The Arbitrage Model: Betting Both Sides When Sportsbooks Disagree

Most bets come down to who wins. An arbitrage doesn’t. When two sportsbooks disagree enough on the same market, you can bet both sides and come out ahead whatever happens.

Those gaps are small, uncommon, and usually gone fast. The Arbitrage model in Optimal+ hunts for them across sportsbooks and does the stake math for you.

What Is Arbitrage Betting?

Every price has an implied probability. At a single sportsbook, the two sides of a market add up to more than 100%. The extra is the vig.

Nothing says you have to take both sides at the same book, though. Take the best price on each side at different books, and the total can dip below 100%. That’s an arbitrage.

A Simple Example (illustrative numbers)

Yankees at Red Sox, total 8.5 runs:

Bet $100 on each side, $200 in total:

• Over wins: DraftKings returns $205. The FanDuel bet loses. Profit: $5

• Under wins: FanDuel returns $205. The DraftKings bet loses. Profit: $5

Either way you collect $205 on $200 staked, a 2.5% return regardless of the final score. The combined implied probability tells you the size of the gap:

Arbitrage return = (1 ÷ Combined Implied Probability) − 1

Here that’s (1 ÷ 0.976) − 1 = 2.5%. Anything below 100% combined is an arbitrage. You can check any two prices with the hold calculator. A negative hold means an arb.

Try the hold-calculator→

How to Split Your Stakes

When the two sides have different odds, equal stakes won’t work. Size each bet so both outcomes return the same amount:

Stake B = (Stake A × Decimal Odds A) ÷ Decimal Odds B

Say BetMGM has the Bills -2.5 at +110 (2.10) and Caesars has the Dolphins +2.5 at -102 (1.98):

1. Bet $100 on the Bills. If they cover, you get back $100 × 2.10 = $210

2. Bet $210 ÷ 1.98 = $106.06 on the Dolphins. If they cover, you get back $106.06 × 1.98 = $210

3. Total staked: $206.06. Either way you collect $210, a profit of $3.94, or a 1.9% return

Each arbitrage play in Optimal+ shows a stake split like this, along with the profit and the percentage return. Scale the stakes to your own size, and recalculate if either price has moved. The hedge calculator runs the same equal-payout math.

Try the hedge-calculator→

How the Arbitrage Model Finds Arbs

Finding an arb by hand means watching the same market at every sportsbook at once and acting before the gap closes. The Arbitrage model handles the search:

1. Find the best price on each side. For each market, it takes the best available price on each side across sportsbooks.

2. Match the market exactly. Both legs must be the same bet at the same line: the same total, the mirror-image spread, or the same player, stat, and line on a prop. Different lines aren’t an arbitrage.

3. Require two different books. The legs always come from different sportsbooks.

4. Check the math. If the combined implied probability is under 100%, the model calculates the stake split and the return.

5. Throw out the too-good-to-be-true. A huge arb is usually a stale or broken line, not free money. Implausibly large returns are filtered out.

6. Pregame only. Plays come off the feed once the game starts.

How Arbitrage Plays Are Graded

For most Optimal+ models, grades weigh an edge against the uncertainty of the result. An arbitrage doesn’t carry that uncertainty once both bets are placed.

So arbitrage grades come down to one thing: the size of the return. The bigger the gap between the books, the higher the grade.

What Can Go Wrong

The math of an arbitrage has no outcome risk. The execution does. Experienced arb bettors plan for all of these.

The line moves before your second bet

Arbs exist because one book is out of line, and books correct those prices. If you place one leg and the other price moves, you’re left holding a one-sided bet. Have both sportsbooks open before you start, and place the leg most likely to move first, which is usually the outlier price.

Bet limits

A book may cap your stake below what the split requires. Check the maximum before committing to the first leg.

Different house rules

Two books can settle the same event differently. Common examples include whether a player prop is voided when the player doesn’t play, whether overtime counts, and baseball rules on listed pitchers. If one leg is voided and the other is graded, the arb is gone. Read each book’s rules for the market.

Obvious-error rules

Sportsbooks reserve the right to void bets on clearly mispriced lines. The bigger and stranger the gap, the more likely a book calls it an error.

Account limits

Sportsbooks can limit accounts that consistently bet into stale prices, and steady arbitrage betting can draw that attention. Treat your account access as part of your bankroll.

Arbitrage vs. +EV Betting

Arbitrage and +EV betting aren’t rivals, and plenty of bettors use both. If you’re weighing arbs against hedging an existing bet, see hedge betting explained.

Tips for Using Arbitrage Plays

1. Keep accounts funded at several sportsbooks. Arbs rarely last long enough to wait on a deposit.

2. Confirm both prices before placing either bet.

3. Recalculate if anything moved. The stake split only works at the odds shown.

4. Start small until you know each book’s rules and limits.

5. Check both tickets after placing them, and keep a record of every leg.

Key Takeaways

• An arbitrage exists when the best prices on both sides, at different books, add up to less than 100% implied probability

• Size stakes so both outcomes pay the same: Stake B = Stake A × Odds A ÷ Odds B

• The Arbitrage model matches markets exactly, requires two different books, filters implausible returns, and grades by the size of the return

• There’s no outcome risk once both bets are in, but line moves, limits, house rules, and error rules are real

• Arbs are small and short-lived, so speed and funded accounts matter

Find arbitrage plays with the stakes already split in Optimal+.