How To Convert Odds
What are betting odds? What is implied probability? How do you convert odds to probability? And how do you convert probability to decimal odds? Understanding betting odds and the probabilities they reflect is key to sports betting. In this guide we will take you through the basics of betting odds.
In this guide:
- Betting Odds Explained
- How to Convert Decimal Odds to Probability
- How to Convert Fractional Odds to Probability
- How to Convert Moneyline Odds to Probability
- How to Convert Probability to Decimal Odds
- How to Convert Probability to Fractional Odds
- How to Convert Probability to Moneyline Odds
- How to Convert Decimal Odds to Fractional Odds
- Odds Conversion Chart
The ‘How to convert odds’ video is age-restricted. Make sure you are logged into your YouTube account before playing.
How To Convert Odds – Quick Reference Guide
Below you will find the formulas for converting popular odds formats to probability and the formulas for converting probability to popular odds formats. You will find each further explained below.
| Convert To Probability | Formula |
|---|---|
| How to convert decimal odds to probability | 1 / decimal odds |
| How to convert fractional odds to probability | denominator / (denominator + numerator) |
| How to convert minus moneyline to probability | minus moneyline / (minus moneyline – 100) |
| Converting plus moneyline to probability | 100 / ( plus moneyline odds + 100 ) |
| Convert To Odds | Formula |
|---|---|
| How to convert probability to decimal odds | 1 / probability percentage |
| How to convert probability to fractional odds | (1 / probability percentage ) -1 |
| How to convert probability to minus moneyline odds | – ( implied probability / (1 – implied probability)) x 100 |
| How to convert probability to plus moneyline odds | (1 – implied probability) / implied probability x 100 |
Betting Odds & Chance
To understand betting odds and how to convert odds from one format to another, we have to first understand the concept of chance.
Chance is the likelihood of an event happening. It is often expressed in percentages, also referred to as the probability.
Let’s roll a dice.
Rolling a dice yields a probability of 1 out of 6 for each outcome.
The chance of the dice landing on any of the 6 numbers is equal. In percentages this means a 16.66% chance (or probability) of any of the six numbers to coming up.
How is this calculated?
Simply by dividing 100% by the 6 possible outcomes.
Betting Odds Explained
Knowing how to convert odds to probability and alternative odds formats can be very helpful. In fact, if you don’t know how to convert betting odds into their respective implied probabilities, you’re not helping your chances in the competitive world of sports betting. Understanding the implied probability behind the odds on offer is key to assessing the potential value in a particular betting market.
And it is just as important when assessing the value that exists with regards to specific odds on a particular outcome. If the implied probability is less than your own assessed probability of a particular outcome occurring, that outcome represents a value betting opportunity.
If, however, you want to learn how to convert odds to probability and how to covert implied probability to various odds formats, please read on. This article explains in detail how to convert the three most popular odds formats in the world – decimal, fractional and American – into their implied probabilities and how to convert an implied probability into either of these odds formats.
How To Convert Odds – Step By Step
- Are the odds Decimal, Fractional or American?
- Convert the odds to their implied probability.
- Convert the implied probability to your preferred odds format.
For example, “Decimal Odds” of 3.00 has an implied probability of 33.3% which can then be converted to fractional odds of 2/1.
This article discusses this process of odds conversion in detail with the use of step by step real world examples.
How To Convert Odds To Probability
- Decimal Odds: represented as 1.65 or 2.95 etc.
- Fractional odds: represented as 5/2 or 3 to 2 ‘on’ etc.
- Moneyline odds: represented as -120 or +140 etc.
They all reflect the same thing – the return you will receive as a ratio of the sum of money placed on a bet. To convert your odds to implied probabilities or an implied probability to odds you can use an odds conversion calculator.
Or you can do it by hand by applying the formulas provided below the calculator.
How To Convert Decimal Odds To Probability
Decimal Odds are a simple reflection of the return you will receive for each single unit placed.
For example, let’s say bookmaker bet365 is offering odds of 1.65 for Manchester United to win. This means that for every 1.00 you bet on that particular outcome, you will receive a profit of 0.65 should Manchester United win.
To convert these odds to their respective implied probabilities we make a simple calculation.
Converting Decimal Odds to probability formula:
| Implied probability | = | 1 / Decimal Odds |
Let’s look at an example, in which Manchester United to win is odds of 1.65.
Example: How to convert Decimal Odds to probability
| 1 / 1.65 | = | 0.606 | = | 60.6% |
Multiplied then by 100 to express as an implied probability percentage of 60.6%.
So given the odds of 1.65, Manchester United are a 60.6% chance to win the game.
How To Convert Fractional Odds To Probability
Fractional odds are generally the most traditional form of expressing betting odds. They are a simple reflection of the return you will receive for a particular amount bet.
So for example, let’s say bookmaker Ladbrokes is offering odds of 5/2 for a particular horse to win an upcoming race.
The odds of 5/2 (expressed as “5 to 2”) means that for every 2 units that you bet, you will receive 5 back as profit. So if you bet £200 on that horse, you would have received £500 profit in return plus your original stake of £200.
Converting Fractional Odds to probability formula:
| Implied probability | = | denominator / (denominator + numerator) |
Let’s look at an example, in which Chelsea are at odds of 5/2 to win a game in the Champions League.
Example: How to convert Fractional Odds to probability
| 5 / 2 | = | 2 / (2 + 5) | = | 2 / 7 | = | 0.2857 | = | 28.57% |
Multiplied then by 100 to express as a implied probability percentage of 28.57%
So given the odds of 5/2, Chelsea are considered a 28.57% chance to win the game.
How To Convert Moneyline Odds To Probability
Moneyline odds, also known as ‘American odds’ are probably the most foreign odds format to those of us outside of North America. And at first they appear a little confusing. But it is helpful to understand what these odds represent especially when listening to Americans speaking about gambling odds in sports broadcasts or podcasts. So, let’s see how we can convert Moneyline odds into their respective implied probabilities.
There are two instances of Moneyline odds: ‘minus’ moneylines and ‘plus’ moneylines.
The first are ‘minus’ moneylines. This is expressed as for example, -120.
What does this mean exactly? Well, let’s say bookmaker is offering odds of -120 for the Los Angeles Lakers to win a game. This is essentially saying that to win $100 you have to bet $120. In other words, if you place $120 on that outcome, you will receive a profit of $100.
The other instance are ‘plus’ moneylines. This is expressed as for example +180.
In this case, let’s say a bookmaker have offered odds of +180 for the New York Yankees to win a game. This simply means that if you bet $100, you will win $180.
So how do we convert the the ‘minus’ and the ‘plus’ moneyline odds into their implied probabilities? Let’s start out with the ‘minus’ moneyline conversion:
Converting ‘minus’ moneyline odds into implied probability formula:
| Implied probability | = | minus moneyline / (minus moneyline – 100) |
So let’s take an example, in which a bookmaker offers the following bet:
New York Jets to win against the New England Patriots at odds -120.
Example: How to convert ‘minus’ moneyline odds to its implied probability
| -120 (-120 – 100) | = | -120 / -220 | = | 0.545 | = | 54.5% |
Multiplied then by 100, we get the implied probability percentage of 54.5%.
So based on the odds of -120, the bookmakers have the Jets as a 54.5% chance of winning the game.
Converting a ‘plus’ moneyline is a bit different. Calculating the implied probabilities on these look like this:
Converting ‘plus’ moneyline odds into implied probability formula:
| Implied probability | = | 100 / ( plus moneyline odds + 100 ) |
So let’s take an example, in which a bookmaker offers odds +180 for Los Angeles Lakers to beat the Miami Heat.
Example: How to convert ‘plus’ moneyline odds to its implied probability
| 100 / (180 + 100 ) | = | 100 / 280 | = | 0.357 | = | 35.7% |
Multiplied then by 100, we get the implied probability percentage of 35.7%.
Again, based on these odds, the bookmakers have the Lakers are 35.7% chances of winning the game.
How To Calculate Odds From Probability
Knowing how to convert one form of odds to another can be helpful, especially if you have come into possession of a large amount of betting data that has odds formatted in an unfamiliar way.
To do this, we first need to convert any odds format to their implied probability. Once we have done this, the calculations are fairly straight forward.
How To Calculate Decimal Odds From Probability
Converting Decimal Odds from probability formula:
| Decimal Odds | = | 1 / implied probability |
Let’s take an example. In this example we think that Arsenal has a 75 % probability of defeating Stoke. To calculate decimal odds from probability, we want to covert 75 % into odds:
Example: How to calculate Decimal Odds:
| 1 / 0.75 | = | 1.33 |
Implied probability of 75% would return Decimal Odds of 1.33.
How To Calculate Fractional Odds From Probability
Converting Fractional Odds from probability formula:
| Fractional odds | = | ( 1 / implied probability ) -1 |
Let’s look at an example, where we think Wayne Rooney has 25% probability of scoring a goal. In this example, the fractional odds target will be calculated as:
Example: How to calculate Fractional Odds:
| (1 / 0.25) – 1 | = | 4 – 1 | = | 3 |
The outcome of this formula is 3, meaning we will express the odds as fractional odds, 3 /1.
How to Calculate Moneyline Odds From Probability
Converting implied probability into moneyline is a bit more complicated than converting it into decimal or fractional odds. The calculation depends on whether the implied probability is above 50% or below.
When the implied probability is above 50%, we make the following calculation.
Converting Moneyline Odds from probability (50% and above):
| Moneyline Odds | = | – ( implied probability / (1 – implied probability)) x 100 |
Let’s look at an example, where we think Liverpool has a 75 % chance of beating Everton. In this example, the moneyline odds target will be calculated as:
Example: How to calculate minus Moneyline Odds:
| – (0.75 / (1 – 0.75)) x100 | = | – (0.75 / 0.25) x 100 | = | – 3 x 100 | = | – 300 |
Moneyline odds = – 300.
When the implied probability is below 50%, the calculation is adjusted a little.
Converting Moneyline Odds from probability (below 50%):
| Moneyline odds | = | (1 – implied probability) / implied probability x 100 |
Let’s look at an example, where we think West Ham has a 25 % chance of defeating Manchester City. In this example, the moneyline odds target will be calculated as:
Example: How to calculate plus Moneyline Odds:
| 0.75 / 0.25 x 100 | = | 3 x 100 | = | 300 |
Moneyline odds = + 300.
How To Convert Decimal Odds To Fractions
Decimal odds and fractional odds are the most popular odds formats in the world, at least outside North America. Fortunately learning how to convert decimal odds to fractions is easy.
If your decimal odds are a round number, such as 7.0, then we simply subtract 1 from the decimal odds and apply a denominator of 1.
For example, odds of 7.0 would be fractional odds of 6/1.
But what if our decimal odds are not a round number? For example odds of 5.25?
First step is to subtract 1 from the decimal odds and apply a denominator of 1. This gives us fractional odds of 4.25/1.
Bookmakers never display fractional odds with a fraction within the fraction. So the next step is to round out the numerator. To do this we simply multiply the numerator by the number of times required to make it a round number.
So in this case, we must multiply the 4.25 by 4, to give us a numerator of 17. We then apply the number of times we multiplied the odds, in this case 4, as the denominator.
This then gives us fractional odds of 17/4, the equal of decimal odds 5.25.
Odds Conversion Chart
As a quick comparison guide, we’ve created an odds conversion chart which displays the odds and implied probability across each odds format.
If you want to know how to convert decimal odds to fractions or fractional odds to moneyline odds or moneyline odds to decimals, refer to this handy quick reference chat.
| Implied Probability % | Decimal Odds | Fractional Odds | American Odds |
|---|---|---|---|
| 99.0 | 1.01 | 1/100 | -10000 |
| 98.0 | 1.02 | 1/50 | -5000 |
| 97.1 | 1.03 | 1/33 | -3333 |
| 96.2 | 1.04 | 1/25 | -2500 |
| 95.2 | 1.05 | 1/20 | -2000 |
| 94.3 | 1.06 | 3/50 | -1667 |
| 93.5 | 1.07 | 7/100 | -1429 |
| 92.6 | 1.08 | 2/25 | -1250 |
| 91.7 | 1.09 | 9/100 | -1111 |
| 90.9 | 1.10 | 1/10 | -1000 |
| 90.1 | 1.11 | 11/100 | -909 |
| 89.3 | 1.12 | 3/25 | -833 |
| 88.5 | 1.13 | 13/100 | -769 |
| 87.7 | 1.14 | 7/50 | -714 |
| 87.0 | 1.15 | 3/20 | -667 |
| 86.2 | 1.16 | 4/25 | -625 |
| 85.5 | 1.17 | 17/100 | -588 |
| 84.7 | 1.18 | 9/50 | -556 |
| 84.0 | 1.19 | 19/100 | -526 |
| 83.3 | 1.20 | 1/5 | -500 |
| 82.6 | 1.21 | 21/100 | -476 |
| 82.0 | 1.22 | 11/50 | -455 |
| 81.3 | 1.23 | 23/100 | -435 |
| 80.6 | 1.24 | 6/25 | -417 |
| 80.0 | 1.25 | 1/4 | -400 |
| 79.4 | 1.26 | 13/50 | -385 |
| 78.7 | 1.27 | 27/100 | -370 |
| 78.1 | 1.28 | 7/25 | -357 |
| 77.5 | 1.29 | 29/100 | -345 |
| 76.9 | 1.30 | 3/10 | -333 |
| 76.3 | 1.31 | 31/100 | -323 |
| 75.8 | 1.32 | 8/25 | -313 |
| 74.6 | 1.33 | 33/100 | -303 |
| 74.1 | 1.34 | 17/50 | -294 |
| 73.5 | 1.35 | 35/100 | -286 |
| 73.0 | 1.36 | 9/25 | -278 |
| 72.5 | 1.37 | 37/100 | -270 |
| 71.9 | 1.39 | 39/100 | -256 |
| 71.4 | 1.40 | 2/5 | -250 |
| 70.9 | 1.41 | 41/100 | -244 |
| 70.4 | 1.42 | 21/50 | -238 |
| 69.9 | 1.43 | 43/100 | -233 |
| 69.4 | 1.44 | 11/25 | -227 |
| 69.0 | 1.45 | 9/20 | -222 |
| 68.5 | 1.46 | 23/50 | -217 |
| 68.0 | 1.47 | 47/100 | -213 |
| 67.6 | 1.48 | 12/25 | -208 |
| 67.1 | 1.49 | 49/100 | -204 |
| 66.7 | 1.50 | 1/2 | -200 |
| 65.8 | 1.52 | 13/25 | -192 |
| 64.9 | 1.54 | 27/50 | -185 |
| 64.1 | 1.56 | 14/25 | -179 |
| 63.3 | 1.58 | 29/50 | -172 |
| 62.5 | 1.60 | 3/5 | -167 |
| 61.7 | 1.62 | 31/50 | -161 |
| 61.0 | 1.64 | 16/25 | -156 |
| 60.2 | 1.66 | 33/50 | -152 |
| 59.5 | 1.68 | 17/25 | -147 |
| 58.8 | 1.70 | 7/10 | -143 |
| 58.1 | 1.72 | 18/25 | -139 |
| 57.5 | 1.74 | 37/50 | -135 |
| 56.8 | 1.76 | 19/25 | -132 |
| 56.2 | 1.78 | 39/50 | -128 |
| 55.6 | 1.80 | 4/5 | -125 |
| 54.9 | 1.82 | 41/50 | -122 |
| 54.3 | 1.84 | 21/25 | -119 |
| 53.8 | 1.86 | 43/50 | -116 |
| 53.2 | 1.88 | 22/25 | -114 |
| 52.6 | 1.90 | 9/10 | -111 |
| 52.1 | 1.92 | 23/25 | -109 |
| 51.5 | 1.94 | 47/50 | -106 |
| 51.0 | 1.96 | 24/25 | -104 |
| 50.5 | 1.98 | 49/50 | -102 |
| 50.0 | 2.00 | 1/1 | -100 |
| 49.5 | 2.02 | 51/50 | 102 |
| 49.0 | 2.04 | 26/25 | 104 |
| 48.5 | 2.06 | 53/50 | 106 |
| 48.1 | 2.08 | 27/25 | 108 |
| 47.6 | 2.10 | 11/10 | 110 |
| 46.5 | 2.15 | 23/20 | 115 |
| 45.5 | 2.20 | 6/5 | 120 |
| 44.4 | 2.25 | 5/4 | 125 |
| 43.5 | 2.30 | 13/10 | 130 |
| 42.6 | 2.35 | 27/20 | 135 |
| 41.7 | 2.40 | 14/10 | 140 |
| 40.8 | 2.45 | 29/20 | 145 |
| 40.0 | 2.50 | 3/2 | 150 |
| 38.5 | 2.60 | 8/5 | 160 |
| 37.0 | 2.70 | 17/10 | 170 |
| 35.7 | 2.80 | 9/5 | 180 |
| 34.5 | 2.90 | 19/10 | 190 |
| 33.3 | 3.00 | 2/1 | 200 |
| 31.3 | 3.20 | 11/5 | 220 |
| 29.4 | 3.40 | 12/5 | 240 |
| 27.8 | 3.60 | 13/5 | 260 |
| 26.3 | 3.80 | 14/4 | 280 |
| 25.0 | 4.00 | 3/1 | 300 |
| 23.8 | 4.20 | 16/5 | 320 |
| 22.7 | 4.40 | 17/5 | 340 |
| 21.7 | 4.60 | 18/5 | 360 |
| 20.8 | 4.80 | 19/5 | 380 |
| 20.0 | 5.00 | 4/1 | 400 |
| 19.2 | 5.20 | 21/5 | 420 |
| 18.5 | 5.40 | 22/5 | 440 |
| 17.9 | 5.60 | 23/5 | 460 |
| 17.2 | 5.80 | 24/5 | 480 |
| 16.7 | 6.00 | 5/1 | 500 |
| 16.1 | 6.20 | 26/5 | 520 |
| 15.6 | 6.40 | 27/5 | 540 |
| 15.2 | 6.60 | 28/5 | 560 |
| 14.7 | 6.80 | 29/5 | 580 |
| 14.3 | 7.00 | 6/1 | 600 |
| 13.3 | 7.50 | 13/2 | 650 |
| 12.5 | 8.00 | 7/1 | 700 |
| 11.1 | 9.00 | 8/1 | 800 |
| 10.0 | 10.00 | 9/1 | 900 |
| 9.1 | 11.00 | 10/1 | 1000 |
| 8.3 | 12.0 | 11/1 | 1100 |
| 7.7 | 13.0 | 12/1 | 1200 |
| 7.1 | 14.00 | 13/1 | 1300 |
| 6.7 | 15.00 | 14/1 | 1400 |
| 5.0 | 20.00 | 19/1 | 1900 |
| 3.3 | 30.00 | 29/1 | 2900 |
| 2.5 | 40.00 | 39/1 | 3900 |
| 2.0 | 50.00 | 49/1 | 4900 |
| 1.0 | 100.00 | 99/1 | 9900 |
| 0.7 | 150.00 | 149/1 | 14900 |
| 0.5 | 200.00 | 199/1 | 19900 |
