We all love playing games which involve throwing the dice. Whether you want to find out the probability of your success in the games you play or you just want to learn more about probabilities, this dice probability calculator will help you out. We will also discuss how you can make basic calculations which involve dice.
Table of Contents
How to use the dice probability calculator?
Without having to enter any values, this dice calculator already provides you with values for the Number of Success and the Probability. Of course, you may also use your own values to find the result you need. To use the dice roll probability calculator, follow these steps:
- First, enter the value for the Number of Trials.
- Then enter the value for the Probability of Success.
- Upon entering these two values, the dice probability calculator will automatically generate the Number of Successes and Probability values.
How to calculate dice probability?
The simplest way to learn how to calculate dice probability without the use of a dice odds calculator is by acquiring a specific value using a single die. You can get the dice average by looking at how many possible outcomes are there compared to the outcome you’d like to see. So for a single die which has six sides, one roll would give you 6 possible outcomes. You can also perform a manual calculation using the following formula:
Probability = Number of desired outcomes ÷ Number of possible outcomes
We express the values of probability as a number between 0 and 1. If you want to get a percentage value, multiply it by 100.
How many combinations can 2 dice make?
When you roll two dice, you have to differentiate them. For instance, assign the first die as “a” and the second die as “b.” Then you can create a table which shows all of the possible outcomes when you roll both dice at the same time. To help out, here’s the table:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
As you can see, there are 36 different combinations you may get when you roll two dice. You can also compute for this value manually using a formula:
Number of combinations = number of possibilities of a * number of possibilities of b
What are the odds of rolling a 12 with two dice?
Using a dice calculator, you will be able to acquire the probability of rolling a 12 using 2 dice which is 2.78%. The probability of getting any specific total equals how many ways you can acquire that total and divided by how many possible combinations are there which, as discussed earlier is 36. Let’s calculate to check the accuracy of the value given value:
Probability = 1 (how many ways you can acquire 12) ÷ 36 (total number of combinations)
= 0.0278 or 2.78%
What are the odds of rolling dice?
If you don’t want to perform manual calculations, you can use the dice probability calculator. However, if you want to learn more about probability and you’d like to compute the values manually, you can still use the dice roll probability calculator to check your answers. When rolling two dice, working out the probabilities is a simple process.
For instance, if you would like to know the probability of rolling two 6s, you’re calculating “independent probabilities.” This means that the outcome of one die doesn’t affect or depend on the outcome of the other. Therefore, you’re left with individual one-in-six possibilities. When calculating independent probabilities, simply multiply their separate probabilities to get the final result. Here’s the formula:
Probability of both = Probability of outcome one × Probability of outcome two
If you’re working with matching numbers like when you’re rolling dice, it’s easier to use fractions. Let’s use the formula:
Probability = 1/6 × 1/6 = 1/36
If you need a numerical result, simply divide the numerator of the fraction by the denominator:
Probability = 1 ÷ 36 = 0.0278 or 2.78%
If you need to get the probability of acquiring two different numbers when you roll a pair of dice, the calculation becomes a bit different. Let’s say you need the probability of rolling a 5 and a 4. In such a case, you may also use the same principle as the previous one. Out of the 36 possible outcomes, you’re interested in two specific ones. Therefore:
Probability = Number of desired outcomes ÷ Number of possible outcomes
= 2 ÷ 36 = 0.0556 or 5.56%
You can also calculate the possibility when you roll more than two dice. To get the probability, you can use the same formula:
Probability = Number of desired outcomes ÷ Number of possible outcomes
First, you have to determine the total number of outcomes. Do this by multiplying the number of sides on one of the dice by the number of sides on the other die. Of course, this would require more work on your part because you need to consider the dice individually. If you want to get a total score of 4 when you roll 2 dice, you can get this by rolling:
- a 1 and a 3
- a 2 and a 2
- a 3 and a 1
Since you’re considering the individual dice, this means that getting a 1 on the first die and a 3 on the second differs from an outcome where you get a 3 on the first die and a 1 on the second. Therefore, to get a 4, there are 3 different ways to consider out of the 36 total possible outcomes. Now we can perform the calculation using the formula:
Probability = Number of desired outcomes ÷ Number of possible outcomes
= 3 ÷ 36 = 0.0833 or 8.33%
When you roll 2 dice, the number 7 has the highest probability as there are 6 ways for you to get it.
