An arbitrage calculator tells you whether the prices on every outcome of a market add up to under 100%, and how to split one stake so each result pays back about the same. It also takes a commission rate for an exchange leg, rounds stakes to the cent, 10c, $1 or $5, and shows what the outcome paying least is worth.
Prices only add up to under 100% when bookmakers disagree, and how arbitrage betting works covers where that disagreement comes from.
How to use the arbitrage calculator
The boxes open with a two-way market already typed in; an empty commission box means 0.
- Outcomes to cover: 2 for a head to head, 3 for a draw market, up to 4.
- Total stake: $0.01 to $1,000,000, split across the outcomes.
- Round stakes to: cents, 10c, $1 or $5, matching what your bet slip takes.
- Outcome A to D odds: decimal prices from $1.01 to $10,001.
- Outcome A to D commission %: 0 at a bookmaker, or your exchange account's rate.
Each outcome gets a row: the price used, the stake, the return if it lands and the profit. The book percentage prints to one decimal place, the arbitrage percentage to two, worked from the exact split before rounding. The Outlay tile is the rounded stakes added up, and profit is measured against it.
The formulas the calculator runs
- price used = 1 + (odds - 1) x (1 - commission rate)
- implied probability of an outcome = 1 / price used
- book percentage = the sum of those implied probabilities
- stake on an outcome = total stake x (1 / price used) / book percentage
- profit = total stake / book percentage - total stake
- arbitrage percentage = 1 / book percentage - 1, the profit per dollar staked
A worked two-way arbitrage example
With illustrative prices of $2.90 and $1.60 at two bookmakers and a $250 stake:
| Step | Working | Result |
|---|---|---|
| Outcome A chance | 1 / 2.90 | 0.344828 |
| Outcome B chance | 1 / 1.60 | 0.625000 |
| Book percentage | 0.344828 + 0.625000 | 0.969828, or 97.0% |
| Stake on A | 250 x 0.344828 / 0.969828 | $88.89 |
| Stake on B | 250 x 0.625000 / 0.969828 | $161.11 |
| Return either way | 250 / 0.969828 | about $257.78 |
| Profit | 257.78 - 250 | about $7.78 |
That profit is 7.78 / 250 = 3.11% of the stake, the arbitrage percentage. Rounded to the cent both legs pay $257.78, from exact returns of $257.781 and $257.776, so the result reports the outcome paying least rather than one profit figure.
Risk: Betting involves risk. An arbitrage only works if every bet is accepted at the price shown, and there is no guarantee of profit. See responsible gambling for limits and support.
Three outcomes, and what the stake split does
A third outcome adds one term to the sum and nothing else. With illustrative prices of $2.55, $3.60 and $3.10 at three bookmakers, the book is 1 / 2.55 + 1 / 3.60 + 1 / 3.10 = 0.992515. On $300 the first stake is 300 x (1 / 2.55) / 0.992515 = $118.53, with $83.96 and $97.50 the same way, and each returns about 300 / 0.992515 = $302.26: a profit of about $2.26, or 1 / 0.992515 - 1 = 0.75% of the stake. A dutching calculator runs the same split over only the selections you pick, so an uncovered result loses the lot; an arb covers every outcome.
Risk: Betting involves risk. That book leaves about $2.26 on $300, so with the other two stakes on, the $2.55 leg taken at $2.53 returns 118.53 x 2.53 = $299.88 against the $299.99 those three stakes add up to, a loss. See responsible gambling for limits and support.
What exchange commission takes out of an arb
Commission is charged on net winnings in a market, not on the stake and not on a losing position, so only the profit part of the price is reduced.
Back the $1.60 leg on an exchange at an illustrative 5% instead. The price after commission is 1 + 0.60 x 0.95 = $1.57, the book moves from 0.969828 to 1 / 2.90 + 1 / 1.57 = 0.981770, the arbitrage percentage falls to 1 / 0.981770 - 1 = 1.86%, leaving 250 / 0.981770 - 250 = about $4.64 instead of $7.78. Taking 5% off the whole price reads $1.52, which adds to over 100% and shows a loss that is not there. Rates vary by account and by market, so the calculator never fills one in.
Rounding stakes, and when it eats the margin
Put the same illustrative prices on a $50 stake. The exact split is $17.78 and $32.22; in $5 units that is $20 and $30, so outcome B returns 30 x 1.60 = $48 on a $50 outlay.
| Round to | Stake A | Stake B | Worst return | Worst profit |
|---|---|---|---|---|
| Cents | $17.78 | $32.22 | $51.55 | +$1.55 |
| 10c | $17.80 | $32.20 | $51.52 | +$1.52 |
| $1 | $18.00 | $32.00 | $51.20 | +$1.20 |
| $5 | $20.00 | $30.00 | $48.00 | -$2.00 |
Judge the position on the Worst outcome tile, which assumes every leg gets on at that price.
What the calculator refuses, and what it cannot know
It refuses a price under $1.01 or over $10,001, a stake outside $0.01 to $1,000,000, a commission rate of 100% or more, and anything that is not a plain number, so a box without a usable number leaves the result blank rather than wrong. A book over 100% still calculates: the exact stakes stay positive and the profit comes out negative, and a $0 rounded stake leaves that outcome uncovered.
What it cannot see is anything after you press place: whether a leg is accepted, whether the price is still there, or how each bookmaker settles. A gap between two sets of rules is its own problem, covered by arbitrage rule mismatches. The arbitrage screener on B337 lists sports markets whose prices add up to under 100%, and a free account sees the live count with the rows locked; you place every leg yourself.
Risk: Betting involves risk. Many bookmakers restrict or prohibit automated betting, third-party access and multiple accounts in their terms, and a bookmaker can limit your stakes, void bets or close your account under them. Whether arbitrage betting is legal is a separate question, and B337 does not give legal advice. See responsible gambling for limits and support.
Mistakes that turn an arb into a loss
With illustrative numbers, on the $250 example:
| Mistake | What it costs | The fix |
|---|---|---|
| Leaving the draw out | Both legs lose if the draw lands: the whole $250 | Set Outcomes to cover to 3 |
| Using the quoted price on an exchange leg | Split on $1.60, the $161.11 leg returns $252.94 after 5%: that outcome makes $2.94 | Type the rate in its commission box |
| Counting a bonus bet as cash | It normally pays the winnings only under the bookmaker's terms, and nothing if it loses | Work it out in the bonus bet converter |
Getting only one leg on has a name: a one legged arb is an ordinary bet at the price you took, so the order you place in matters. Betting strategy covers position sizing.