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▌ Calculator · arbitrage · updated 2026-05-09

Two books.
One guaranteed
profit.

An arbitrage exists when two bookmakers disagree enough on the same event that you can bet both sides and guarantee profit. The math: if the combined implied probability of both outcomes is below 100%, the gap is yours. This calculator finds the optimal stake split and shows your guaranteed return before you place a single bet.

The arb percentage is typically 1–5%. Small, but risk-free by construction. The real constraint is not the math — it's account limits. Books that allow arbing without restriction (Pinnacle, Betfair) typically have tighter lines.

Check for arb How arb math works

Calculator

Live · client-side · zero tracking

▌ Two-way arb inputs

$

▌ Leg A — Outcome 1

▌ Leg B — Outcome 2

▌ Arb analysis

✓ Arbitrage opportunity

Guaranteed profit

+2.91

ROI: 2.91% on $100.00

Optimal stake allocation

Book A

$33.20

At odds

3.100

Payout

$102.91

Book B

$66.80

At odds

1.541

Payout

$102.91

Sum of inverses: 0.9717

Arb exists when sum < 1.0000. Current: ✓ below 1.

▌ Derivation · arb math

How arbitrage math works

The arb condition: an opportunity exists when the sum of implied probabilities across all outcomes is below 100%. For two outcomes at decimal odds A and B: 1/A + 1/B < 1.0.

Optimal stake split

We want equal payout regardless of outcome. If total stake is S, stake on leg A is S_A = S × (1/A) / (1/A + 1/B). Stake on leg B is S_B = S × (1/B) / (1/A + 1/B).

Verification: payout if A wins = S_A × A = S / (1/A + 1/B). Payout if B wins = S_B × B = S / (1/A + 1/B). Both yield the same payout — the guaranteed return.

Arb profit percentage

Arb ROI = (1 / (1/A + 1/B) − 1) × 100%. Or equivalently: (1 − sum_of_inverses) / sum_of_inverses × 100%. At sum = 0.98: ROI = (1/0.98 − 1) × 100 = 2.04%.

Worked example: +210 vs −185

Convert to decimal
+210 → 3.10 decimal · −185 → 1.541 decimal
Sum of inverses
1/3.10 + 1/1.541 = 0.323 + 0.649 = 0.971 (< 1.0 ✓ arb exists)
Arb ROI
(1/0.971 − 1) × 100 = 2.98% guaranteed
Stake split ($100 total)
Leg A: $100 × 0.323 / 0.971 = $33.27 · Leg B: $66.73
Payout if A wins
$33.27 × 3.10 = $103.14 total (+$3.14 profit)
Payout if B wins
$66.73 × 1.541 = $102.84 total (+$2.84 profit)

Note: minor rounding in this example. The calculator provides precise stake splits.

▌ FAQ

Common questions

What is sports betting arbitrage?
Arbitrage (arb) occurs when the combined implied probability of two outcomes at different bookmakers is below 100%. This happens when books set different odds on the same event — you bet both sides with optimal stake splits and guarantee profit regardless of outcome. Example: Book A offers +210 on Team A, Book B offers -185 on Team B. The sum of implied probabilities is less than 100%, so betting both sides returns guaranteed profit.
How do I find arbitrage opportunities?
Arbs exist when two books disagree significantly on odds. They most commonly appear when: (1) a line moves at one book but not another, (2) sharp bettors have moved the line at one book, creating a gap with soft books, (3) an event is obscure enough that books haven't aligned their models. In 2026, arbs typically last minutes before closing — arb scanners (OddsJam, SharpSide) are needed for real-time detection.
How do I calculate the optimal stake split?
For two outcomes with decimal odds A and B: Sum of inverses = 1/A + 1/B. If sum < 1.0, an arb exists. Stake on outcome A = (total stake × (1/A)) / (1/A + 1/B). Stake on outcome B = (total stake × (1/B)) / (1/A + 1/B). This allocation guarantees identical payout regardless of which outcome wins. The calculator handles this automatically.
What is a typical arbitrage profit percentage?
Most retail sports betting arbs yield 1–5% profit. The arb percentage = (1 / sum_of_inverses − 1) × 100. A sum of inverses of 0.98 gives a 2.04% arb. Middles and steam moves can yield 5–10%+, but these are brief windows. Most arbers target 1–3% consistently rather than chasing larger single arbs that may not be real.
What is the difference between arbitrage and hedging?
Hedging reduces risk on a position you already hold — typically to guarantee a profit after one side is already live. Arbitrage involves placing both sides before any outcome is known, using odds differences between books. Both produce guaranteed outcomes, but arb requires an opportunity to exist upfront while hedging adjusts an existing position. See the hedge calculator for single-event risk management.
Can I be banned for arbing?
Yes — soft US bookmakers (DraftKings, FanDuel, Caesars) routinely limit or close accounts of arbers. Pinnacle, Betfair, and other sharp-accepting books are more tolerant. The practical constraint is that profitable arbers lose access to soft lines. Matched bettors mitigate this by mixing bonus bets with occasional losing positions to appear as recreational bettors.
Does arbitrage work on three-way markets?
Yes. For a three-outcome market (home / draw / away), the sum of inverses is 1/A + 1/B + 1/C. If this sum is below 1.0, a three-way arb exists. The stake split uses the same proportional logic: stake per leg = (1/odds) / sum_of_inverses × total_stake. Three-way arbs are rarer because finding divergent odds across three legs simultaneously is harder.

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