How it's calculated
P = favorable outcomes ÷ sⁿ
n = number of dice, s = sides per die, sⁿ = total equally likely rolls; favorable = number of rolls that make the chosen sum (or a ≥/≤ range). Mean = n(s+1)/2, SD = √(n(s²−1)/12).
Worked examples
| Roll | Target | Probability |
|---|---|---|
| 2d6 | Exactly 7 | 16.67% |
| 2d6 | Exactly 2 | 2.78% |
| 2d6 | Exactly 12 | 2.78% |
| 1d6 | Exactly 4 | 16.67% |
| 2d6 | At least 10 | 16.67% |
Common questions
What are the odds of rolling a 7 with two dice?
1 in 6, or about 16.7 percent. There are six ways to make 7 out of 36 combinations, more than any other total.
Why are 2 and 12 the hardest to roll?
Each has only one combination, double-1 or double-6, so each is just 1 in 36 (about 2.8 percent).