How to Calculate an Arbitrage Bet (Worked Examples)
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Key takeaways
- Quick check with American odds: a plus price and a minus price form an arb when the plus number is bigger than the minus number (+115 vs −105).
- Stake on each outcome = total × (1 ÷ its decimal odds) ÷ the sum of all 1 ÷ odds.
- If a book caps your bet, fix that stake and size the other legs so every outcome returns the same amount.
- Round stakes to $5 or $10 to look less like an arber. It costs a small slice of profit.
Spotting an arbitrage is only half the job. You also need to know how much to put on each side so every outcome pays the same, and how to adjust when a book won’t take your full stake. This guide works through the math with real numbers. The arbitrage calculator handles all of it automatically, but it’s worth understanding what it’s doing.
Step 1: Check whether it’s an arb
Convert each outcome’s best price to decimal odds and add up the implied probabilities (1 ÷ decimal odds). Under 100% means arb.
The American odds shortcut
For a two-way market with one plus price and one minus price, you can skip the conversion. It’s an arb when the plus number is larger than the minus number.
- +115 vs −105 → 115 is larger than 105 → arb
- +110 vs −115 → 110 is smaller than 115 → no arb
- +102 vs −102 → equal → break-even
Two plus prices on opposite sides are always an arb. Two minus prices never are.
Step 2: Split the stake
Two-way example
Team A +115 (2.15) at Book 1, Team B −105 (1.952) at Book 2, $1,000 total.
- 1/2.15 = 0.4651 and 1/1.952 = 0.5122, so I = 0.9773
- Stake on A: 1,000 × 0.4651 ÷ 0.9773 = $475.91
- Stake on B: 1,000 × 0.5122 ÷ 0.9773 = $524.09
- Return either way: 1,000 ÷ 0.9773 = $1,023.22
- Profit: $23.22 (2.32%)
Run the numbers: Do these prices guarantee a profit, and how much goes on each side? Open the Arbitrage Calculator
Fixed-stake arbs: when a book limits you
Often one book won’t take the full amount. Maybe it caps the bet or you’ve been limited. In that case, fix the stake at that book and size the rest around it.
Example: Book 1 will only take $250 on Team A at +115.
- Target return: 250 × 2.15 = $537.50
- Stake on B: 537.50 ÷ 1.952 = $275.30
- Total staked: $525.30. Profit: $12.20 either way (2.32%).
The percentage stays the same; only the size changes. In the calculator, switch to Fixed stake on A.
Rounding without giving away the edge
Stakes like $475.91 are a giveaway. Recreational bettors bet round numbers. Rounding helps your accounts last, at the cost of unequal outcomes.
Example: Round the $1,000 arb to the nearest $5: $475 on A and $525 on B.
| Outcome | Stake | Returns | Profit |
|---|---|---|---|
| Team A wins | $475 | $1,021.25 | +$21.25 |
| Team B wins | $525 | $1,025.00 | +$25.00 |
Your guaranteed profit drops from $23.22 to $21.25, the worst of the two. For most arbs, rounding to $5 or $10 costs only a few dollars. The calculator shows the worst-case profit after rounding.
Three-way arbs
Soccer 1X2 markets have three outcomes: home, draw, away. The math is the same, with a third term.
Example: Home +155 (2.55) at Book A, Draw +270 (3.70) at Book B, Away +215 (3.15) at Book C.
With $1,000 total:
| Outcome | Stake | Returns |
|---|---|---|
| Home | $400.21 | $1,020.53 |
| Draw | $275.82 | $1,020.53 |
| Away | $323.98 | $1,020.53 |
Profit: about $20.53 whichever way the match goes.
Make sure all three markets are the same type. Soccer 1X2 markets settle on regulation time (90 minutes plus stoppage time) at nearly every book, but confirm before you mix them with moneylines that include extra time.
Find arbs without refreshing twelve apps
ProfitDuel's Arb Matcher scans dozens of sportsbooks and thousands of events, flags live arbitrage opportunities, and sizes each stake for you.
Start the $1 ProfitDuel trialAffiliate link. The $1, 3-day trial applies to ProfitDuel's Starter plan as listed in September 2026. 21+ and in states where online sports betting is legal.Middles: a close cousin
A middle uses two different lines instead of two prices on the same line.
Example: Over 44.5 at −110 at Book 1 and Under 47.5 at −110 at Book 2, $110 each.
- Total lands 45, 46, or 47: both bets win, +$200.
- Total lands 44 or lower, or 48 or higher: one wins, one loses, −$10.
Whether a middle is worth it depends on how often the result lands in the gap. NFL totals and spreads that cross key numbers (3, 7, 10 for spreads) can make middles attractive. Unlike an arb, a middle isn’t guaranteed.
A pre-bet checklist
- Confirm both prices are live. Refresh right before betting.
- Confirm the markets match: same line, same settlement rules, same period.
- Size the stakes and round sensibly.
- Place the leg at the book most likely to move first.
- Place the other leg immediately. If the price moved, recalculate before placing, or hedge at the best available price to limit the damage.
- Log both bets. You’ll need records for taxes; see sports betting taxes in 2026.
Frequently asked questions
Are two plus-money prices always an arbitrage?
Yes, for a genuine two-outcome market. Each side implies less than 50%, so the total is under 100%. If you ever see +105 and +105 on opposite sides at two books, it’s an arb (assuming both markets settle the same way).
Should I stake to guarantee equal profit or bias toward one side?
Equal profit is the default. Some arbers bias stakes so one outcome breaks even and the other wins more, which can make sense if one side is also +EV against a sharp line. It’s no longer a pure arb, though.
How do I handle a 3-way arb with only two books?
You can’t cover three outcomes with two prices unless one book offers a combined bet, such as a double chance (home or draw). Pair a double-chance price at one book with the remaining outcome at another.
Find arbs without refreshing twelve apps
ProfitDuel's Arb Matcher scans dozens of sportsbooks and thousands of events, flags live arbitrage opportunities, and sizes each stake for you.
Start the $1 ProfitDuel trialAffiliate link. The $1, 3-day trial applies to ProfitDuel's Starter plan as listed in September 2026. 21+ and in states where online sports betting is legal.