# Arbitrage Betting Calculator: Excel Formula & Explanation

Arbitrage betting, or “arbing,” has become increasingly popular among sports bettors seeking to exploit discrepancies in odds offered by different bookmakers.

This guide will help you to understand the theory behind arbitrage betting formulas and show you how to determine if an arbitrage opportunity exists with calculation formulas.

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I will also provide an explanation of the formula to calculate how much stake you need to place on each side of a two-way arbitrage bet.

I also covered the 3-way arbitrage calculation formula and provide examples for each concept.

But I want to mention that after checking the theory, using an arbitrage betting finder to spot opportunities and using their arbitrage betting calculator to find out the right stakes is the fastest and easiest way to practice this strategy.

## Theory Behind Arbitrage Betting Formulas

Arbitrage betting is based on the principle of identifying and taking advantage of differences in odds across multiple bookmakers to guarantee a profit, regardless of the outcome of the event.

The key to successful arbitrage betting is finding these discrepancies and acting quickly, as odds can change rapidly.

### 1. Understanding Betting Odds

Before diving into arbitrage betting formulas, it’s crucial to understand betting odds.

Odds are expressed as fractions, decimals, or moneyline odds, depending on the region and sportsbook.

For this arbitrage betting formula guide, I will use the decimal format of odds.

Decimal odds represent the potential return on a successful bet, including the original stake.

For example, if you bet \$100 on an outcome with odds of 2.00, you would receive \$200 in return if the outcome you placed the bet on wins (\$100 stake + \$100 profit).

## Arbitrage Betting Formula

The basic formula to find out if an arbitrage opportunity exists is as follows:

1 / Decimal Odds (Outcome 1) + 1 / Decimal Odds (Outcome 2) + … + 1 / Decimal Odds (Outcome n) = Total

If the total is less than 1, an arbitrage opportunity exists.

### Identifying Arbitrage Opportunities

To determine if an arbitrage opportunity exists, follow these steps:

1. Find two or more bookmakers offering odds on the same event.
2. Convert the odds to their implied probabilities. Divide 1 by the decimal odds for each outcome.
3. Add the implied probabilities together. If the sum is less than 1, you’ve found an arbitrage opportunity.

Example:

Let’s say we have two bookmakers offering odds on a tennis match:

• Bookmaker A: Player 1 – 1.90, Player 2 – 2.20
• Bookmaker B: Player 1 – 2.00, Player 2 – 1.80

First, convert the odds to their implied probabilities:

• Player 1 (Bookmaker A): 1 / 1.90 = 0.5263
• Player 2 (Bookmaker A): 1 / 2.20 = 0.4545
• Player 1 (Bookmaker B): 1 / 2.00 = 0.5000
• Player 2 (Bookmaker B): 1 / 1.80 = 0.5556

Next, add the implied probabilities together for each bookmaker:

• Bookmaker A: 0.5263 + 0.4545 = 0.9808
• Bookmaker B: 0.5000 + 0.5556 = 1.0556

In this case, an arbitrage opportunity exists with Bookmaker A, as the sum of the implied probabilities is less than 1.

## Calculating Stakes for Two-Way Arbitrage Bets

Once you’ve identified an arbitrage opportunity, the next step is to calculate the optimal stakes you should place on each outcome.

The arbitrage bet 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:
1. Player 1: (1000 * 0.5263) / 0.9808 = \$536.51
2. 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

Regardless of the outcome, you’re guaranteed a profit of around \$18.

### Examples of the Arbitrage Betting Formula in Action

Let’s look at an example of the arbitrage 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 1.90, Djokovic to win 2.00

To determine if an arbitrage opportunity exists, we need to calculate the 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 / 1.90 = 52.63%

Implied probability of Djokovic winning with Bookmaker B = 1 / 2.00 = 50.00%

The sum of the implied probabilities is 205.81%, which is greater than 100%.

Therefore, an arbitrage opportunity exists.

To determine the bet sizes for each outcome, we need to allocate our total stake in proportion to the implied probabilities:

Total stake = \$100 Bet size for Nadal to win with Bookmaker A = \$100 x (55.56% / 205.81%) = \$27.03

Bet size for Djokovic to win with Bookmaker A = \$100 x (47.62% / 205.81%) = \$23.38

Bet size for Nadal to win with Bookmaker B = \$100 x (52.63% / 205.81%) = \$25.61

Bet size for Djokovic to win with Bookmaker B = \$100 x (50.00% / 205.81%) = \$24.97

The total bet size is \$100, and the potential profit is \$4.55, which is guaranteed regardless of the outcome of the match.

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## Steps of calculation of an arbitrage betting opportunity

### 1. Identifying Arbitrage Opportunities

To identify arbitrage opportunities, bettors need to compare odds offered by different bookmakers for a given sporting event.

If the total of the implied probabilities of all possible outcomes is less than 100%, an arbitrage opportunity may exist.

### 2. Calculating Implied Probability

Implied probability is the probability of an event occurring based on the odds offered by a bookmaker.

To calculate implied probability, divide 1 by the decimal odds offered by the bookmaker and multiply by 100.

For example, if the decimal odds offered by a bookmaker for a team to win are 1.50, the implied probability is 66.67% (1 / 1.50 x 100).

### 3. Determining Arbitrage Bet Sizes

To determine the bet sizes for each outcome, bettors need to allocate their total wager in proportion to the implied probabilities of each outcome.

For example, if the total wager is \$100 and the implied probability of Team A winning is 50% and the implied probability of Team B winning is 50%, the bet size for each outcome would be \$50.

## Explanation of the Arbitrage Betting Formula

The formula for arbitrage betting is:

Profit = (Total Stake / Implied Probability) – Total Stake

This formula calculates the profit that can be made from an arbitrage opportunity.

The total stake is the sum of all bets made, and the implied probability is the probability of each outcome based on the odds offered by the bookmakers.

To apply this simple arbitrage betting formula, you will need need to follow these steps:

1. Identify an arbitrage opportunity by comparing odds offered by different bookmakers either by arbitrage betting software or manually.
2. Calculate the implied probability of each outcome.
1. Determine the total stake by dividing the desired profit by the sum of the implied probabilities. For example, if a bettor wants to make a \$100 profit and the sum of the implied probabilities is 90%, the total stake would be \$111.11 (\$100 / 0.90).
2. Determine the bet size for each outcome by multiplying the total stake by the implied probability for each outcome. For example, if the implied probability of Team A winning is 50% and the total stake is \$111.11, the bet size for Team A would be \$55.56 (\$111.11 x 0.50).
3. Place the bets with different bookmakers to ensure a profit regardless of the outcome.

## Three-Way Arbitrage Calculation Formula and Example

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

The process for identifying opportunities and calculating stakes, however, remains similar.

Example:

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

First, convert the odds to their implied probabilities:

• Team A (Bookmaker A): 1 / 2.50 = 0.4000
• Team B (Bookmaker A): 1 / 3.00 = 0.3333
• Draw (Bookmaker A): 1 / 3.40 = 0.2941
• Team A (Bookmaker B): 1 / 2.40 = 0.4167
• Team B (Bookmaker B): 1 / 2.90 = 0.3448
• Draw (Bookmaker B): 1 / 3.50 = 0.2857

Next, add the implied probabilities together for each bookmaker:

• Bookmaker A: 0.4000 + 0.3333 + 0.2941 = 1.0274
• Bookmaker B: 0.4167 + 0.3448 + 0.2857 = 1.0472

In this case, no arbitrage opportunities exist, as the sum of the implied probabilities is greater than 1 for both bookmakers.

## Arbitrage betting formula excel

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

Here’s a simple Excel-based arbitrage betting calculator that you can use for two-way and three-way bets. Follow these steps to create your own calculator:

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.

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

`=`SUM`(C2:C4)`

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

=C5

1. In cells H1 to J1, enter the following headers: Outcome, Stake, and Potential Return.
2. In cells H2 to H4, enter the possible outcomes: Outcome 1, Outcome 2, and Outcome 3 (for three-way bets; otherwise, leave H4 blank).
3. 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.

1. 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.

1. In cell J5, enter the following formula to calculate the guaranteed profit:

=MIN(J2:J4) – F1

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

Remember that this calculator assumes you’ve already identified an arbitrage opportunity with a total implied probability less than 1.

## Conclusion: Arbitrage Betting Formula & Calculation

By understanding the arbitrage betting formulas and methods outlined in this guide, you can increase your chances of success and potentially secure consistent profits from sports betting. Remember, however, that odds can change quickly, so acting fast is essential when you spot an arbitrage opportunity.

Relevant articles:

FAQ

What is the formula for arbitrage betting?

The formula for arbitrage betting is the following: 1 / Decimal Odds (Outcome 1) + 1 / Decimal Odds (Outcome 2) + … + 1 / Decimal Odds (Outcome n) = Total

Where can I find an arbitrage betting formula in excel?

This article includes the step-by-step method to build your own arbitrage betting calculation tool with the formula included. You can also download the arbitrage betting formula excel file from this site.