Arbitrage betting (or "arbing") is the math-purest way to make money from sportsbooks: you bet on every possible outcome of an event, distributed across two or more sportsbooks at prices that don't agree, locking in a guaranteed profit no matter who wins. There's no probability estimation, no edge over the bookmaker on the actual outcome — just exploiting the fact that two or more bookmakers have priced the same market inconsistently.
Arbitrage betting (or "arbing") is the math-purest way to make money from sportsbooks: you bet on every possible outcome of an event, distributed across two or more sportsbooks at prices that don't agree, locking in a guaranteed profit no matter who wins. There's no probability estimation, no edge over the bookmaker on the actual outcome — just exploiting the fact that two or more bookmakers have priced the same market inconsistently.
The math is straightforward. The execution is operational: finding the prices fast enough, placing both legs before the market moves, and managing the inevitable account restrictions that follow. This post is the complete reference: the formulas, how to find arbs, what edges and durations are realistic, and how the account-longevity meta-game compares to matched betting.
1/decimal_odds for each outcome. Sum. If it's < 1, there's an arb.(1 / sum) − 1. Typical edges are 0.5–3% on liquid markets; rare 5%+ arbs appear briefly on niche or promotional pricing.For any market with N possible outcomes priced at decimal odds d1, d2, ..., dN, an arbitrage opportunity exists when:
1/d₁ + 1/d₂ + ... + 1/dₙ < 1
The sum represents the implied probability across all outcomes plus the bookmaker's vig. Within a single sportsbook, this sum is always > 1 (that's how the book makes money). Across multiple sportsbooks, if the prices are inconsistent enough, the sum can be < 1 — arbitrage.
Once you've confirmed an arb exists, the profit margin (edge) is:
edge = (1 / sum) − 1
A sum of 0.97 → edge of (1/0.97) − 1 = 3.09%. A sum of 0.98 → edge of 2.04%. A sum of 0.995 → edge of 0.50% — barely worth the time.
Given a total bankroll S and the inverse-sum sum, the optimal stake on each outcome is:
stake_i = (1/dᵢ) / sum × S
This produces equal returns regardless of which outcome wins. The same return on every leg is what makes the bet "guaranteed profit."
A tennis match. Sportsbook A has Player A at decimal 2.10. Sportsbook B has Player B at decimal 2.10 (an unusually rich offer on the underdog).
Sum: 1/2.10 + 1/2.10 = 0.476 + 0.476 = 0.952. Edge: (1/0.952) − 1 = 5.04%.
On a $1,000 total bankroll: - Stake on A: 0.476/0.952 × $1,000 = $500 - Stake on B: 0.476/0.952 × $1,000 = $500
If Player A wins: $500 × 2.10 = $1,050 returned. If Player B wins: $500 × 2.10 = $1,050 returned. Profit: $50 regardless. 5% guaranteed.
5%+ arbs are rare on liquid 2-way markets — they show up most often on promotional boosts or after rapid line moves at slow-to-update sportsbooks.
NFL moneyline. Sportsbook A has Patriots at +180 (decimal 2.80). Sportsbook B has Bills at −160 (decimal 1.625).
Sum: 1/2.80 + 1/1.625 = 0.357 + 0.615 = 0.972. Edge: (1/0.972) − 1 = 2.84%.
On a $2,000 total bankroll: - Stake on Patriots: 0.357/0.972 × $2,000 = $735 - Stake on Bills: 0.615/0.972 × $2,000 = $1,265
If Patriots win: $735 × 2.80 = $2,058. Profit $58 (2.9%). If Bills win: $1,265 × 1.625 = $2,055. Profit $55 (2.75%).
Returns aren't perfectly equal due to rounding — about 2.8% guaranteed.
Premier League match. Three different sportsbooks pricing Home / Draw / Away:
Sum: 0.294 + 0.286 + 0.455 = 1.035.
Sum > 1 → no arb exists. The prices, while across three sportsbooks, don't disagree enough to create a guaranteed profit.
3-way arbs are rarer than 2-way arbs because three outcomes give the sportsbooks more places to price conservatively. Most 3-way arbs in soccer are short-lived (under a minute) and appear after late price moves. The Arbitrage Calculator detects them automatically when you input three decimal prices.
Three approaches in increasing infrastructure:
Open four to six sportsbooks side by side. Pick a market (e.g., a tennis match). Note the best price for each side. Compute the sum. Repeat across markets.
This works for hobbyists with a few hours a week. It also requires willingness to wait — most markets across most sportsbooks won't show an arb most of the time. You'll spend hours scanning to find a single 1.5% arb.
Many free sites aggregate prices across major sportsbooks. They don't always flag arbs explicitly but they let you eyeball prices in seconds rather than minutes. Useful for catching obvious mispricings.
Services like RebelBetting, OddsJam, BetBurger (and others) scan dozens of sportsbooks in real time, calculate inverse-decimal sums automatically, and alert you to arbs above a threshold (typically 1–2%). Subscription costs $30–$100/month.
For sustained arbing, paid services are essentially required. The volume of arbs available manually is too small to justify the time investment for most bettors.
What's a realistic arb to chase?
For most arbers, 1.5%+ is the practical threshold. Below that, the risk of one leg moving before you place the second leg eats your edge.
Speed is operational. Set up your sportsbook tabs, fund accounts, and have stakes pre-calculated before the arb appears.
Sportsbooks track every customer's behavior. Sustained arbing produces detection within weeks at most major books. The signs:
You place leg 1 at 2.10. Before you can place leg 2, the price drops from 2.10 to 1.90. Your "guaranteed" profit is now an actual exposure on the underlying outcome. Two solutions:
You arb a boosted price; the sportsbook later voids the promo claiming "abuse." Read promo T&Cs before relying on the boosted price as part of your arb math.
Some sportsbooks show stale prices but apply current prices at bet placement. The arb you saw and the arb you placed may differ. Refresh and confirm before clicking.
A 3% arb is theoretical until you can actually place the calculated stakes. If sportsbook B caps you at $50 but the math wants $500, the arb is unworkable.
Arbing across international sportsbooks means foreign exchange spreads, withdrawal fees, and timing delays. A 2% arb minus 1.5% in conversion costs is a 0.5% arb. Run the full math.
Closely related but distinct techniques.
| Feature | Arbitrage | Matched Betting |
|---|---|---|
| Source of edge | Cross-book price differences | Promotional offers |
| Profit per bet | Low (0.5–3%) | High (free bet face value) |
| Volume needed | High (many bets/day) | Low (few bets/week) |
| Setup difficulty | High (services, multiple books) | Low (free bet + exchange) |
| Account-longevity risk | Very high | High |
| Recurrence | Continuous opportunities | Promo-by-promo |
| Math | Inverse-decimal sum across all outcomes | Back/lay with free-bet structure |
Some bettors do both. Matched betting captures signup-offer value; arbitrage extracts ongoing price-difference value as accounts mature. Both end the same way: account restrictions.
In most jurisdictions, arbitrage profits are taxable income. Track every bet — both the back and the lay (or both legs of the cross-book arb) — for accurate reporting.