Arbitrage calculator
Enter the best price you can get on each outcome and this works out whether an arbitrage exists, how to split the stake so every result pays the same, and what the locked profit is. Two-way and three-way markets both work.
2.100 decimal · 47.6% implied
2.100 decimal · 47.6% implied
+5.00% on stake
Total implied probability is 95.24% — under 100%, so the prices disagree enough to lock a profit. Split the stake as above and every outcome returns $1050.00. Read the execution risks below before treating this as free money.
How arbitrage works
Every price implies a probability — 1 ÷ decimal odds. Add up the implied probabilities of every outcome in a market and you normally get more than 100%; the excess is the book's margin, which is how it makes money.
Occasionally two books disagree enough that taking the best price on each side brings that total below 100%. When that happens you can back every outcome and profit regardless of the result. Not a prediction — an accounting fact about the prices.
Worked example
A +200 underdog at one book against a −167 favourite at another — decimal 3.00 and 1.60. Implied probabilities are 33.33% and 62.50%, totalling 95.83%. Under 100%, so it is an arb.
On $1,000 total you stake $347.83 on the underdog and $652.17 on the favourite. Either result returns $1043.48 — a locked $43.48, or 4.35% on the stake.
What an arb looks like next to a normal market
| Market | Total implied | On $1,000 |
|---|---|---|
A real two-way arb Both sides at +110 across two books — a 5.0% lock. | 95.24% | +$50.00 |
An asymmetric arb A +200 underdog at one book against a −167 favourite at another. | 95.83% | +$43.48 |
No arb — the usual case Both sides at −110 at the same book. This is what the vig looks like. | 104.71% | −$45.00 |
The third row is the normal case — both sides at −110 at one book. That is what a market with its margin intact looks like, and it is what you will find the overwhelming majority of the time.
What these calculators usually leave out
The arithmetic above is exact. The practical picture is more complicated, and it is the part worth reading before treating an arb as free money.
- Books limit accounts for it. The pattern is recognisable — stakes that match arb splits, bets only on stale prices, an account that never loses. The usual response is reduced maximum stakes rather than closure, but a limited account cannot arb. The strategy has a shelf life per book.
- Execution risk is real. You place one leg and the other price moves before you get there. Now you hold a directional bet you never intended. The faster the market, the more often this happens.
- The margin is thin. Typically 1–3% of total stake. To earn real money you commit real balances across several books, and that capital sits idle between opportunities.
- Rules differ between books. Voided legs, cancelled events, palpable-error price voids and different definitions of a settled result can each break the lock after both bets are placed.
- Getting the split wrong undoes it. Equal stakes on unequal prices is not an arbitrage. It is two bets with an accidental lean.
Arbitrage versus positive expected value
These get conflated and they are different trades. An arb is a small certain profit that needs no opinion about the game. A positive-EV bet is a larger uncertain edge on one side, and it needs a probability estimate you actually trust.
Arbitrage is limited by capital and by how long your accounts survive. Positive EV is limited by whether your read is genuinely better than the market's. Our board works the second problem — comparing every book's price against the devigged fair price.
Three-way markets
Soccer and other draw sports have three outcomes, so three implied probabilities have to sum below 100%. Arbs are marginally more common there because the extra outcome gives books one more thing to disagree about — but the execution problem gets worse, since you now need three prices to hold still at once.
Terms used on this page
- Implied probability — the chance a price is quoting, 1 ÷ decimal.
- Hold — the margin that normally keeps the total above 100%.
- Hedging — the same stake-splitting maths applied to a bet you already hold.
- Payout — what a single stake returns at a given price.
Questions
What is arbitrage betting?
Backing every outcome of the same market at different books, at prices that together guarantee a profit whichever way it lands. It works when the implied probabilities across the best available prices add up to less than 100% — the books disagree by more than their combined margin.
How do I know if an arbitrage exists?
Convert each outcome’s best price to implied probability — one divided by the decimal odds — and add them up. Below 100% is an arb. At or above 100%, the margin is intact and there is nothing there, which is the normal state of a market.
How much should I stake on each side?
In proportion to each outcome’s implied probability. Stake the total multiplied by that outcome’s implied probability divided by the sum of them all. Get the split wrong and you no longer have a locked position — you have two bets with a directional view you did not intend.
How much does arbitrage actually pay?
Typically 1–3% of the total staked, occasionally 5%. It is a small margin on a large committed balance, and it is not compounding quickly — you tie up money across several books to earn it.
Will sportsbooks limit me for arbitrage betting?
Very likely, and this is the fact these pages tend to bury. Books monitor for the pattern — stake sizes that match arb splits, bets placed only on stale prices, accounts that never lose. The usual outcome is limited stakes rather than a ban, but a limited account cannot arb, so the strategy has a shelf life per book.
What is the biggest practical risk?
Execution. You place one leg, the price moves before the second lands, and the arb becomes a normal bet with real risk. Voided legs, a book cancelling a palpable-error price, and different rules on what counts as a settled event can all break the lock after the fact.
Is arbitrage better than +EV betting?
They are different trades. Arbitrage takes a small certain profit and needs no view on the outcome. Positive expected value takes a larger uncertain edge on one side and needs a probability estimate you trust. Arbitrage is capital- and account-constrained; +EV is knowledge-constrained.
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