Sports Arbitrage Betting Calculator: 2-way, 3-way, 4-way

The calculators below model potential pricing imbalances across markets with multiple outcomes.

The first tool focuses on two-outcome markets and allows users to fix one stake amount to observe how the remaining stake would need to be adjusted under the selected odds.

In this setup, the calculator displays the total theoretical exposure and the corresponding wager amount allocation for the opposite outcome, based purely on mathematical relationships between quoted prices.

Surebet stake calculator with multiple outcomes

For readers primarily interested in spreadsheet-based modeling, a downloadable Excel file is available below.

Here you go:

How does the Arbitrage Calculator work?

Such tool is a mathematical tool that compares odds across two or more outcomes and illustrates whether a theoretical pricing imbalance exists when combining those odds.

The calculator can also estimate how stakes would need to be distributed if a user chooses to cover all listed outcomes, assuming the prices remain unchanged.

This model displays percentage differences and theoretical ROI values, which represent modeled outcomes, not guaranteed results.

These outputs are sensitive to real-world factors, including price movement, bet acceptance, stake limits, and execution timing.

If you prefer working with fractional odds, a converter is available to assist with format conversion, as this calculator does not directly support that type.

What is a sure bet calculator used for?

A sure bet calculator is commonly used to evaluate whether odds from different sources mathematically offset each other under ideal conditions.

Price-based betting is often described as a low-exposure approach, but it still involves execution risk, operational constraints, and account-level limitations.

This approach requires placing proportional stakes on every possible outcome of a market, typically across multiple platforms.

Each wager must be sized precisely, based on the quoted prices used, and placed successfully for the modeled result to remain valid.

If all steps are completed without rejection, delays, or odds changes, the model shows how returns could converge to a narrow range.

The arbitrage result is calculated as:

Total returns minus total wager amount, under the assumption that all bets are accepted at the listed odds.

If you enter odds for a two-way or three-way market and define a total stake, the tool will indicate whether a theoretical arbitrage condition exists and how stakes would be proportionally allocated.

For readers interested in understanding how these situations are identified, the related educational article on finding arbitrage opportunities explains common methodologies and limitations.

The next and more advanced step after arbing is implementing middle betting in your strategy. Check the following middle bet calculator to learn more about this approach.

Tool Features

• Allows input of quoted prices for each outcome
• Requires a total exposure value to perform calculations
• Displays proportional proportional distribution based on implied probabilities
• Supports additional outcomes for multi-way markets
• Includes a reset function to restore default inputs

Are you into value betting as well? Check our closing line value calculator.

Two-way arbitrage calculator

After identifying a potential arbitrage structure, the next step is to allocate stakes proportionally, based on implied probabilities.

The stake formula for this is:

Stake (Outcome) = (Total Investment * Implied Probability (Outcome)) / Total Implied Probability

Example:

Continuing with our tennis match example, let’s assume you want to invest $1000 in this arbitrage bet:

1. Calculate the total implied probability for Bookmaker A: 0.5263 (Player 1) + 0.4545 (Player 2) = 0.9808
2. Calculate the stake for each outcome:

2. Player 1: (1000 * 0.5263) / 0.9808 = $536.51
3. Player 2: (1000 * 0.4545) / 0.9808 = $463.49

So, you would place a $536.51 bet on Player 1 with Bookmaker A and a $463.49 bet on Player 2 with Bookmaker A.

To determine the profit, simply multiply the stake by the odds and subtract the total investment:

• If Player 1 wins: (536.51 * 1.90) – 1000 = $18.36
• If Player 2 wins: (463.49 * 2.20) – 1000 = $18.68

These figures represent theoretical outcomes and assume all bets are accepted at the listed odds without delay or adjustment.

Examples of the arbing Formula in Action

Let’s look at an example of the price-based betting formula in action.

Suppose there is a tennis match between Rafael Nadal and Novak Djokovic, and two bookmakers offer the following odds:

Bookmaker A: Nadal to win 1.80, Djokovic to win 2.10;

Bookmaker B: Nadal to win 2.0, Djokovic to win 1.90;

To determine if a cross-market discrepancy exists, we need to calculate the value implied probabilities of each outcome:

Implied probability of Nadal winning with Bookmaker A = 1 / 1.80 = 55.56%

Implied probability of Djokovic winning with Bookmaker A = 1 / 2.10 = 47.62%

Implied probability of Nadal winning with Bookmaker B = 1 /2.0 = 50%

Implied probability of Djokovic winning with Bookmaker B = 1 / 1.90 = 52.63%

The sum of the implied probabilities is 97.62%, which is less than 100%.

Under these prices, the combined implied probability falls below 100%, indicating a theoretical imbalance.

To determine the bet sizes for each outcome, allocate the total exposure in proportion to these implied probabilities (best price only):

Total wager amount = $100
Bet size for Nadal to win with Bookmaker B = $100 × (50.00% / 97.62%) = $51.22
Bet size for Djokovic to win with Bookmaker A = $100 × (47.62% / 97.62%) = $48.78

If Nadal wins: return = $51.22 × 2.00 = $102.44
If Djokovic wins: return = $48.78 × 2.10 = $102.44

The total bet size is $100, and the potential profit is $2.44, which is guaranteed regardless of the outcome of the match.

Related to value betting: check the following betting simulator and find out the risk and possible returns with value betting.

Three-Way Calculator in action

Three-way arbitrage bets are more complex, as they involve three possible outcomes.

Suppose we have two bookmakers offering odds on a soccer match with three possible outcomes: Team A win, Team B win, or Draw:

Bookmaker A: Team A – 2.50, Team B – 3.00, Draw – 3.40
Bookmaker B: Team A – 2.40, Team B – 2.90, Draw – 3.50

To determine if an cross-market discrepancy exists, use the best odds for each outcome and calculate their implied probabilities:

Team A (best price 2.50 at Bookmaker A): 1 / 2.50 = 40.00%
Team B (best price 3.00 at Bookmaker A): 1 / 3.00 = 33.33%
Draw (best price 3.50 at Bookmaker B): 1 / 3.50 = 28.57%

The sum of the implied probabilities is 101.90%, which is greater than 100%.
Therefore, no arbitrage opportunity exists with these prices.

Arbitrage betting formula excel

You can download it below (or build it for yourself from the information provided):

Here’s a simple Excel-based odds-comparison tool that you can use for two-way and three-way bets. Follow these steps to create your own software:

1. Open a new Excel workbook.
2. In cells A1 to C1, enter the following headers: Outcome, Odds, and Implied Probability.
3. In cells A2 to A4, enter the possible outcomes: Outcome 1, Outcome 2, and Outcome 3 (for three-way bets; otherwise, leave A4 blank).
4. In cells B2 to B4, input the best odds you’ve found for each outcome.
5. In cells C2 to C4, enter the following formula to calculate the implied probability for each outcome:

=1/B2/B2

Copy this formula down to cells C3 and C4 if needed.

6. In cell C5, enter the following formula to calculate the total implied probability:

=SUM(C2:C4)

7. In cells E1 and E2, enter the headers Total Investment and Total Implied Probability, respectively.
8. In cell F1, input your desired total investment amount.
9. In cell F2, enter the following formula to reference the total implied probability from cell C5:

=C5

10. In cells H1 to J1, enter the following headers: Outcome, Stake, and Potential Return.
11. In cells H2 to H4, enter the possible outcomes: Outcome 1, Outcome 2, and Outcome 3 (for three-way bets; otherwise, leave H4 blank).
12. In cells I2 to I4, enter the following formula to calculate the optimal stake for each outcome:

=(F1 * C2) / F2

Copy this formula down to cells I3 and I4 if needed.

13. In cells J2 to J4, enter the following formula to calculate the potential return for each outcome:

=I2 * B2

Copy this formula down to cells J3 and J4 if needed.

14. In cell J5, enter the following formula to calculate the theoretical surplus:

=MIN(J2:J4) – F1

Your Excel-based odds-comparison calculation formula is now ready to use. Input the best odds you’ve found for each outcome in cells B2 to B4, and the tool will determine the optimal wager amount, potential returns, and guaranteed profit for your arbitrage bet.

Remember that this calculator assumes you’ve already identified a cross-market discrepancy with a total implied probability of less than 1.

While this arbitrage calculator comes in handy many times, the integrated calculator of each arbitrage finder mentioned on this site has more features and allows you a faster process of finding out the right stakes for your bets.

If you start learning about value betting, make sure you check my positive EV calculator. It’s different from the ones you can find on other sites.

You truly can calculate the + Expected Value of a bet with the help of it.