How dice probability works
This dice roller uses JavaScript's built-in random number generator to simulate two independent six-sided dice. While each roll is unpredictable on its own, rolling repeatedly reveals a clear, predictable pattern governed by the laws of classical probability.
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% |
Frequently asked questions
What is the Law of Large Numbers?
The Law of Large Numbers states that as you repeat an experiment many times, the observed average converges toward the theoretical expected value. Ten dice rolls may look uneven; five hundred rolls will closely mirror the expected bell curve. You can see this in action with the live distribution — the more you roll, the closer the blue bars align with the red expected markers.
Are online dice rollers truly random?
Close, but not perfectly. This roller uses Math.random(), a pseudorandom number generator built into every browser. Results are statistically uniform and every roll is independent of past rolls — making it accurate enough for classroom demonstrations, tabletop gaming, or statistics assignments. For cryptographic-grade randomness, a hardware random number generator would be needed.
Why is 7 the most likely sum?
Because it has the most combinations — six out of 36 total outcomes. Every other sum has fewer routes to reach it. The distribution forms a symmetric triangle peaking at 7, which is why 7 is the key number in games like craps.
What does the red line in the distribution chart represent?
The red marker shows the theoretical expected percentage for each sum — how often that sum should appear over a very large number of rolls. The blue bar shows your actual live percentage. The closer you get to the red line on each sum, the more your session reflects true probability.
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.