How to Calculate Arbitrage Betting

Step 1: convert decimal odds to implied probability

For decimal odds, divide 1 by the odds. Odds of 2.05 have an implied probability of about 48.78%; odds of 2.10 have an implied probability of about 47.62%.

Implied probability = 1 ÷ decimal odds

Add the implied probabilities for every mutually exclusive outcome that completely covers the market.

Arbitrage test = (1 ÷ odds 1) + (1 ÷ odds 2) [+ (1 ÷ odds 3)]

If the total is below 1.00, or 100%, the entered prices form a theoretical arbitrage. If it equals or exceeds 100%, they do not.

Worked 2-way example

Assume the best price for Outcome A is 2.05 and the best price for Outcome B is 2.10. The combined implied probability is:

1 ÷ 2.05 + 1 ÷ 2.10 = 0.963995, or 96.40%

For a total stake of $100, first calculate the equal theoretical return:

Equal return = $100 ÷ 0.963995 = $103.73

Then divide that return by each outcome's odds:

• Outcome A stake: $103.73 ÷ 2.05 = $50.60
• Outcome B stake: $103.73 ÷ 2.10 = $49.40

The stakes total $100 and each unrounded leg returns about $103.73. The theoretical profit is about $3.73, or 3.73% of the total stake.

Worked 3-way example

For a full-time home/draw/away football market, suppose the best prices are 3.00, 3.70 and 2.65.

1 ÷ 3.00 + 1 ÷ 3.70 + 1 ÷ 2.65 = 0.9810, or 98.10%

With a $1,000 total stake, the equal return is approximately $1,019.36. The unrounded stakes are approximately $339.79 on home, $275.50 on draw and $384.68 on away. Always recalculate using the actual accepted odds and stakes rather than copying an example.

Two different percentages are often called “arb percentage”

Some tools show 100% − combined probability. Others show the actual theoretical profit on the total stake: 1 ÷ combined probability − 1. These figures are close but not identical. ArbScanner labels combined implied probability and theoretical profit margin separately so the result is clear.

Rounding stakes safely

Exact formulas often produce awkward cents. Rounding each stake independently can make one outcome return less than the others. After rounding, multiply each proposed stake by its odds and compare every possible return. The lowest return—not the average—is the relevant worst case.

1. Calculate exact stakes.
2. Round only to increments that the relevant bookmaker accepts.
3. Recalculate each leg's return.
4. Compare the lowest return with the new total stake.
5. Stop if the worst case is no longer acceptable.

Calculate your own prices

Use the interactive tool for either two or three outcomes.