Odds Calculator

Probability and odds are often used when making predictions. Probability and odds are not synonymous terms. There are some differences between the probability and the odds.

Definition of probability

The probability of the event indicates the chance that an event will occur. In other words, the fraction of possible possibilities that result in the desired event.

Let's use an example to understand this clearly.

Example of probability

There are 12 face cards in a standard deck of 52 cards. King, queen and jack in each suit of four.

Assume your friend shuffled the deck and then asked you to draw a card at random from that shuffled deck. You think that you can win at betting. Therefore, you bet that if you cannot draw a face card, you will give him $1. Otherwise, he will give you $5.

Find the winning probability.

The winning probability is the chance of getting a face card out of all possible outcomes. There are a total of 52 cards. This implies that there are 52 possible outcomes in all. Your preferred event is receiving a face card. There are 12 potential outcomes for the desired event because the shuffled deck of cards has 12 face cards.

You describe the total number of desired occurrences in relation to the total number of outcomes. That is 12/52. The winning probability is computed in this manner.

Definition of odds

Odds measure how probable something is to happen that compares the number of desirable outcomes to the number of undesirable outcomes. In other words, odds are a way to represent the relationship between the proportion of positive outcomes to those that are unfavorable in a specific situation.

Let's use the previous example to understand this clearly.

Example of odds

In the above example, your favorable outcome is drawing a face card. As a result, there are 12 favorable outcomes. The number of unfavorable outcomes is calculated by subtracting the total number of favorable outcomes from the total number of outcomes. You have to subtract 12 from 52 because there are a total of 52 outcomes.

No. of unfavorable outcomes = Total no. of outcomes - No. of favourable outcomes = 52 - 12 = 40

You now use a ratio to express the total number of desired outcomes in relation to the total number of undesired outcomes. This is called odds.

Probability calculation

Probability is calculated by dividing the number of desired outcomes by the total number of outcomes.

Probability = No. of desired outcomes / Total no. of outcomes

Let us now compute the winning probability for the previous example.

The winning probability = No. of face cards / Total no. of cards in the deck = 12 / 52 = 3 / 13

We will now compute the probability of losing. This is similar to estimating the probability of the complement event of the desired event.

If the desired event is A, the complement event is Aᶜ or A¹. The probability of a complement event is calculated by deducting the probability of the desired event from 1.

P(Aᶜ) = 1 - P(A)

Let's calculate the probability of losing for the previous example.

We already calculated the winning probability as 3 / 13. Therefore,

Probability of losing = 1 - Winning Probability = 1 - 3 / 13 = 10 / 13

Odds calculation

Odds are computed by finding the lowest ratio between the number of desired outcomes and the number of undesired outcomes. This can also be determined by calculating the ratio between the probability of desired outcomes and the probability of undesirable events.

There are two types of odds calculations:

• the odds in favor,
• the odds against.

The odds in favor

The lowest ratio of the number of outcomes that can happen to the desired event to the number of outcomes that cannot happen to the desired event is known as the odds in favor. Let's say our desired event is A. Then the odds in favor of event A are calculated as below.

Based on the number of outcomes

The odds in favour of event A = n(A) : n(Aᶜ)

Based on probability

The odds in favour of event A = P(A) : P(Aᶜ)

Let's calculate the odds in favor of winning in the example given above.

1. Based on the number of outcomes

In the previous example, the desired event was the drawing of a face card.

No. of the desired outcomes = 12

No. of undesired outcomes = Total no. of outcomes - No. of desired outcomes = 52 - 12 = 40

Therefore,

The odds are in favor = No. of desired outcomes / No. of undesired outcomes = 12 / 40 = 3 / 10

2. Based on probability

The desired event is the drawing of a face card.

The winning probability = No. of desired outcomes / Total no. of outcomes = 12 / 52 = 3 / 13

The probability of losing = 1 - The winning probability = 1 - 3 / 13 = 10 / 13

The odds in favour = The winning probability / The probability of losing = 3 /13 : 10 / 13 = 3:10

The odds against

The odds against are the lowest ratios of the number of outcomes that cannot happen to the desired event to the number of outcomes that can happen to the desired event. Let's assume that the desired event is A. The odds against event A are then computed as follows.

Based on the number of outcomes,

The odds against event A = n(Aᶜ) : n(A)

Based on probability,

The odds against event A = P(Aᶜ) : P(A)

Let's calculate the odds against winning for the example given above.

1. Based on the number of outcomes

The desired event is the drawing of a face card.

No. of the desired outcomes = 12

No. of undesired outcomes = Total no. of outcomes - No. of desired outcomes = 52 - 12 = 40

Therefore,

The odds against winning = No. of undesired outcomes : No. of desired outcomes = 40 : 12 = 10 : 3

2. Based on probability

The desired event is the drawing of a face card.

The winning probability = No. of desired outcomes / Total no. of outcomes = 12 / 52 = 3 / 13

The probability of losing = 1 - The winning probability = 1 - 3 / 13 = 10 / 13

The odds against winning = The probability of losing : The winning probability = 10 / 13 : 3 / 13 = 10 : 3

Expression

Expression of probability

Probabilities can be expressed as a decimal, a percentage, a fraction, or a ratio.

In the previous example, we calculated the winning probability as a fraction.

• The winning probability = No. of desired outcomes / Total no. of outcomes = 12 / 52 = 3 / 13

We can express the winning probability as a decimal.

• The winning probability = No. of desired outcomes / Total no. of outcomes = 12 / 52 = 3 / 13 = 0.2308

The winning probability can be expressed as a percentage.

• The winning probability = (No. of desired outcomes / Total no. of outcomes) × 100% = (12 / 52) × 100% = (3 / 13) × 100% = 23.08%

A ratio can be used to represent the probability of winning.

• The winning probability = No. of desired outcomes : Total no. of outcomes = 12 : 52 = 3 : 13

To summarize,

• The winning probability = 3 / 13 = 0.2308 = 23.08%

Expression of odds

Odds are usually expressed as a ratio in the lowest terms.

According to the example,

• The odds in favor = No. of desired outcomes: No. of undesired outcomes = 12 : 40 = 3 : 10

• The odds against = No. of undesired outcomes : No. of desired outcomes = 40 : 12 = 10 : 3

The range

The range of probability

When an event is unquestionably going to happen, its probability is 1. When an event is not going to happen, its probability is 0. As a result, a given event's probability is always between 0 and 1. If the probability is expressed as a percentage, it will be between 0% and 100%.

The range of odds

The odds in favor are infinite when an event is certain to occur. If the event is never going to happen, the odds are zero. Therefore, odds are represented as a number between 0 and infinity.

As per the example,

• The odds in favour = 3 : 10 = 0.3

• The odds against = 10 : 3 = 1.02

Converting odds to probability

As you already learned, odds are a way to represent the relationship between the proportion of positive outcomes to those that are unfavorable in a specific situation.

Odds are not an expression of how likely that event will happen. So, when odds are given, you may have to convert those odds to probability to know how likely that event will happen. You can convert odds to probability as follows.

The favorable event is A,

you know that,

n(S) =n(A) + n(Aᶜ)

Therefore,

$$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{n\left(A\right)}{n\left(A\right)+n(A^c)}$$

Example of calculating the conversion of odds to probability

In our example,

• The odds in favor = 3 : 10

So,

• Probability of winning = No. of desired outcomes / (No. of desired outcomes + No. of undesired outcomes) = 3 / (3 + 10) = 3 / 13

In our example,

• The odds against = 10 : 3

So,

• Probability of losing = No. of undesired outcomes / (No. of undesired outcomes + No. of desired outcomes) = 10 / (10 + 3) = 10 / 13

It is no longer difficult to convert odds to probability and odds to their lowest ratio. The odds probability calculator can help you convert winning odds to winning probability and odds for winning to their lowest ratio. It will reduce the odds against winning to their lowest ratio and convert the odds against to the probability of losing.

To compute the answers for the previous example using the odds probability calculator, input 12 for A and 40 for B, choose "Odds are for winning," and then calculate. You can get the same results if you enter 40 for A and 12 for B and choose "The odds are against winning." The answers will be ready in a split second.

The significance of odds

There are several applications for odds in multiple areas.

The scientific research sector, particularly concerning the transmission of illnesses, frequently uses odds. To understand how a disease spreads and to create treatments and remedies, scientists might use odds to compare the ratio of a population that develops an illness to the ratio that does not.

Financial experts can utilize odds to determine whether a given investment might provide a more significant risk or gain to assist them in making investment decisions.

Betting and gambling are other major areas that use odds. The displayed odds never accurately represent the probability of an event happening or not happening. The bookmaker always adds a profit margin to these odds. Thus, the payment to the winning wagerer is always lower than it would have been if the odds had properly represented the probabilities.