Sports arbitrage calculator: stakes and profit across outcomes

To calculate an arbitrage, convert each outcome's best price to decimal odds, take 1 divided by each, and add them up. If the sum is under 1, the prices leave room for a profit whichever side wins. Your stake on each outcome is the total you want to spend times that outcome's share of the sum.

That's the whole calculator. This page gives the math for two-way and three-way markets, then the fees and rules that decide whether the number you calculated is the number you get.

Two-way arbitrage

A two-way market has two outcomes, such as a moneyline without a draw. Book A has Team X at +125. Book B has Team Y at -110. (An illustration, chosen so the numbers are easy to follow. It is not a result.)

	Team X at Book A	Team Y at Book B
American odds	+125	-110
Decimal odds	2.250	1.909
Implied probability (1 / decimal)	44.44%	52.38%
Sum	96.82%

The sum is under 100 percent, so there's an arbitrage. The margin is 1 / 0.9682 - 1 = 3.28 percent.

Now split a total stake of 1000. Each stake is the total times that outcome's implied probability divided by the sum:

• Team X: 1000 x 0.4444 / 0.9682 = 459.03
• Team Y: 1000 x 0.5238 / 0.9682 = 540.97

Check both results:

• X wins: 459.03 x 2.25 = 1032.82
• Y wins: 540.97 x 1.909 = 1032.80 (rounding)

Either way you collect about 1032.80 on 1000 staked, a profit of about 32.80. That is the 3.28 percent margin, and the stakes are set so the return is the same on both sides.

Three-way arbitrage

Soccer and some hockey markets have three outcomes: home, draw, away. The method is the same with a third term.

	Home	Draw	Away
Decimal odds (best across books)	2.10	3.60	4.20
Implied probability	47.62%	27.78%	23.81%
Sum	99.21%

The margin is 1 / 0.9921 - 1 = 0.80 percent. With 1000 to stake: 480 on home, 280 on the draw, 240 on the away side. Each returns 1008 (480 x 2.10, 280 x 3.60, 240 x 4.20), a profit of 8.

Note how much thinner this is than the two-way example. A third outcome means a third bet, and more chances for any one price to move or any one book to limit you. It also means you need the best price on all three outcomes at once.

Rounding your stakes

Real bets come in whole dollars or cents, not 459.03. Rounding moves the returns slightly. If you round to the nearest 5 (460 and 540), X returns 1035 and Y returns 1031, so the worst case is now 1031 on 1000, a profit of 31 instead of 32.80. On a margin this wide that is fine. On a 0.5 percent margin, rounding can swallow a meaningful share of the profit, so a rounding option matters. The quant+ scanner's stake split has one: cents, whole dollars, or the nearest 5 or 10.

What the calculation doesn't include

Fees. Sportsbooks build their fee into the price. Prediction markets charge separately. Polymarket's documented sports taker fee is fee = shares x 0.05 x price x (1 - price), and makers pay nothing. At a price of 0.50, that's 0.05 x 0.25 = 1.25 cents per share, or 2.5 percent of the 50-cent cost. A leg like that wipes out a 1 percent arbitrage by itself. Kalshi describes its fee as a charge on the expected earnings of the contract and publishes the formula in a separate fee schedule, and some markets differ. Add the fees for each leg before you decide a margin is real.

Price moves. The two prices don't stay put while you place the bets. If the second price moves before you get it down, you hold one side only. Economist Steven Levitt found that bookmakers adjust prices in small, infrequent steps, which is why disagreements appear. It's also why they close, and not on a schedule you control. Place the less certain leg first.

Rules that differ. Two venues can settle the same bet differently: overtime counted or not, a prop voided if a player doesn't start, a game postponed. A calculation that treats two contracts as opposite sides is wrong if they aren't.

Limits and restrictions. Researchers who bet using publicly available odds described an industry that responds to successful bettors with discriminatory practices. Books can cap stakes or close accounts, and arbitrage patterns are easy to spot. A calculator can't tell you your limit.

Arbitrage versus the other ways to use the same prices

An arbitrage uses prices at two or more books to lock in a return if everything holds. Related ideas get mixed up with it:

• A middle accepts a small loss in most outcomes for a shot at winning both bets.
• A +EV bet takes one side because the price is above fair value, with no certainty about any single bet. The expected value calculator shows that math, and the fair odds calculator shows where the fair price comes from.
• A hedge locks in a result on a bet you already hold.

How quant+ does this

The arbitrage scanner takes the best price per outcome across sportsbooks and prediction markets and flags any set where the implied probabilities sum to less than 1. Opening a row shows the stake split for your total, with rounding, and the theoretical return. It is the calculation on this page run on live prices. The odds comparison view shows every other book's price for the same market.

quant+ doesn't place bets, hold funds or connect to your accounts. The split shows the theoretical return, and whether you get it depends on the fees, the speed and the rules above. Log the ones you place in the bet journal so you can see how many you got down at the quoted prices.

Check that sports betting, and prediction markets if you use them, are legal where you live, and read the risk disclosure.

Quant+ is analytics for informational purposes. 21+. If you or someone you know has a gambling problem, call 1-800-GAMBLER.