Converts an array or Excel range of US-style odds to decimal parlay odds. Example: US2Dec(-110,-110) ≈ 3.644628099. Get real-time scores, betting lines, and betting odds for all your favorite sports.

How does the arbitrage calculator work?

• Las Vegas Betting Lines at VegasInsider.com. Specializing in free sports picks, gambling handicappers, Internet sports betting odds and online sportsbooks.
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Our arbitrage calculator allows you to enter the odds of two (or more) different bets to determine how much you should stake on each to guarantee a profit.

Use the Arbitrage Calculator here

Enter Odds & Stake

Stake

Stake Bet 1

Stake Bet 2

Payout

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Payout Bet 2

What is an arbitrage bet?

An arbitrage (or arb for short) also known as 'surebets', 'surewins' and 'miraclebets' are bet types whereby a bettorwagers on a series of events that guarantees a profit no matter the outcome of a given event, or at worst, guarantees that no money can be lost but money can still be won depending on the result of an event.

Arbitrage bets work by taking advantage of discrepancy in prices of the same event with different Sportsbooks in a way that can ensure the bettor can't lose money no matter the outcome of the event.

What is a sports arbitrage betting example?

Arbitrage opportunities can pop-up in betting markets for a variety of reasons, most commonly being a disagreement in Sportsbook opinions on a certain event.

For example, say an NBA game was being played between the Houston Rockets and the Cleveland Cavaliers. 'Sportsbook A' may open up their market at:

Houston Rockets $1.50 (e.g -200)

Cleveland Cavaliers $2.50 (e.g +150)

And 'Sportsbook B' may open up their market at:

Houston Rockets $1.80 (e.g -125)

Cleveland Cavaliers $2.20 (e.g +120)

You can see here, that there a discrepancy in the odds, or a disagreement between the sportsbooks over the winning chances of each team. In this scenario, the bettor could place $55.55 on the Houston Rockets with Sportsbook B, to receive a payout of $100 if Houston win and the bettor can place $40.00 on the Cleveland Cavaliers with Sportsbook A, to also receive a payout of $100 if Cleveland win.

In this scenario, no matter who wins the game, the bettor has outlaid $95.55, but will receive back $100 no matter what the outcome. This a sports betting arbitrage, an opportunity to guarantee yourself a profit no matter the result (e.g + to your bankroll!)

What are the risks associated with arbitrage betting?

Arbitrage betting can be very profitable as long as you demonstrate patience and capitalise on the many opportunities that arise every day. Where you can lose big amounts with online Sportsbooks is if you outlay large sums on a bet that potentially could be a sportsbook error. That is, imagine there is a bet that is $51 when it should be $1.01 and all other Sportsbooks have it as $1.01. You may then feel the urge to place an arbitrage on the $51 and their opponent at big odds as well on another Sportbook, and outlay large amounts assuming you are in for a massive payday. That is until the Sportsbook cancels the market that had an error (Sportsbooks may be able to do this even after the event has started, read their terms and conditions). You are then stuck in a situation where you have a large amount of money on a huge underdog. Stick to non-error arbitrage opportunties where there is generally a 1-5% guaranteed return. You can however place single bets on the sportsbook errors, because if they get cancelled, you get your money back.

Implied probability is the conversion of betting odds into a percentage. This tells us how often we need to win in order to break-even. Implied probability is used to isolate profitable wagers and calculate the bookmaker’s margin. This guide will teach you how to convert American, Decimal, and Fractional odds into implied probability as well as evaluating how big of an advantage any given sportsbook has over you.

What is Implied Probability

Implied probability is the direct conversion of the betting odds available at a sportsbook into a percentage. Because the bookmaker’s commission is factored in this reveals the break-even percentage. One can only justify placing a bet if they believe it will win more often than the implied probability.

Bookmaker’s adjust their markets in an attempt to attract an even amount of action to both sides of the game. This creates margins between the implied probability and the outcome probability. Taking advantage of this is the key to long-term sportsbetting success.

Let’s start off by taking a look at how we can convert American, Decimal, and Fractional odds into percentages. This will be a direct calculation from the bookmaker’s posted line so their commission will be factored in. This percentage will allow us to determine the break-even percentage.

American Odds into Implied Probability

When converting American odds into implied probability we need to differentiate between plus and minus odds. The calculations will be different for each one. Let’s take a look at the following NFL game:

For minus odds we we will divide the absolute value of the odds by itself augmented by 100. Here is the formula:

IP = Minus Moneyline Odds /( Minus Moneyline Odds + 100)

In the example above the Miami Dolphins have -150 odds to win the game. This means that their implied probability will be 150/(150 + 100) which simplifies to 150/250. This comes out to 0.6 which is 60%. When we have plus odds we will divide 100 by the odds augmented by 100:

IP = 100/(Plus Moneyline Odds + 100)

The Baltimore Ravens have +130 odds to win the match. Their implied probability is given by 100/(130 + 100) which simplifies to 100/230. This comes out to 0.435 which is 43.5%.

Decimal Odds into Implied Probability

This is the easiest odds format to convert into implied probability. The only thing you need to do is take the reciprocal of the odds by dividing it into 1:

IP = 1/Decimal Odds

Manchester United have 1.36 odds to defeat Swansea. Their implied probability is represented by 1/1.36 = 0.735 = 73.5%. You would need to win this wager 73.5% of the time in order to break even. Swansea’s match odds are 9.50 which means their implied probability is 1/9.50 = 0.105 = 10.5%. You would need to win this wager 10.5% of the time in order to break even.

Fractional Odds into Implied Probability

How Do Sportsbooks Calculate Odds

Fractional odds can be converted into implied probability by dividing the denominator by the sum of the denominator and numerator:

IP = denominator/(denominator + numerator)

Let’s take Bournemouth with 10/11 odds against Watford. The numerator is 10 and the denominator is 11. We will retrieve the implied probability with 11/(11+10) = 11/21 = 0.524 = 52.4%. If you believe Bournemouth have more than a 52.4% chance of emerging victorious then you would be making a good bet!

Bookmaker Margins

You should have noticed that in the calculations above the implied probability for all sides of a given betting market do not add up to 100%. This surplus reflects the bookmaker’s margin. Their odds to not represent the statistical probability of an event. Knowing how to calculate bookmaker margins is crucial to ensuring that you are not getting ripped off. The larger the margin the more advantage the bookmaker has over you.

Calculating Bookmaker Margins

The margin will be expressed as a percentage above or below 100%. A market that is deemed fair would sit exactly at 100%. In order to calculate a bookmaker’s margin on a given betting market by summing the implied probability of all possible outcomes. Let’s look at an example:

In the match between Norwich and QPR the set of possible outcomes have odds of 1.80, 3.80, and 4.75 respectively. Converting these into implied probabilities gives us the following values:

1/1.80 = 0.556 = 55.6%

1/3.80 = 0.263 = 26.3%

1/4.75 = 0.211 = 21.1%

Next we will take the sum of all possible outcomes: 55.6% + 26.3% + 21.1% = 103%. The implied probability is 3% higher than a theoretical fair market. This means the bookmaker’s margin for this betting market is 3%.

What is a Good Margin?

Calculating Sports Betting Odds

As bettors we want to find bookmakers that offer the lowest margins possible. The industry average for most spreads, moneylines, and totals is around 5%. Anything higher than this should be avoided as you are putting yourself at an unnecessary disadvantage.

Removing Vig/Juice from Moneylines

Since implied probabilities are direct conversions of betting odds into percentages the bookmaker’s margin is factored in. The implied probability represents how often you would need to win a wager of those odds in order to break even. We can perform an additional calculation to remove the margin to get the true probabilities.

Calculating Payouts Sports Odds

Start off by calculating the implied probabilities of all possible outcomes for the betting market you are working with. Let’s use the money line market for this NFL match between the Buffalo Bills and Philadelphia Eagles:

The Buffalo Bills implied probability is 1/2.70 = 0.370 = 37.0% and the Philadelphia Eagles implied probability is 1/1.50 = 0.667 = 66.7%. Next we will sum up the implied probabilities of all possible outcomes in order to evaluate the bookmaker’s margin. Here we have 37.0% = 66.6% = 103.7% for a margin of 3.7%. In order to calculate the true probabilities we will need to make it out of 100%. This is accomplished by dividing the implied probability by the sum of the implied probabilities of all possible outcomes:

True Probability = Implied Probability/(Bookmaker Margin + 100%)

Calculating Sports Odds

This means the true probabilities are 37.0%/103.7% = 0.357 = 35.7% for the Buffalo Bills and 66.7% / 103.7% = 0.643 = 64.3%. The sum of your true probabilities should add up to 100% (which is the case here).

Profitable Sportsbetting

Calculating Sports Odds

To become a winning sportsbettor one must place wagers that hold positive expected value. There exists a margin between the real life winning percentage of a given betting market and that implied by the bookmaker’s odds. In the next guide we will discuss how to create a projection model in order to estimate the real winning percentages of multiple betting markets. Comparing these numbers to the implied probabilities we learned how to calculate today will reveal which wagers have the most value.