Probability calculator
8.33%
out of 36 equally likely combinations of 2d6
Full distribution
| Total | Ways | Odds | |
|---|---|---|---|
| 2 | 1 | 2.78% | |
| 3 | 2 | 5.56% | |
| 4 | 3 | 8.33% | |
| 5 | 4 | 11.11% | |
| 6 | 5 | 13.89% | |
| 7 | 6 | 16.67% | |
| 8 | 5 | 13.89% | |
| 9 | 4 | 11.11% | |
| 10 | 3 | 8.33% | |
| 11 | 2 | 5.56% | |
| 12 | 1 | 2.78% |
How dice probability is calculated
Each die is independent, so rolling n dice with s sides produces sⁿ equally likely outcomes. The probability of a given total is simply the number of combinations that produce that total divided by sⁿ.
With two six-sided dice there are 36 outcomes. Six of them sum to 7, which is why 7 comes up 16.67% of the time and 2 or 12 only 2.78% each. The calculator above runs this convolution for any dice count up to eight.
Reading the distribution
- Ways — how many distinct dice combinations produce that sum.
- Percent — ways divided by total outcomes.
- At least / at most — cumulative probability, the number you actually want when deciding whether to bet.
Common two-dice odds
- Rolling a 7: 6 in 36 = 16.67%
- Rolling 7 or 11: 8 in 36 = 22.22%
- Rolling doubles: 6 in 36 = 16.67%
- Rolling 10 or higher: 6 in 36 = 16.67%
Frequently asked questions
What are the odds of rolling a 7 with two dice?
6 of the 36 possible outcomes sum to 7, so the probability is 6/36 = 16.67%, the highest of any single total.
How do I calculate probability for three or more dice?
Count the combinations that produce your target and divide by sides^dice. For three six-sided dice there are 216 outcomes; the calculator above does the counting for you.
Are dice probabilities affected by previous rolls?
No. Dice have no memory. Every roll is independent, so a run of sixes does not change the odds of the next roll.