Arbitrage Calculator

An arbitrage exists when the prices available on every outcome of a market add up to less than 100% of implied probability. Backing all of them in the right proportions returns the same amount whichever one lands.

Enter two or three prices to see whether an arb is there, what each side should be staked, and what the locked return comes to.

The Test And The Split

Convert every price to implied probability and add them up. Under 100% is an arbitrage; over 100% is a normal market with the book's margin in it.

Worked example. One book has +115 on a side, another has -105 on the other. In decimal those are 2.15 and 1.9524, implying 46.51% and 51.22%. The total is 97.73%, comfortably under 100, so an arb exists with a margin of 2.32%.

Stakes are allocated in proportion to each side's implied probability. On a $1,000 total: side A gets 1,000 × (0.4651 ÷ 0.9773) = $475.91, side B gets $524.09.

Check it. A wins: 475.91 × 2.15 = $1,023.22. B wins: 524.09 × 1.9524 = $1,023.22. Either way the return is $1,023.22 on $1,000 staked — a locked profit of $23.22, or 2.32%.

The margin is simply (1 ÷ total) − 1, so a total of 97.73% yields 2.32%. That is the realistic scale of an arb: two to three percent, occasionally five, and never the twenty percent an advertisement implies.

Why Arbs Exist, And For How Long

Books price independently and disagree. A soft book that has not moved after a sharp book took a large bet leaves a gap, and for a few minutes the two prices together are under 100%.

They close fast, because the soft book is watching the same market you are. In liquid markets an arb of any size lives for seconds to minutes. In obscure ones it can last longer, which is usually a warning: an unmoved price on a small-college game often means one book has information the other has not processed, and the "arb" is really you taking the wrong side of a stale line while the other leg gets voided.

Which is the first practical hazard. If one leg is cancelled — a voided market, an obvious error, a limit applied mid-placement — you are not arbitraging. You are holding a single unhedged bet at a price you never wanted, which is how a 2% locked profit turns into a 50% loss on the position.

What Makes It Hard In Practice

The arithmetic takes seconds; everything around it is the actual job.

Execution speed. Both legs have to be placed before either price moves. That means funded accounts at several books, both bet slips open, and the stakes worked out in advance rather than during.

Stake limits. The soft side often caps you well below the size the arb deserves. The fixed-stake field handles this: enter what the limited book will actually take and the calculator sizes the other side around it.

Capital. A 2% return needs the whole stake at risk on both sides, spread across books, and settlement can take days. Turning $10,000 into a $200 profit per cycle is only interesting if the cycle repeats often.

Limits and closures. This is the one that ends most arbitrage careers. Books identify arbitrage patterns quickly — odd stake sizes, bets placed only at outlying prices, no losing recreational action — and they respond by cutting your maximum to a few dollars or closing the account. Read account limits before treating this as a business plan.

Arbitrage Versus Actually Having An Edge

Arbitrage is risk-free in theory and operationally fragile in practice. It also has a ceiling: your profit is capped by the size the softest book allows, and every cycle brings the closure of that account closer.

The alternative is taking the good side and skipping the hedge. If one book has +115 on something whose fair price is +105, the arb pays 2.32% on the whole position, while betting only the +115 side pays around 4.5% of expectation on half the capital. The expected value calculator shows the comparison directly, and the same de-vigging step is in the vig calculator.

Most bettors who find arbs regularly are better served by using the same price-comparison habit to find value bets instead. That is what line shopping is for, and arbitrage betting covers the trade-off in full.

Frequently Asked Questions