Arbitrage Calculator

What This Arbitrage Calculator Does

This arbitrage calculator checks whether a set of bookmaker odds creates a surebet opportunity and, if it does, calculates how to split your total stake across all outcomes to lock in a guaranteed profit.

All monetary values are displayed in the selected currency. For example, a total stake of $100.00 will be split across the outcomes to target the same payout regardless of the result.

How the Arbitrage Calculation Works

An arbitrage opportunity exists when the sum of the implied probabilities of all outcomes is less than 100%. In that case, you can distribute your stake across every outcome in such a way that the payout is the same no matter what happens.

1. Convert each set of odds into an implied probability
2. Adjust the odds for commission if needed
3. Sum all implied probabilities
4. Check whether the total is below 100%
5. Calculate the optimal stake split for each outcome
6. Calculate the guaranteed payout, profit, and ROI

Formulas Used in the Calculation

Adjusted Odds With Commission

If commission applies, the calculator first adjusts the decimal odds to reflect the fee charged on profits:

Adjusted odds = 1 + (Odds − 1) × (1 − Commission)

For example, if the odds are 3.00 and the commission is 5%, the adjusted odds become 2.90.

Implied Probability

Each set of adjusted decimal odds is converted into an implied probability:

Implied probability = 1 / Adjusted odds

When Arbitrage Exists

Arbitrage exists when the sum of all implied probabilities is less than 1, or less than 100%:

(1 / Odds₁) + (1 / Odds₂) + ... + (1 / Oddsₙ) < 1

If the total implied probability is below 100%, a surebet opportunity exists.

Arbitrage Percentage

The arbitrage percentage shows the size of the edge:

Arbitrage % = (1 − Total implied probability) × 100

Stake Distribution

To guarantee the same payout across all outcomes, the total stake is distributed proportionally to each implied probability:

Stakeᵢ = Total stake × (Implied probabilityᵢ / Total implied probability)

Payout and Guaranteed Profit

Once the stake is distributed, the payout for each outcome is:

Payout = Stake × Adjusted odds

The guaranteed profit is then:

Guaranteed profit = Payout − Total stake

The guaranteed ROI is:

ROI = Guaranteed profit / Total stake

Example Arbitrage Calculation

Suppose you place a total stake of $100.00across a market where the combined implied probability is below 100%.

If an arbitrage exists, the calculator will show how much of your total stake should be placed on each outcome to target the same payout regardless of the result.

What the Results Mean

• Total implied probability shows how expensive the market is after combining all outcomes.
• Arbitrage percentage measures how far the total implied probability is below 100%.
• Stake tells you how much to place on each outcome.
• Payout shows the return if that specific outcome wins.
• Profit shows your net gain after subtracting the total stake.
• Guaranteed ROI shows the actual return on your total stake after the optimal stake distribution.
• The ROI may be slightly higher than the arbitrage percentage because ROI is calculated relative to the invested stake rather than the total payout.

Notes About Arbitrage Betting

• This calculator assumes that all bets can be placed successfully at the listed odds.
• Real-world arbitrage opportunities may disappear quickly if odds move before all bets are placed.
• Commission reduces effective odds and can remove an arbitrage opportunity entirely.
• Rounding, stake limits, and bookmaker restrictions can also affect real-world results.
• All monetary values in this calculator are shown in the selected currency.