What is the arbitrage formula?

An arbitrage exists when the sum of (1/odds) across all outcomes is less than 1. The guaranteed profit percentage is (1 divided by the sum) − 1.

How do I split the stakes in a sure bet?

For each outcome the stake is (1/odds) divided by the sum of implied probabilities, times your total capital. This makes the return the same whichever outcome occurs.

Do I need an arbitrage calculator?

To learn how it works, calculating by hand is useful. In practice odds move within seconds, so you need automatic calculation. ArbPlay computes the percentage and the stake split for you in real time.

How to Calculate a Sure Bet

Updated: 21 June 2026 · 5 min read

A sure bet is calculated in two moves: first you check whether the sum of (1/odds) across all outcomes is less than 1 — if so, an arbitrage exists. Then you split your capital proportionally, so the return is the same whichever outcome occurs.

The formula

Arbitrage check

(1/odds₁) + (1/odds₂) + … < 1

Profit percentage

profit % = (1 / sum) − 1

Stake split

stakeᵢ = (1/oddsᵢ) / sum × capital

The steps

Collect the best odds for each outcome, from different bookmakers or a betting exchange.
Convert to implied probability: 1 ÷ odds for each outcome.
Sum and check: if the sum < 1, an arbitrage exists.
Calculate the profit percentage: (1 ÷ sum) − 1.
Split your capital with the stake-split formula.
Place both legs quickly.

Worked example

A tennis match, two outcomes. Best available odds:

Player A @ 2.08 (bookmaker X)
Player B @ 2.00 (bookmaker / exchange Y)

Step	Calculation	Result
1/odds A	1 ÷ 2.08	0.4808
1/odds B	1 ÷ 2.00	0.5000
Sum	0.4808 + 0.5000	0.9808 < 1 ✓
Profit %	(1 ÷ 0.9808) − 1	≈ 1.96%

Splitting €100 of capital

→ Player A: (0.4808 ÷ 0.9808) × 100 = €49.02 @ 2.08 = return €101.96
→ Player B: (0.5000 ÷ 0.9808) × 100 = €50.98 @ 2.00 = return €101.96

Whoever wins, you get €101.96 — a guaranteed profit of €1.96 on €100 of capital.

With three outcomes (1-X-2)

The same formula works for football with three outcomes — you just add the 1/odds of the draw to the sum, and split across three stakes instead of two.

Two things that eat your profit

Exchange commission: if one leg is a lay on an exchange, commission (2%–5%) reduces your net margin. See how betting exchanges work.
Odds movement: by the time you calculate by hand, the price changes. In practice margins are small (0.5%–3%), so speed is critical.

Why you don't do it by hand

Manual calculation is perfect for understanding the logic — but odds change within seconds. ArbPlay scans the markets, applies exactly these formulas (commission included) every 1–2 seconds, and gives you the percentage and the split ready to use.