The formula at a glance
- V = Σ(1 / odds) — add up 1 divided by each outcome's odds.
- V < 1 → it's a surebet (guaranteed profit).
- Profit margin = (1 / V − 1) × 100%.
- Stake per outcome = (total stake / V) / odds.
- Skip the maths — the surebet calculator does all of it instantly.
What is the arbitrage betting formula?
Decimal odds contain an implied probability: an outcome priced at odds O is the bookmaker saying it has a 1 / O chance of happening. Add the implied probabilities of every outcome of an event together and you get V:
V = 1/odds₁ + 1/odds₂ + … + 1/oddsₙ
For a single bookmaker, V is always above 1 — that extra slice above 100% is the bookmaker's margin (the “overround”). But when you take the best odds for each outcome across different bookmakers, V can drop below 1. When it does, the outcomes are collectively priced at under 100% and a guaranteed profit exists. That is a surebet.
How to calculate if a bet is an arbitrage
Follow five quick steps:
- Convert each outcome's odds to implied probability: 1 ÷ odds.
- Add them together to get V.
- If V < 1, you have a surebet.
- Work out the margin: (1 ÷ V − 1) × 100%.
- Split your stake so every outcome returns the same payout (formula below).
Worked example: a 2-way surebet
Bookmaker 1 offers 2.10 on Player A; Bookmaker 2 offers 2.10 on Player B.
- V = 1/2.10 + 1/2.10 = 0.476 + 0.476 = 0.952 → below 1, so it's a surebet.
- Margin = (1 / 0.952 − 1) × 100 = 5.0%.
- With a €100 total stake: payout = 100 / 0.952 = €105.04. Stake = 105.04 / 2.10 = €50.02 on each.
- Whichever player wins, you collect €105.04 for a €5.04 profit.
Try it yourself in the 2-way arbitrage calculator.
Worked example: a 3-way surebet (1X2)
Best odds: Home 2.70, Draw 3.40, Away 3.10.
- V = 1/2.70 + 1/3.40 + 1/3.10 = 0.370 + 0.294 + 0.323 = 0.987 → a surebet.
- Margin = (1 / 0.987 − 1) × 100 ≈ 1.3%.
- With €100: payout = 100 / 0.987 = €101.3. Stakes: Home 101.3/2.70 = €37.52, Draw 101.3/3.40 = €29.79, Away 101.3/3.10 = €32.68.
- Any result returns ~€101.3, a ~€1.3 profit.
The 3-way arbitrage calculator does this in one click.
How to calculate your stakes and profit
Once you know V, two formulas finish the job for a total stake S:
- Stake on outcome i = (S / V) / oddsᵢ — makes every payout equal.
- Guaranteed profit = S × (1 / V − 1) — the same whichever outcome wins.
The maths is identical for any number of outcomes — just keep adding 1/odds terms to V. Our main calculator handles 2 to 15 outcomes, and there are dedicated versions for 4-way, 5-way and 6-way markets.
What about free bets?
Free bets change one term in the formula: a free bet returns (odds − 1) × stake because the stake isn't returned. Our free bet calculator applies that automatically — tick which stakes are free bets and it solves the rest.
Frequently asked questions
- What is the arbitrage betting formula?
- V = 1/odds1 + 1/odds2 + ... + 1/oddsN. If V is below 1, the event is priced at under 100% across bookmakers and a guaranteed profit (surebet) exists.
- How do you know if a bet is an arbitrage?
- Add up 1 divided by each outcome's odds. If the total (V) is less than 1, it is an arbitrage. The lower the V, the bigger the profit.
- How do you calculate arbitrage stakes?
- Stake on each outcome = (total stake ÷ V) ÷ that outcome's odds. This makes every outcome return the same payout, so your profit is identical whichever result lands.
- What is a good arbitrage percentage?
- Most surebets return roughly 1-5%. Higher margins exist but are rarer and disappear quickly as bookmakers correct their odds.
- Do I have to calculate it by hand?
- No. Our calculators apply the formula instantly for 2 to 15 outcomes — just enter the odds and your stake.