# Dice probability calculator

The dice probability calculator is a great tool if you want to estimate the dice roll probability over numerous variants. There are may different polyhedral die included, so you can explore the probability of a 20 sided die as well as that of a regular cubic die. So, just evaluate the oddsand play a game! In the text, you'll also find a short descriptions of each of the options.

Everybody knows what a regular 6 sided die is, and, most likely, many of you have already played thousands of games where the one or more was used. But, did you know that there are different types of die? Don't worry, we take each of these dice into account in our dice probability calculator. You can choose whichever you like, and e. Well, the question is more complex than it seems at first glance, but you'll soon see that the answer isn't that scary! It's all about maths and statistics.

First of all, we have to determine what kind of dice roll probability we want to find. We can distinguish a few which you can find in this dice probability calculator.

Before we make any calculations, let's define some variables which are used in the formulas. The probability of rolling the same value on each die - while the chance of getting a particular value on a single die is pwe only need to multiply this probability by itself as many times as the number of dice.

We want to rolled value to be either 654or 3. The probability of rolling all the values equal to or lower than y - this option is almost the same as the previous one, but this time we are interested only in numbers which are equal to or lower than our target.

The probability of rolling exactly X same values equal to y out of the set - imagine you have a set of seven 12 sided dice, and you want to know the chance of getting exactly two 9s. It's somehow different than previously because only a part of the whole set has to match the conditions.

This is where the binomial probability comes in handy. The binomial probability formula is:. As you may expect, the result is a little higher.

Sometimes the precise wording of the problem will increase your chances of success. The probability of rolling an exact sum out of the set - unfortunately, there isn't a single formula for this problem. One approach is to find the total number of possible sums.

With a pair of regular dice, we can have 2,3,4,5,6,7,8,9,10,11,12but these results are not equivalent! The number of permutations with repetitions in this set is The higher the number of dice, the closer the distribution function of sums gets to the normal distribution. As you may expect, as the number of dice and faces increases, the more time is consumed evaluating the outcome on a sheet of paper.

Luckily, this isn't the case for our dice probability calculator! The probability of rolling a sum out of the set, not lower than X - like the previous problem, we have to find all results which match the initial condition, and divide them by the number of all possibilities. Taking into account a set of three 10 sided dice, we want to obtain a sum at least equal to As we can see, we have to add all permutations for 272829and 30which are 10, 6, 3, and 1 respectively.

The probability of rolling a sum out of the set, not higher than X - the procedure is precisely the same as for the prior task, but we have to add only sums below or equal to the target. Having the same set of dice as above, what is the chance of rolling at most 26? If you were to do it step by step, it would take ages to obtain the result to sum all 26 sums.Probability is the chance that the given event will occur. Use this online probability calculator to calculate the single and multiple event probability based on number of possible outcomes and events occurred.

Probability is about finding the likelihood of some events to happen. It is expressed as a number between 0 and 1. Here 1 is considered as certainty True and 0 is taken as impossibility False. Use our online probability calculator to find the single and multiple event probability with the single click. The best example of probability would be tossing a coin, where the probability of resulting in head is.

It can be calculated by dividing the number of possible occurrence by the total number of options. The higher the probability of an event, the more certain that the event will occur. Probabilities in general describes the underlying mechanics and regularities of complex systems. Make use of probability calculators to solve the probability problems with ease. Simple Probability Calculator. Single Event Probability Number of possible outcomes: Number of events occured:.

Result P A :. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. Related Articles: Single event probability Multiple event probability. Calculators and Converters.

### Dice Probability Calculator

Ask a Question.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.

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:. 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. 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:. We express the values of probability as a number between 0 and 1. If you want to get a percentage value, multiply it by When you roll two dice, you have to differentiate them.

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:. Using a dice calculator, you will be able to acquire the probability of rolling a 12 using 2 dice which is 2. 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 When rolling two dice, working out the probabilities is a simple process.

When calculating independent probabilities, simply multiply their separate probabilities to get the final result. 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. In such a case, you may also use the same principle as the previous one. You can also calculate the possibility when you roll more than two dice. To get the probability, you can use the same formula:. 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:.

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:. When you roll 2 dice, the number 7 has the highest probability as there are 6 ways for you to get it. Dice Probability Calculator.

Table of Contents.Backgammon is a game that employs the use of two standard dice. The dice used in this game are six-sided cubes, and the faces of a die have one, two, three, four, five or six pips. During a turn in backgammon a player may move his or her checkers or draughts according to the numbers shown on the dice. The numbers rolled can be split between two checkers, or they can be totaled and used for a single checker. For example, when a 4 and a 5 are rolled, a player has two options: he may move one checker four spaces and another one five spaces, or one checker can be moved a total of nine spaces.

To formulate strategies in backgammon it is helpful to know some basic probabilities. Since a player can use one or two dice to move a particular checker, any calculation of probabilities will keep this in mind. For a single die that is not loaded, each side is equally likely to land face up.

Short cut for Probability for 2 Dice

A single die forms a uniform sample space. There are a total of six outcomes, corresponding to each of the integers from 1 to 6. When we roll two dice, each die is independent of the other.

The probability of rolling two dice and getting at least one of a number from 1 to 6 is straightforward to calculate. If we wish to determine the probability of rolling at least one 2 with two dice, we need to know how many of the 36 possible outcomes include at least one 2. The ways of doing this are:. There is nothing special about 2 in the preceding discussion.

### Coin & Dice Probability: Using a Tree Diagram

For any given number n from 1 to Therefore there are 11 ways to roll at least one n from 1 to 6 using two dice. Any number from two to 12 can be obtained as the sum of two dice. The probabilities for two dice are slightly more difficult to calculate. Since there are different ways to reach these sums, they do not form a uniform sample space.

For instance, there are three ways to roll a sum of four: 1, 32, 23, 1but only two ways to roll a sum of 5, 66, 5. At long last we have everything we need to calculate probabilities for backgammon. Rolling at least one of a number is mutually exclusive from rolling this number as a sum of two dice. Thus we can use the addition rule to add the probabilities together for obtaining any number from 2 to 6. Other probabilities can be calculated in a similar manner.

Share Flipboard Email. Courtney Taylor. Professor of Mathematics. Courtney K. Taylor, Ph. There are five ways to roll exactly one of that number on the first die. There are five ways to roll exactly one of that number on the second die. There is one way to roll that number on both dice. The probability of rolling a sum of a particular number is as follows:.When the number of respects and the number of dice are input, and "Calculate the probability" button is clicked, the number of combinations from which dice when the number of specified dice are shaken come up and the probability of becoming a total of the eyes are calculated.

From the number and the number of sides of the dice, the probability that out of the sum of the dice combination is calculated. The combination and the probability of sum when throw it specification piece are displayed by the list.

## 2 dice roll Calculator

Calculate time Calculate date Calculate calendar Calculate biorhythm Convert character Convert unit Calculate map Calculate random numbers Calculate probability Calculate area Calculate volume Calculate triangle Calculate divisor and multiple Calculate progression Information About exemption matters.

Front page Calculate probability Probability of the sum of the dice. Probability that a specified number of shake the dice, the total value of exits is calculated.

Calculate probability. Probability of the dice Probability of the sum of the dice Probability of a coin Probability of drop item Probability of complete Probability of lottery Probability of continuously win. Simple Calculator. Save results in a temporary. Popular page. Calculate entrance and graduation year 2.

Christian era and japanese calendar conversion table 5. Convert volume 6. Convert length 7. Convert space 8. Convert time 9. Convert weight Convert area.During these challenging times, we guarantee we will work tirelessly to support you.

We will continue to give you accurate and timely information throughout the crisis, and we will deliver on our mission â€” to help everyone in the world learn how to do anything â€” no matter what. Thank you to our community and to all of our readers who are working to aid others in this time of crisis, and to all of those who are making personal sacrifices for the good of their communities.

We will get through this together. Updated: November 19, References. Lots of people think that if you roll three six sided dice, you have an equal chance of rolling a three as you have rolling a ten. This is not the case, however, and this article will show you how to calculate the mean and standard deviation of a dice pool.

Learn the terminology of dice mechanics. Dice are usually of the 6 sided variety, but are also commonly found in d2 Coinsd4 3 sided pyramidsd8 Octahedrad10 Decahedrad12 Dodecahedraand d20 Icosahedra. A dice roll follows the format Number of Dice Shorthand Dice Identifierso 2d6 would be a roll of two six sided dice.

This method gives the probability of all sums for all numbers of dice. It can be easily implemented on a spreadsheet. To calculate multiple dice probabilities, make a probability chart to show all the ways that the sum can be reached. For example, with 5 6-sided dice, there are 11 different ways of getting the sum of Keep in mind that not all partitions are equally likely.

For instance, with 3 6-sided dice, there are 6 ways of rolling but only 3 ways of rolling and 1 way of rolling To work out the total number of outcomes, multiply the number of dice by the number of sides on each die. For 5 6-sided dice, there are possible combinations. For more tips, including how to make a spreadsheet with the probability of all sums for all numbers of dice, read on!

There are only two possible results we discount the chance that it will land on the edge that is crown or piano. The dice probability calculator that the next throw is heads is 1 in 2. Based only on that, if the next roll comes up as tails, then logically the next roll after which must heads - after all, it's a 1 in 2 chance, and that would be the second throw. But that's not how the dice probability works. Previous throws do not affect or determine later throws. If you get heads 20 times in a row, the chances of the next throw coming up tails are still 1 in 2, because there are only 2 possible outcomes, every single time.

So how does it work with dice? Provided we use standard 6-sided dice, rolling a single die gives a 1 in 6 chance that any number will come up, provided the die is perfectly manufactured and not weighted on one side. The chances of the same number coming up on a later roll are 1 in 6.

It never changes. But when you add another die in the mix, it becomes interesting. The possible results of throwing two dice are in the range of 2 to 12, so 11 results in all. You might think that the dice probability of getting a particular number is 1 in 11 - but you would be wrong. The total is now dependent on two factors, not one. If you roll a total of 2, you can only get one way - both dice must show a 1. If you roll 12, you can only get one way too-both dice must show a 6.

Simple so far, right? If you roll a 3, there are two ways to get it. The probability of rolling 3 is twice as likely as rolling a 2. As you progress through this math exercise, you will realize the easiest number to roll is 7. We know this is a bit complicated, but we are working on a dice probability calculator, which will make calculations for you.

As you move away from 7, the combinations decrease. For 6 or 8, there are 5 combinations, for 5 or 9, there are 4 combinations, and so on. The total number of combinations corresponds to the number of faces on each matrix multiplied by each other - This means that the probability of rolling 7 is 6 in 36, or 1 of 6. The dice probability of rolling 5 is 4 in 36, or 1 of 9.

The probability of rolling 2 is 1 at Adding a third die to the mix gives you a total of possible outcomes, with at least a score of 3 or Who said Dice's probability calculation was simple?

Dice probability calculator.