# Random Dice Roller

URL: https://speedycalculator.com/calculators/statistics/random-dice-roller/
Last updated: 2026-10-30

> The random dice roller throws a set of dice of any type – three d6s by default – and can repeat the whole set many times in one go, listing every total, their average and a chart of how often each total came up compared with what to expect.

## Inputs

- Number of dice in the set
- Dice type
- Number of sides (custom die)
- Roll the set this many times

## Results

- Total of the first roll
- Dice in the first roll
- Totals of all rolls
- Average of your totals
- Expected average total
- Possible totals
- How often each total came up

## Formula

```
Total of n dice with s sides: average n(s + 1)/2 · after many repeated rolls the share of each total approaches its exact probability
```

## Explanation

Rolling the same set of dice over and over is the quickest way to see probability at work. One roll of three dice tells you very little, but roll them fifty or a thousand times and a clear shape appears: totals near 10 and 11 pile up, while 3 and 18 hardly ever appear. That shape is the probability distribution, and the more rolls you make, the closer the tally gets to it.

This roller is built for that kind of experiment as well as for everyday games. Choose how many dice and which type – any of the common shapes from the three-sided prism to the 120-sided disdyakis triacontahedron, or a custom number of sides – and how many times to roll the whole set. With a single roll you get the dice, the total and the exact chance of that total. With repeated rolls you get the full list of totals, their mean and a bar chart of how often each total occurred.

Use it to demonstrate the law of large numbers in class, to generate a batch of random stats for a game, or simply to roll whatever dice you need.

### How to use the Random Dice Roller

- **Number of dice in the set**
- **Dice type**
- **Number of sides (custom die)**
- **Roll the set this many times**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Each die is an independent secure random integer from 1 to its number of sides. Repeated sets are rolled independently and their totals are tallied; the expected average comes from n(s + 1)/2.

### Worked example

Rolling 3d6 fifty times produced an average total of 10.62, close to the expected 10.5. The exact probability of a total of 10 is 27/216 = 12.5%, so about 6 of the 50 rolls should be 10s; seeing anywhere from 2 to 10 is normal in a run of 50.

### Expected tallies for 100 rolls of 3d6

TotalProbabilityExpected count in 100 rolls3 or 180.46%0.56 or 154.63%4.69 or 1211.57%11.610 or 1112.5%12.5

## Worked example

Inputs — Number of dice in the set: 3; Dice type: Cube – d6 (6 faces); Roll the set this many times: 50.

Results — **Total of the first roll = 8**; Dice in the first roll = 2, 3, 3; Totals of all rolls = 8, 14, 12, 7, 9, 12, 9, 12, 8, 8, 13, 11, 12, 10, 6, 5, 11, 12, 6, 11, 11, 14, 12, 11, 12, 9, 12, 7, 12, 10, 8, 6, 9, 11, 9, 12, 10, 11, 7, 10, 10, 10, 15, 7, 14, 13, 9, 9, 14, 9; Average of your totals = 10.18; Expected average total = 10.5; Possible totals = 3 to 18.

## Key terms

- **Law of large numbers**: Averages of many independent trials converge to the expected value.
- **Frequency**: How many times an outcome occurred in a series of trials.
- **Relative frequency**: The frequency divided by the number of trials – an estimate of the probability.

## FAQ

**How many times should I roll to see the distribution?**
A few hundred rolls of the set already show the shape clearly; 1,000 rolls usually match the exact probabilities within a percentage point or two.

**What is the expected average of three d6?**
10.5. Your average over 50 rolls will typically land between 9.7 and 11.3.

**Is every roll independent?**
Yes. Earlier rolls never influence later ones – a run of low totals does not make a high total "due".

**Can I roll unusual dice?**
Yes – choose from 20 shapes between 3 and 120 sides, or enter any number of sides from 2 to 1,000.

**What is the law of large numbers?**
As the number of rolls grows, the average of the results gets closer to the expected value and the share of each total approaches its probability.

**Can I use it for random character stats?**
Yes – set 3 dice, d6 and 6 repetitions for classic 3d6 ability scores.


## Sources

- [Wolfram MathWorld – Dice](https://mathworld.wolfram.com/Dice.html)
- [OpenStax – Introductory Statistics 2e](https://openstax.org/details/books/introductory-statistics-2e)