Arbitrage Calculator

This arbitrage calculator shows you how to split a stake across two sportsbooks pricing opposite sides of the same game, using American odds like -105 and +115, so you lock in a guaranteed profit in dollars no matter which team wins.

What Is Arbitrage Betting?

Arbitrage betting turns a pricing disagreement between two sportsbooks into a risk-free profit. When one book prices a team high enough and another prices its opponent high enough, backing both sides in the right proportion guarantees you come out ahead no matter who wins.

The whole play rests on the combined implied probabilities of the two prices falling below 100%. Every American price implies a probability of that side winning, and normally the two sides of a market add up to more than 100% because the book builds in its own margin. An arbitrage opportunity exists on the rare occasion when two different books’ prices on opposite sides add up to less than 100% between them. That gap below 100% is your locked-in margin, kept regardless of the final score.

The calculator’s job is to size each leg so the return is identical on both outcomes, then show the profit the arb produces. You enter each book’s American odds and your total stake, and it works out how many dollars go to each side, so the outcome becomes irrelevant to your bottom line — what matters is that both prices hold until both legs are placed.

How Arbitrage Betting Is Calculated

The calculator starts by converting both American prices to decimal odds. A price like -105 becomes a decimal of 1.95, and a price like +115 becomes a decimal of 2.15. Decimal odds tell you the total return per dollar staked, making it easy to compare two different-looking American prices on the same footing.

Next, it takes the inverse of each decimal — 1 divided by 1.95, and 1 divided by 2.15 — which gives the implied probability of each side. Add those two inverses together, and if the sum comes out below 1.00, the pairing is a genuine arbitrage: the two books disagree enough that their combined implied probability sits under 100%.

From there, the calculator splits your total stake in proportion to each leg’s inverse, so the money on the -105 side and the money on the +115 side return exactly the same dollar amount whichever team wins. That equal return minus the total stake is your profit; divide profit by total stake for the ROI — the percentage return locked in regardless of the result.

Every part of this depends on both prices standing exactly as quoted when you place your bets. Move either price and the split, return, and profit all need recalculating — which is why doing this math by hand under time pressure is where arbs get missed or miscounted.

What the Calculator Shows You

Once you enter each book’s American odds and your total stake, the calculator returns a full breakdown of the arb. For each leg, it shows the stake to place at that book and the return that stake produces if that side wins. Both legs’ returns should match exactly — that’s the whole point of the split. It also shows the combined implied probability of the two prices together, which tells you whether an arb exists and how thin the margin is. Finally, it shows the total profit in dollars across the two legs and the ROI as a percentage of your total stake, so you can see how profitable the play is before committing money to either book.

Worked Example

Book A prices one team at -105 and Book B prices the other at +115. You have $200 to split between them.

Converting each price to decimal gives 1.95 for Book A and 2.15 for Book B. Their implied probabilities add up to 97.73% combined, which is under 100% — so this pairing is a genuine arbitrage, and the gap between 97.73% and 100% is the margin you’re locking in.

The calculator splits your $200 so that both legs return the same amount whichever team wins. On Book A, you stake $104.82 on Team X at -105; if Team X wins, that returns $204.64. On Book B, you stake $95.18 on Team Y at +115; if Team Y wins, that returns $204.64 as well.

Since you put in $200 total and get back $204.64 no matter who wins, your profit is $4.64. Divide that $4.64 by the $200 you staked and you get a 2.32% ROI — a guaranteed return, not a gamble on the game itself.

This is a textbook example of how thin these margins run. A 2.32% return on $200 comes out to less than five dollars, and it only exists because the two books’ prices, at 51.2% and 46.5% implied probability, add up to 97.73% instead of the more typical figure above 100%. The size of the guaranteed profit is fixed the moment both legs are placed — it doesn’t move with the score or anything that happens once the game starts. That’s the appeal of arbitrage and also its limit: the $4.64 is the ceiling, not a starting point.

Locked Profit on a $200 Arb by Combined Implied Probability

The size of your guaranteed profit is driven entirely by how far below 100% the combined implied probability of the two legs falls. The table below shows what a $200 arb returns at different combined percentages, from a healthy margin down to a pairing that isn’t actually an arb at all.

Once the combined percentage crosses 100%, there’s no arb left to lock in — the pairing at 101.00% would actually cost you $1.98 on a $200 stake rather than pay you.

The Two Arb Legs in Each Odds Format

This calculator works in American odds, but it’s worth seeing the two legs of the worked example side by side in decimal form and as implied probabilities, since that’s the language sportsbooks and arbitrage tools use interchangeably.

Add those two implied percentages together and you get the 97.73% combined figure from the worked example — the gap below 100% that made this pairing an arb in the first place.

Why Arbitrage Is Fragile

Arbs are real, but they’re fragile. The margin is thin — a couple of percent is a good one — so a line that moves before your second leg is placed can erase the edge entirely or, worse, leave you exposed on one side with no offsetting bet at all.

Books also actively limit or close accounts that arb consistently. Sportsbooks want two-way action from bettors who might lose, not guaranteed-profit plays that only cost them money, so consistent arbing tends to get flagged and restricted over time. A voided leg, a palpable-error void, or a maximum-stake cap can also break the pair after you’ve already committed the first bet — leaving you with one live wager and no guarantee at all.

Currency conversion, withdrawal timing, and capital tied up across two separate accounts all eat into a return that’s only around 2% to begin with, so the headline profit rarely survives intact once you account for the friction of running money through two books. The math behind arbitrage is guaranteed only if both legs stand exactly as priced when you place them. Treat arbitrage as a discipline of execution speed and account management, not a money printer.

When Arbitrage Betting Makes Sense

Arbitrage makes the most sense when you can act fast across multiple sportsbook accounts and the margin on offer is large enough to survive the friction of placing two bets. Because the profit is small relative to the money involved, it rewards bettors who already have funded accounts at several books, can place both legs within moments of each other, and don’t mind tying up capital across separate platforms while a game plays out.

It makes far less sense as a primary strategy for a bettor with one account, limited bankroll, or a preference for larger single payouts. The guaranteed nature of the profit is attractive, but the dollar amounts are modest, and every dollar of stake sits on two different platforms rather than working for you in one place. Bankroll management here is less about staking a percentage on any single outcome, since the outcome doesn’t matter, and more about keeping capital ready across enough books that a genuine gap doesn’t slip past.

Arbitrage also suits bettors comfortable with the account-management side of the game — monitoring limits, spreading action across books, and accepting that some books will eventually restrict how much they’ll take. If you’d rather take a single position and accept the risk of losing for a potentially larger return, a straight bet at one book is the simpler path.

Common Mistakes

Placing the first leg quickly and only then discovering the second book has already moved its line, so the arb has disappeared before the pair could be completed. Miscounting the stake split between the two legs, so one side ends up returning a different dollar amount than the other instead of matching exactly. Ignoring a sportsbook’s maximum-stake limit, which can cap one side well below what the arb actually needs in order to balance both legs. Forgetting that books track betting patterns closely, and that consistent arbing gets accounts flagged, then limited or closed entirely.

Arbitrage vs a Straight Bet

Arbitrage trades a smaller, guaranteed return spread across two books for the single-outcome risk of a straight bet at one book. A straight bet can win big or lose everything on the result; an arb pays a small, locked-in amount whichever side comes in, provided both legs get placed before the lines move.