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What is Implied Probability? | Implied Probability Formula Conversion

If you want to play at the best odds bookmakers, you need to learn implied probability: This betting term is more important than you think. Bookies set their odds according to these calculations, and if you understand the odds implied probability concept correctly, you can easily find the famous “value bets” everyone is looking for.

In this article, we will answer the what is implied probability question first, explain it in detail, and give implied probability formula examples. When you are done reading, you will be able to play at the bookmakers with the best odds margins!

What is implied probability and what does it mean?

Obviously, we should start with the “what is implied probability” question. Probability means how likely an outcome to occur and it is expressed as a percentage. For example, if I have a coin with only two sides and throw it in the air, the probability of getting a head or a tail is 50%, so both outcomes are equal to each other. Therefore, the probability of winning such a game is 50%.

Implied probability, on the other hand, is the percentage that appears after adding the bookmaker margin over the actual probability values. To put it simply:

  1. The Bookmaker determines the actual probability percentages of all outcomes in an event before offering a bet for that event. For example, suppose there is a match between Team A and Team B, and the bookmaker is preparing to offer a bet on who will win this match. Bookmaker researches Team A and Team B to find out which one is more likely to win the match. This process is called “capping” and the actual probability percentages emerge at the end. Let’s assume that these are 40% for Team A and 60% for Team B, for example. The most important thing you need to know here is that the total of the (real) probability percentages found at the end of the capping process is always 100.
  2. The Bookmaker slightly changes these probability percentages to secure a profit for itself and raises the grand total to over 100 (e.g. 42% for Team A, 63% for Team B). The new values ​​that arise at the end of this process are called “implied probability”. The more the bookmaker goes above 100, the more profit it will make. For more information on this topic, we recommend that you check out our articles on how do bookies set odds and how do bookies make money.

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Implied probability formula list for different conversions

In order to teach you how to calculate implied probability in betting, we need to talk about different types of odds and give lots of examples: This is the only way to truly understand implied probability meaning. You can see these examples below with formulas: To learn more, we recommend checking our general sports betting guide and sports betting strategies article. 

First, let’s find out how to calculate implied probability from odds. There are three types of odds we can use, decimal, fractional, and moneyline (American). They all show how much you can win for betting a specific amount but they represent this differently and therefore, the calculations are different too. In order to learn more about odds, we recommend reading our make money with sports betting, betting odds explained, and the easiest sport to bet on guides.

1. Convert decimal odds to implied probability

Decimal odds are the most common and they are used almost everywhere. These odds show how much you can win for betting 1 unit. For example, 2.00 odds mean that if you bet 10 EUR and win, the payout will be 20 EUR. 

The implied probability formula for decimal odds conversion:

➤ (1/decimal odds) x 100 = implied probability
➤ So, for example, if the odds for Team A to win is 3.50, the calculation will be:
➤ (1/3.50) x 100 = 28.57%

2. Convert fractional odds to implied probability

Fractional odds are also known as “British” or “traditional” odds. They are written as a fraction, i.e. 4/1. The right digit shows your bet and the left digit shows the payout. So, in this example, if you bet 10 EUR, the payout will be 40 EUR. 

The implied probability formula for fractional odds conversion:

denominator / (denominator + numerator) x 100 = implied probability
➤ So, for example, if the odds for Team A to win is 6/1, the calculation will be: 
➤ 1 / (1+6) x 100 = 14.28%

3. Convert American odds to implied probability

This is also known as “betting on the moneyline”. These are the American odds and they can be seen on the websites of US bookmakers. There are two kinds of American odds, positive and negative. If it is negative, it indicates how much you need to wager to win 100 USD. If it is positive, it indicates how much you can win when you wager 100 USD. For example: 

  • +200 = If you wager 100 USD and win, the payout will be 200 USD
  • -200: In order to win 100 USD, you must wager 200 USD.

The implied probability formula for positive American odds conversion:

100 / (positive American odds + 100) x 100 = implied probability moneyline
➤ So, for example, if the odds for Team A to win is +350, the calculation will be: 
➤ 100 / (350 + 100) x 100 = 22.22%

The implied probability formula for negative American odds conversion:

Negative American odds / (Negative American odds + 100) x 100 = implied probability moneyline
➤ So, for example, if the odds for Team A to win is -250, the calculation will be: 
➤ 250 / (250 + 100) x 100 = 71.42%

How to convert implied probability to odds?

Of course, we can also do the opposite and convert implied probability to odds. In this section, we will take a look at how to convert probability to odds. However, since you learned the basic concepts, we will just provide the formulas this time.

Implied probability into decimal odds formula:

100 / implied probability = odds
➤ For example, if the implied probability is 25%,
➤ 100 / 25 = 4.00 odds

Implied probability into fractional odds formula:

(100 / implied probability) – 1 = odds
➤ For example, if the implied probability is 20%,
➤ (100 / 20) – 1 = 4.00, which can be shown as 4/1

Implied probability into American odds formula:

If the implied probability is over 50%, the formula will be: 
➤ (implied probability / (100 – implied probability)) x 100 = negative odds
➤ So, for example, if the probability is 60%: (60 / (100 – 60)) x 100 = -150

If the implied proability is under 50%, the formula will be: 
➤ ((100 – implied probability) / implied probability) x 100 = positive odds
➤ So, for example, if the probability is 20%: ((100 – 20) / 20) x 100 = +400

Lastly, remember that you can use an implied probability calculator instead of doing them manually.  If you are a beginner (or not good with sports betting math), implied probability calculation may seem a little complex. More importantly, it can mislead you. Therefore, using a calculator will be the better choice: You can find them at the websites of the biggest betting companies and/or sites dedicated to this job. 

Or you could use this chart below, containing the most common odds and their implied probability:

European Decimal

UK Fractional

American Moneyline

Implied Probability

1.01
UK Fractional
1/100
American Moneyline
-10,000
Implied Probability
99.01%
1.10
UK Fractional
1/100
American Moneyline
-1,000
Implied Probability
90.91%
1.20
UK Fractional
1/5
American Moneyline
-500
Implied Probability
83.33%
1.25
UK Fractional
1/4
American Moneyline
-400
Implied Probability
80.00%
1.33
UK Fractional
1/3
American Moneyline
-300
Implied Probability
75.00%
1.50
UK Fractional
1/2
American Moneyline
-200
Implied Probability
66.67%
1.57
UK Fractional
4/7
American Moneyline
-175
Implied Probability
64.00%
1.80
UK Fractional
4/5
American Moneyline
-125
Implied Probability
55.56%
1.91
UK Fractional
10/11
American Moneyline
-110
Implied Probability
52.00%
2.00
UK Fractional
1/1
American Moneyline
+100
Implied Probability
50.00%
2.20
UK Fractional
6/5
American Moneyline
+120
Implied Probability
45.45%
2.50
UK Fractional
3/2
American Moneyline
+150
Implied Probability
40.00%
2.75
UK Fractional
7/4
American Moneyline
+175
Implied Probability
36.36%
3.00
UK Fractional
2/1
American Moneyline
+200
Implied Probability
33.33%
3.25
UK Fractional
9/4
American Moneyline
+225
Implied Probability
30.77%
3.50
UK Fractional
5/2
American Moneyline
+250
Implied Probability
28.57%
3.75
UK Fractional
11/4
American Moneyline
+275
Implied Probability
26.67%
4.00
UK Fractional
3/1
American Moneyline
+300
Implied Probability
25.00%
7.50
UK Fractional
12/2
American Moneyline
+650
Implied Probability
13.33%
10.00
UK Fractional
9/1
American Moneyline
+900
Implied Probability
10.00%

The difference between probability and implied probability

So, if we make an implied probability vs probability comparison, what is the difference? Actually, the difference is simple:

👉 Probability shows how likely a particular outcome can occur.

👉 Implied probability shows the same but with the bookmaker’s margin added to this value. It is used to calculate the odds that will be offered by the bookie.

As we explained in our other guides, the bookmaker can secure a profit no matter what the outcome is by offering you high payouts but also asking for high entry fees, aka bets. That’s why the how to beat the bookies tips may sometimes not work. Simply put, it asks you to pay 1.20 units to win 1.10 units, for example. By using the difference in between and using implied probability values to change the odds in its favor, the bookmaker always wins. If this sounds too complex, you should just remember this: Implied probability values never show the actual probability, they are the “bookmaker version” of the real values.

The importance of implied probability in sports betting

There is something called “value betting in sports”: It means finding the betting mistakes made by the bookmaker. For example, if your calculations reveal that the bookmaker’s implied probability odds are simply wrong, you can use this to your advantage. If it is under 100 you can definitely apply the dutch betting strategy. Let’s give a real example by using value football betting:

  • The bookmaker offers 3.50 odds for Team A to win a particular match. This means the bookie thinks that Team A has a 28.57% chance to win that match – we explained how this is calculated above. 
  • However, this is already higher than the actual probability and you may find out that Team A has actually a 32.50% chance to win that match. In other words, Team A is much more likely to win this match. 

This is called a “value bet”: It offers big payouts and higher winning chances. And by using the implied probability formula examples we listed above, you can easily find such bets.

FAQs - Your questions on implied probability answered:

The real probability always equals 100% and the bookmaker must surpass this figure in order to secure a profit. Therefore, the implied probability is always higher.

As long as the thing you are doing can be classified as “betting”, yes, there will always be an implied probability and it will be possible to calculate it, whether you are doing sports betting or hedge trading.

The implied probability formula is: (1/decimal odds) x 100 = implied probability

The implied probability formula is: denominator / (denominator + numerator) x 100 = implied probability

The implied probability formula is:
100 / (positive American odds + 100) x 100 = implied probability
negative American odds / (Negative American odds + 100) x 100 = implied probability

Convert odds to implied probability to find the best offers

We answered what is implied probability question and showed you implied probability formula examples for different types of odds: You are now ready for converting odds to probability or vice versa. Check our lists of the biggest bookmakers in UK or US betting sites and pick one: It is time to place your first bet. And since you learned the betting odds implied probability concept, you can easily find out the “value” bets now: We are sure that you will start winning in no time. Good luck out there!