Roll one or more virtual dice with any number of sides and see each die and the total.
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With two six-sided dice there are 36 equally likely combinations, but a total of 7 can be made 6 ways — about 16.67% — while 2 and 12 can each be made only one way, about 2.78%.
Each die is rolled independently with secure randomness, and every face from 1 to the side count is equally likely, so a d20 gives each face a 5% chance. Rejection sampling avoids the small bias that simpler formulas introduce.
You can roll up to 100 dice at once, with anything from 2 sides up to a million, which covers board games, tabletop dice such as d4, d8, d10, d12 and d20, and classroom experiments. Virtual dice suit games and learning, not regulated gambling, where certified generators and audits are required.
Set the number of dice and the number of sides. Each die is rolled independently with secure randomness, and every face from 1 to the side count is equally likely, so a d20 gives each face a 5% chance. You can roll up to 100 dice at once, with anything from 2 to a million sides, which covers board games, tabletop role-playing dice such as d4, d8, d10, d12 and d20, and simple classroom experiments. The result lists each die and the total.
With two six-sided dice there are 36 equally likely combinations, but totals are not spread evenly. A total of 7 can be made 6 ways, giving 6 of 36 or about 16.67%, while 2 and 12 can each be made only one way, about 2.78%. The average total of two dice is 7. Three dice range from 3 to 18 with an average of 10.5, and extreme totals become rarer as more dice are added. This is why games reward rolls far from the middle.
Rolling at least one 6 in four rolls of a single die happens about 51.77% of the time, slightly better than even, a result that puzzled gamblers in the seventeenth century. Each roll is independent, so a long run without a 6 does not make the next roll more likely to be one. Virtual dice are suitable for games and learning. They are not intended for regulated gambling, where certified random number generators and audits are required.
| Input | Result |
|---|---|
2 × d6 · total 7 | 6 of 36 · 16.67% |
2 × d6 · total 2 | 1 of 36 · 2.78% |
2 × d6 · average total | 7 |
4 × d6 · at least one 6 | 51.77% |
1 × d20 · each face | 5% |
3 × d6 · total range | 3–18 · average 10.5 |
Because totals can be made in different numbers of ways. With two dice, 7 appears 6 of 36 times while 2 and 12 appear once each. The average total of two dice is 7; three dice range from 3 to 18 with an average of 10.5, and extreme totals get rarer as more dice are added — which is why games reward rolls far from the middle.
Rolling a single die four times gives at least one 6 about 51.77% of the time, slightly better than even. That result puzzled gamblers in the seventeenth century, and it is a good reminder that “several chances” does not simply add up to certainty.
No. Each roll is independent, so a dry spell does not change the next roll, which still gives every face the same chance. The same reasoning applies to the d20: each face stays at 5% no matter what came before.