How dice probability works
This dice roller uses JavaScript's built-in pseudorandom number generator to simulate two independent six-sided dice. Each die has six equally likely outcomes, giving 36 possible ordered outcomes when the two dice are combined.
When rolling two dice, there are 36 possible outcomes. The sum 7 appears most often because it has the most combinations — 1+6, 2+5, 3+4, and their reverses, six in total. Sums like 2 and 12 are the rarest, each reachable by only one combination.
Two-dice probability table
| Sum | Combinations | Ways to roll | Probability |
|---|---|---|---|
| 2 | 1+1 | 1 | 2.78% |
| 3 | 1+2, 2+1 | 2 | 5.56% |
| 4 | 1+3, 2+2, 3+1 | 3 | 8.33% |
| 5 | 1+4, 2+3, 3+2, 4+1 | 4 | 11.11% |
| 6 | 1+5, 2+4, 3+3, 4+2, 5+1 | 5 | 13.89% |
| 7 | 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 | 6 | 16.67% |
| 8 | 2+6, 3+5, 4+4, 5+3, 6+2 | 5 | 13.89% |
| 9 | 3+6, 4+5, 5+4, 6+3 | 4 | 11.11% |
| 10 | 4+6, 5+5, 6+4 | 3 | 8.33% |
| 11 | 5+6, 6+5 | 2 | 5.56% |
| 12 | 6+6 | 1 | 2.78% |
Using dice probability for math practice
Two-dice rolls are a simple way to practice probability, relative frequency, and expected value. For example, the theoretical probability of rolling a 7 is 6/36, or 1/6, while the expected sum of two fair six-sided dice is 7. Roll the dice repeatedly and compare your observed results with these theoretical values to see how experimental probability approaches theoretical probability as the number of trials increases.
Frequently asked questions
What is the Law of Large Numbers?
The Law of Large Numbers describes how repeated independent trials tend to produce results closer to their theoretical probabilities as the number of trials increases. Ten rolls can produce an uneven distribution, while hundreds or thousands of rolls will generally make the observed percentages more closely match the expected distribution. You can see this in the live distribution — the more you roll, the more the blue bars tend to align with the red expected markers.
Are online dice rollers truly random?
This roller uses Math.random(), a pseudorandom number generator
provided by the browser. It is suitable for simulations, classroom
demonstrations, tabletop gaming, and ordinary probability experiments,
but it is not designed for cryptographic or security-sensitive use.
Each roll is generated independently by a new call to the browser's
pseudorandom number generator.
Why is 7 the most likely sum?
Because there are six ways to roll a 7 out of 36 equally likely outcomes: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. No other sum has as many combinations. The resulting probability distribution is symmetric and triangular, with its peak at 7.
What does the red marker in the distribution chart represent?
The red marker shows the theoretical probability for each possible sum — how frequently that sum is expected to occur over a very large number of rolls. The blue bar shows your observed percentage from the current session. As you make more rolls, the observed percentages tend to move closer to the theoretical probabilities.
Can I roll with the keyboard?
Yes. Press the Space bar anywhere on the page to roll, as long as a text field is not focused. This makes rapid rolling easier without reaching for the mouse.