Arbitrage calculator
Enter the price on every outcome and the money you are willing to commit. This splits it so every outcome returns the same, then solves the version again in stakes a book will accept and reports the worst leg, which is the only number worth acting on.
Worked example — Worst-case profit at placeable stakes, on this page's own example: $15.00. $1,000 outlay across 2.05 / 2.02, staked in $5 units
Split a real market into placeable stakes
Enter the price on every outcome and the money you are willing to commit. This splits it so every outcome returns the same, then solves the version again in stakes a book will actually accept, and reports the worst leg, which is the only number worth acting on.
Realistic two-way arb: A real 1.7%-class arb, deliberately chosen over the 12% fantasy every screenshot of this query shows.
Annualised return 1
| Outcome | Price | Implied | Ideal stake | Placeable stake | Returns if it settles | Profit if it settles | Loss if this leg voids |
|---|---|---|---|---|---|---|---|
| Outcome A | 2.05 / +105 | 48.78% | $496.31 | $495 | $1,014.75 | $19.75 | $500.00 |
| Outcome B | 2.02 / +102 | 49.50% | $503.69 | $500 | $1,010.00 | $15.00 | $495.00 |
Nearest-unit rounding, which is what most people do by hand, would stake $495 / $505 for a worst case of $14.75. The plan above searches whole-unit allocations inside the same outlay and takes the one with the best worst case, which is $0.25 better here.
An arbitrage is only as large as its smallest leg allows. If that book takes $200, the largest outlay the split supports is cap x (sum of 1/o) x that leg's price, or $403. Staking more on the other legs than this leaves an unhedged position, which is the most common way a posted arb turns into a directional bet.
Arb size and what it's worth, by margin
Five symmetric two-way price pairs, each run through the same solver the calculator above uses, on a $1,000 outlay staked in $5 units. This page's own guidance is to skip anything under about 1% of the outlay: the spread between the ideal and placeable profit, the chance the second price moves, and the void exposure will take more than that out of it over any real sample.
| Price both sides | Implied book | Return on a perfect split | Worst-case profit | Worst-case ROI |
|---|---|---|---|---|
| 2.01 | 99.50% | 0.50% | $5.00 | 0.50% |
| 2.02 | 99.01% | 1.00% | $10.00 | 1.00% |
| 2.03 | 98.52% | 1.50% | $15.00 | 1.50% |
| 2.04 | 98.04% | 2.00% | $20.00 | 2.00% |
| 2.06 | 97.09% | 3.00% | $30.00 | 3.00% |
Worst-case profit is what whole-unit stakes actually pay in the least favourable outcome, which is always less than the perfect-split figure and is the number worth acting on. Anything under roughly 1% of the outlay is thin enough that placement slippage, a stale second price, or a single void can erase it.
What is a good arbitrage percentage?
Skip it if it is under about 1% of the outlay. On this page's own default market, $2.05 against $2.02, that is 1.74% on a perfect split and 1.51% once the stakes are rounded to real, placeable units, a real 1.7%-class arb rather than the 12% fantasy every screenshot of this query shows. The spread between the ideal and placeable profit, the chance the second price moves before both legs are placed, and the void exposure below all take more than 1% out of a thin arb over any real sample, which is why the threshold sits where it does rather than at zero.
Why did my sure bet lose money?
A voided leg returns its own stake and cancels its side of the hedge, leaving the other stake exposed to a single outcome. On this page's own default market that is $503.69 of stake exposed for a play whose entire upside was $17.44, so one void followed by the wrong result costs about 29 successful arbitrages to earn back. Void rules differ by book and by sport, and rule differences between two books on the same event are exactly where posted arbitrages come from, so treat a wide arb as a warning that the two books are not pricing the same bet.
How do I calculate arbitrage stakes?
Convert every price to decimal odds and add each outcome's implied chance, 1 ÷ oi; that total is the implied book. Below 1.00 an arbitrage exists, at or above it none does, and no clever staking changes that. Stake more on the lower-paying outcomes and less on the higher-paying ones until every winner returns the same total. The exact share is (1 ÷ oi) ÷ Σ(1 ÷ oi). The total returned is the outlay divided by the book. Profit is therefore the outlay times (1/book minus 1), a return on everything committed, not on the leg that happens to win. On the default market the book is 98.29%, so a $1,000 outlay splits to $496.31 / $503.69 for a guaranteed $17.44. Nobody can place fractional-cent stakes, which is why the calculator above also searches whole-unit allocations and reports the worst leg.
The smallest leg sizes the whole play
Arbitrages usually appear where one side is priced by a book that will accept very little. If that leg takes $200, the outlay the split supports is $200 times the book times that leg's price, and staking more anywhere else does not scale the position, it unhedges it. This is the mechanism behind most stories about an arb that turned into a loss: the account got its stake cut on one side, the other side stayed on at full size, and what was left was an ordinary directional bet on a price the bettor had no view on.
What this does not model
Prices moving between the first stake and the second, which is how most posted arbitrages disappear. Limits, bonus restrictions, and account closure, which is the standard commercial answer to a winning arbitrage account. Deposit, withdrawal, and currency costs. Exchange commission, which is charged on winnings and would need to be netted off the winning leg before the split is computed. Tax. Any correlation between the outcomes: the arithmetic assumes exactly one of them settles, so it does not apply to a market that can void, tie, or settle two outcomes at once unless every such case is entered as its own outcome.
What I think you should do with it
Assume a posted arbitrage is a stale price until the money is on. Compute the worst leg in whole units before placing anything, and if that number is under about 1% of the outlay, skip it. The returns look enormous when annualised, and the annualised figure the calculator prints above is honest arithmetic on the numbers you typed, but the input that decides it is how many placeable arbs a year you actually find, which for almost everyone is a much smaller number than the first month suggests. If you want to check whether the prices even disagree before sizing anything, the no-vig calculator is the faster first look.
The next question after this one
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More calculators for the same question
The no-vig calculator checks whether prices even disagree before you size anything, and the Kelly calculator sizes a growth bet once an arbitrage tips into an ordinary edge.