Arbitrage Calculator for Sports Betting
An arbitrage calculator takes the odds on each side of a market from two different sportsbooks, plus your total stake, and tells you exactly how to split that money so you collect the same return no matter who wins. Arbitrage betting is one of the rare times in sports betting where you aren’t picking a side. You’re backing numbers. When two books price the same game differently enough, you can cover both outcomes and lock in a profit before the ball is even tipped. The tool below does the math for you (doing it by hand while a line is moving is how you fat-finger a stake), so just enter the odds, enter your total stake, and it shows the per-side stakes and whether the gap is actually worth betting.
Arbitrage Betting Calculator
How Arbitrage Betting Works
Arbitrage works when the combined implied probability of both sides drops below 100%: in decimal terms, when (1 ÷ d1) + (1 ÷ d2) is less than 1, where d1 and d2 are the best decimal odds you can find on each outcome. Each decimal price has a built-in implied probability of 1 ÷ the price, and a single sportsbook always sets its two sides to add up to more than 100% (that overround is the vig, which is how it makes money). But when you pull the best price on side A from one book and the best price on side B from another, those two numbers can total less than 100%, and that gap is your edge.
That gap is the arbitrage margin, calculated as 1 − (1 ÷ d1 + 1 ÷ d2). The bigger the margin, the more guaranteed profit you keep. The whole strategy is just a betting version of the oldest idea in finance: buying and selling the same thing at two different prices to pocket the difference. You can read the general-finance definition in Investopedia’s explainer on arbitrage; sports arbitrage is that exact concept applied to two sportsbooks disagreeing on a price.
An arb exists when (1 ÷ d1) + (1 ÷ d2) is less than 1, using the best decimal odds on each side, and the calculator checks this for you.
A Worked Two-Book Example
Say Book A has one outcome at +110 (decimal 2.10) and Book B has the other outcome at +105 (decimal 2.05), and you want to stake $1,000 total. That’s a real arb worth roughly $37 in guaranteed profit. Here’s how the math gets there. First the test: 1 ÷ 2.10 = 0.47619 and 1 ÷ 2.05 = 0.48780, which sum to 0.96399. That’s below 1, so an arbitrage exists, and the arbitrage margin is 1 − 0.96399 = 3.60%.
Next, the stake split. You weight each side by its share of that 0.96399 total, so the stake on outcome 1 is $1,000 × (0.47619 ÷ 0.96399) = $493.98, and the stake on outcome 2 is $1,000 × (0.48780 ÷ 0.96399) = $506.02. Both sides now return the same amount: $493.98 × 2.10 and $506.02 × 2.05 each pay back about $1,037.35. Against your $1,000 outlay, that’s a guaranteed profit of $37.35 regardless of which side wins.
| Outcome | Best Odds (Decimal) | Your Stake | Returns If It Wins |
|---|---|---|---|
| Outcome 1 (Book A) | +110 (2.10) | $493.98 | $1,037.35 |
| Outcome 2 (Book B) | +105 (2.05) | $506.02 | $1,037.35 |
| Total | — | $1,000.00 | $1,037.35 |
One number that trips people up: the 3.60% margin and the 3.73% return on investment are not the same figure. The margin (3.60%) is what’s left after the two implied probabilities are subtracted from 100%. The ROI (3.73%) is your $37.35 profit measured against the $1,000 you actually put at risk: slightly above the margin, because you only ever stake the discounted total. The calculator reports the ROI, since that’s the number that tells you whether a play clears your own threshold.
How to Use the Calculator
Using the calculator takes four inputs and one click: pick your odds format, enter the price on each outcome, type your total stake, and set the minimum return you’ll accept. There’s nothing to download and no sign-up, and the results appear the moment your numbers are in. Here’s what each input means.
Step 1: Pick Your Format and Enter the Odds
Choose American, decimal, or fractional, and you can mix formats across outcomes if one book lists American and another lists decimal. Type each price exactly as the sportsbook shows it. If you only have a price in one format, our odds calculator converts it in a click.
Step 2: Enter Your Total Stake and Minimum ROI
Type the total you want to bet across all outcomes (not per side), and the calculator splits it for you. Then set the lowest return you’re willing to take; if the gap between the two books doesn’t clear that threshold, the tool tells you to pass instead of forcing a marginal play that fees could wipe out.
Step 3: Calculate and Read the Output
Hit calculate, and you’ll see the exact stake for each side, your total guaranteed return, your profit in dollars, and the ROI as a percentage. If there’s no arbitrage, the tool says so plainly. That’s your cue to either lower your minimum ROI or go hunting for better prices.
How to Find and Place Arbs
You find arbs by comparing the same market across as many sportsbooks as possible and acting fast when two prices disagree enough to clear the test. The more books you shop, the more often you’ll catch a gap before it closes. The same hunt for mispriced lines drives value betting: arbitrage is just the version where you cover every outcome instead of taking a single side. Two habits keep you from getting burned:
- Lock both legs back-to-back. Place the second bet immediately after the first. The danger window is the gap between them: if the price moves before your second leg lands, you’re suddenly exposed on one side.
- Confirm the odds before you submit. Re-check that each price still matches what you typed into the calculator. A line that drifted even a few cents can shrink a thin margin to nothing.
The Real Risks and Limits of Arbitrage Betting
Arbitrage is low-risk, not no-risk: the profit is guaranteed only if every bet lands as planned, and several real-world snags can break that. These are the issues that turn a “sure bet” into a real loss:
- Account limits and flagging. Sportsbooks dislike arbers and watch for them. Get flagged and your maximum bet can be slashed to a few dollars, or your account restricted, which quietly ends the strategy for you.
- Line movement between legs. If a price shifts after your first bet but before your second, you can end up with one-sided exposure instead of a locked arb: a real gamble, not a guaranteed return.
- Stake rounding. The exact stake is often an odd number like $493.98. Bet it to the cent and the precision itself can flag you; round it for cover and you shave a little off the margin. Either way, the cushion shrinks.
- Voided bets. If one leg gets voided for a mispriced “palpable error” or a rule technicality, the other leg is live and unhedged. One voided winner can flip your guaranteed profit into a loss.
- Fees and friction. Withdrawal fees, deposit charges, and currency conversion all eat into a thin margin. On a 2-3% arb, friction matters far more than it would on a normal bet.
A guaranteed profit assumes both legs settle as bet. A single voided leg or a price that moves before your second bet lands can leave you exposed on one side. Treat the calculator’s profit figure as the best case, then subtract for fees, rounding, and the chance one leg doesn’t go through.
Middles: The Arb’s Riskier Cousin
A middle is what you get when the two sides you bet are at different numbers instead of different prices: say Over 44.5 at one book and Under 46.5 at another. If the game lands on 45 or 46, both bets win at once. Land anywhere else and one bet wins while the other loses, costing you only the vig. Unlike an arb, a middle is not guaranteed profit; it is a cheap lottery ticket on the game landing in your window, and the math below tells you exactly what the ticket costs and what it needs to pay off.
The classic case shows why middlers are patient people. Bet both sides of a two-point window at the standard -110 and -110 with $1,000 total, and the calculator splits it $500 each: every miss costs $45.45 in vig, every hit pays $909.09, and the middle needs to land just 4.76% of the time to break even. That low bar is the entire attraction, and it is why football middles cluster around the key numbers of 3 and 7, where final margins land far more often than anywhere else. The discipline is the same as arbitrage: two books, two tickets, and a plan made before the first bet, not after it.
Related Betting Tools
Pair the arbitrage calculator with our other free tools to price every bet before you place it. If you’re combining legs into one ticket, our parlay calculator shows the true payout and implied odds, the no-vig calculator reveals each book’s fair price before you go hunting for a gap, and the Kelly Criterion calculator handles stake sizing when you take a side instead of covering both. Browse the full set on our sports betting tools hub.
Play Safe: Gambling should be fun, not stressful. Set limits, stick to your budget, and never chase losses. If you or someone you know has a gambling problem, call 1-800-MY-RESET or visit ncpgambling.org. For more resources, see our Responsible Gambling page.
Frequently Asked Questions
New to arbitrage and wondering whether it’s legal, profitable, or worth the hassle? Here are the questions bettors ask most before they place their first arb.
Is arbitrage betting legal in the US?
Yes, arbitrage betting is legal anywhere sports betting itself is legal. You aren’t doing anything against the law by betting both sides of a market at two different sportsbooks. The catch is that it goes against sportsbooks’ interests, so while it’s perfectly legal, individual books can limit or close the accounts of bettors they identify as arbers.
How much can you actually make with arbitrage betting?
Most arbitrage opportunities lock in a small edge, usually in the 1-5% range of your total stake, which is why the strategy depends on volume and bigger bankrolls rather than huge wins per bet. The bigger constraint is rarely the margin itself but the stake limits sportsbooks impose once they flag you, which cap how much you can put through on each play.
Why do sportsbooks limit or ban people who arb?
Sportsbooks profit from bettors taking single sides at a built-in margin, and arbers sidestep that by only betting when the numbers guarantee a profit. Because that’s pure cost to the book with no expected return, operators watch for the patterns arbers leave, like oddly specific stake amounts and only ever betting mispriced lines, and respond by cutting your limits or restricting your account.
What’s the difference between a 2-way and a 3-way arbitrage bet?
A 2-way arb covers two possible outcomes, like one team or the other winning a basketball game. A 3-way arb adds a third result, most often a draw, which is why it shows up in soccer and some prop markets. The math is the same idea either way: the calculator checks whether the combined implied probabilities of all outcomes fall below 100% and splits your stake to match.
Can I still lose money on an arbitrage bet?
Yes, if something disrupts the execution. The profit is only guaranteed when both legs settle exactly as planned. A voided leg, a price that moves before you place your second bet, or fees eating a thin margin can all flip an arb into a real loss. That’s why arbitrage is best described as low-risk rather than risk-free.