitrage, or sure bet, is a set of bets that covers every outcome of an event at prices good enough that the total staked is less than the guaranteed return. It happens when two bookmakers disagree enough about a market that their best prices, taken together, imply less than a 100% chance of something happening.

  1. The test is the book percentage: add up one divided by each decimal price.Below 100% is an arbitrage and the gap is your profit margin; at 100% the market is fair; above 100% (the normal case) the difference is the combined margin you would pay. This calculator sums the book for you and, when an arb exists, splits your total stake in proportion to each outcome's implied probability so every result pays back the same amount.

  2. Arbitrage is low-variance but not risk-free in practice: prices move while you are placing the second leg, stakes get limited or voided, and palpable-error rules let bookmakers cancel mistaken prices. Treat the margin shown here as the best case before slippage and account restrictions.

FAQ

Questions players ask

What book percentage counts as an arb?

Anything below 100%, provided the prices cover the whole market. A 98% book on a $100 total returns $102.04 whichever result lands, which is why the page prints two percentages for it: a 2.00% margin, the gap measured against the return, and a 2.04% figure beside the profit, the same gap measured against what you staked. The second is the one that describes your money. Neither of them says how often a book that low is available, or for how long.

Do I have to enter every outcome?

Yes, and it is the one input this page cannot check for you. Back home and away at 2.10 each in a match that can also be drawn and the book reads 95.24%, which is why a two-outcome entry is headlined "Profit if that's the whole market" rather than an unqualified guarantee: a draw takes the whole outlay, and this page has no way to know whether one is possible. A book under 100% is a rate of profit only when exactly one of the prices you entered can land, so a missing result, a dead heat or a void breaks it the same way. Enter the market's third outcome as a row if it has one; if you are deliberately backing part of a field rather than all of it, the dutching calculator is the page that prices that.

Why are my two stakes not equal?

Stakes are sized so each outcome returns the same total, so the shorter price takes a larger stake. Only in a market where both prices are identical do the stakes come out equal.

Can I anchor one stake instead of a total?

Yes. Switch to 'fix one stake' and enter the amount already placed on one side; the calculator sizes the remaining outcomes to equalize the return and shows the total outlay.

Methodology

How this is calculated

Every decimal price becomes an implied probability, 1 divided by the odds, and those add up to the book. The return whichever outcome lands is your total stake divided by the book, and each stake is that return divided by its own price, which is what makes all of them pay the same amount.

Fix one stake runs the same solution from the other end: the return is the stake you have already placed multiplied by its price, the remaining legs are sized to match it, and the total outlay comes out as a result rather than an input.

Profit is the return minus the outlay, which works out as the return multiplied by one minus the book, so it is positive exactly when the book is under 100% and by nothing else. That also explains the two percentages on screen.

Margin is 1 minus the book, the gap as a share of the return, while the figure printed beside the profit is that gap as a share of the stake, which is margin divided by book.

At the shipped 2.10 and 2.10 the book is 95.24%, the margin reads 4.76% and the return reads 5.00% on $100, and both are the same edge counted against a different denominator.

Common misreadings4
  • A book under 100% across part of a market is not an arbitrage, and this is the reading that costs real money. Two prices at 2.10 in a match that can be drawn give a 95.24% book and a $5.00 profit on $100 that only holds if there is no third outcome, which is why a two-outcome entry is headlined that way rather than as an unqualified guarantee. Enter more than two outcomes and the page trusts that the list is complete, because past that point checking is on you: the page checks the arithmetic of the prices you gave it, never whether they are all of them.
  • The percentage beside the profit is a return on one outlay for one event, not a rate you can run a bankroll at. How many of these can actually be placed, at what size, before an account is restricted is the whole question, and it is not on this page.
  • Fix one stake sizes the other legs from a bet already struck, and it takes the remaining prices at face value. If those have moved since you placed the first leg, the figure shown is the position you would have had, not the one still available to you.
  • An equal return is not a matched position until every leg is on. Between the first bet and the last you are holding a single directional bet at a price you picked for a different reason.
Assumptions5
  • Exactly one of the outcomes you entered can land, and one of them must. That is the assumption the word guaranteed rests on, and it is the only one this page cannot verify from your inputs. A three-way market entered as two prices, a market that can be void, and a market that can dead-heat all read as an arbitrage here when they are not one; a two-row entry is exactly the shape that carries the qualified headline for this reason, but three or more rows are taken as a complete list and get the unqualified claim regardless.
  • Every price is live at the same moment, at the stake shown beside it, and is already net of anything that shrinks the return. Exchange commission, currency conversion and a boosted price the operator will not honor at size all come off the odds before they are typed in, not afterwards.
  • The stakes go on exactly as printed, to the cent, and all of them do.
  • Every odds field reads whichever format the odds format control is set to, and only that one. The control exists, rather than a field that takes anything, because 150 is a real decimal price as well as the American price +150: a field reading both would have to guess which you meant on exactly the input where guessing wrong is invisible, since a wrong price of that kind still prints a complete and correctly formatted panel. A price that does not read in the selected format shows nothing rather than a figure, and the page names the format it would read in when there is one. Switching the format rewrites the prices already entered, so a field never holds a number in a format the page is no longer reading, and a fractional price is rewritten to the closest fraction with a denominator of 100 or less.
  • Both operators settle the same event by the same rules. Two books can disagree about an abandoned match, a dead heat, a non-runner or which feed is official, and a leg settled under a different rule is no longer the other half of the position.
Limits6
  • The equal return survives only at the unrounded stakes. On a three-way market at 2.6, 3.5 and 3.4 with $200 the split is $79.76, $59.25 and $60.99 for $207.37 on any result, a profit of $7.37. Round those to whole dollars, 80, 59 and 61, and the three returns become $208.00, $206.50 and $207.40, so the locked figure drops to the worst of them, $6.50. Rounding down is what costs you, and the leg you round down decides the floor.
  • This prices the settled event, not the account. There is no state here for a position that is half on: a leg limited to a fraction of its stake, or voided after the others were matched, leaves the rest live and one-sided at prices chosen for a bet that no longer exists.
  • Six outcomes is the ceiling of the form, so a large outright field cannot be priced here even when the arithmetic would be identical.
  • The assumptions above have exchange commission coming off a price before it is typed in, and that quietly assumes the exchange is a market you can reach. In practice one leg of a two-outcome arbitrage is often a two-sided price rather than a second sportsbook, which is ordinary in the UK and Australia and uneven in the US, where the two-sided prices on offer sit mostly on federally regulated prediction markets rather than on state-licensed sportsbook exchanges. A split placed across two sportsbooks needs none of that. A split with a lay leg needs all of it, so check what is actually open to you before treating these stakes as orders.
  • Nothing on this page estimates how often prices like these appear, how long they last, or how much either operator will accept. Those are what decide whether the strategy pays; the book only says what this one set of prices is worth if you get all of it on.
  • Below a 95% combined book, the panel does not say 'Guaranteed profit' at all, whatever the stakes and profit figures come out to: a book that far under 100% is far more likely a missing outcome or a mis-keyed price than a real arbitrage, so the headline claim is withheld and a warning explaining the same threshold renders in its place. At 95% or above, the unqualified claim shows only once more than two outcomes are entered. With exactly two rows, the page's own default shape, the headline reads 'Profit if that's the whole market' instead: a book that high is not itself proof the prices are wrong, but with only two outcomes listed there is no way to rule out a third result the page never saw.
Evidence

The model is an identity rather than a source.

A stake of return divided by odds pays the return on any winner, so the outlay is the return multiplied by the book, and profit is the return multiplied by one minus the book: positive precisely when the book is under 100%. math.test.ts pins that in both directions, on the two-way arb at 2.10 and 2.10 (equal payouts from a 50/50 split, $5.00 profit, 5% return), on a fair 100% book returning exactly zero, and on an over-round pair at 1.90 and 1.90 whose 105.26% book returns a loss.

It also pins the equal payout across a three-way market and that fix one stake reproduces the same solution from a single fixed leg. What a passing test cannot check is the input the guarantee actually rests on, which is whether the outcomes you typed are all the outcomes there are.

Gambling can cause serious harm. The National Problem Gambling Helpline is free, confidential and open 24/7, call or text 1-800-MY-RESET (1-800-697-3738), or chat at ncpgambling.org/chat.

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