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6 Sided Dice Roller Calculator

Created by Davide Borchia
Reviewed by Komal Rafay
Last updated: Jan 18, 2024


Our 6-sided dice roller calculator will be helpful whether you need a dice to roll or a simple example of random generation of one outcome. Keep reading to learn:

  • The statistics of a 6-sided dice roll;
  • How to calculate a 6-sided dice roll: how to simulate the outcome of a toss; or
  • How to use our 6-sided dice roller calculator.

Dive in, or start playing with our tool!

The statistics of a 6-sided dice roll

A 6-sided (d6) dice roller is nothing but a simulation of the extraction of a random outcome out of six possible results. Traditionally, the outcomes are numbers, from 11 to 66, but it doesn't matter as we won't perform mathematical operations on them.

Each outcome has a defined probability with which it happens. In the case of a fair, 6-sided dice, each outcome has a probability 1/61/6 of happening. In statistical terms, this means that the outcomes are uniformly distributed, and each occurs with the same average frequency. In practical terms, it means that if you roll the dice an adequate number of times, each outcome will happen, more or less, the same number of times. For example, be patient, toss a dice 60006000 times, and count the outcomes: each number will happen about 10001000 times. But of course, statistics is statistics, and there is a chance that all those 6 thousand tosses will result in only one outcome. We can easily calculate this probability:

P6000=166000=18.08×104668P_{6000} = \frac{1}{6^{6000}} = \frac{1}{8.08\times 10^{4668}}

This number is ridiculously low, so much that we can say that its occurrence is impossible in our daily experience.

How to calculate a 6-sided dice roll

The best way to calculate a 6-sided dice roll is to toss a die! If no dice are available, you can still simulate this event on a computer, for example. To do so, we rely on randomness. Computers use pretty complex algorithms to simulate what Nature can do easily: true randomness. The details of the generation of such a number are out of the scope of this article, but generally speaking, you only have to tell your computer the range in which your possible outcomes are and their distribution.

Our 6-sided dice roller calculator does precisely this! We implemented a random number generator with which you can interact: we set the default parameters to a single 6-sided dice, but you can change it to almost all possible (fair) dice you can think of. Change the last variable to roll to simulate the desired event!

FAQ

What is the chance of getting a 6 in a 6-sided dice roll?

The chance of getting a 6 in a 6-sided dice roll is 1/6. This is because there are six possible outcomes, all of them happening with the same chance: to find the probability of a single one of them, we have to divide the unity (chance of any event) by the number of possible events (6).

What is the chance of rolling 10 times 6?

The chance of rolling 10 times 6 is 1/60,466,176 or 0.00000001654 (0.000001654%). To find this result:

  1. Calculate the chance of getting a 6: since a 6-sided dice has a uniform distribution of its outcomes, the probability is 1/6.
  2. Since each toss is independent of the previous ones, we can multiply the chance of each event: 1/6 × 1/6 × 1/6 × ... × 1/6 (10 times).
  3. You can write the same operation as a power: 1/610.
  4. Compute the result numerically, or leave it expressed as a power if you need it for further steps in your homework.

Are dice truly random?

Dices are effectively random: however, since they obey the laws of physics, we can also say that their motions and the outcome of a roll are deterministic. However, the problem is so complicated and involves so many variables that it eludes every possible attempt to describe it mathematically.

Davide Borchia
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