Dice sum probability
One die is flat. Every face is as likely as every other. Add a second and that changes completely.
Why 7 wins on 2d6
There is only one way to roll a 2, both dice showing 1. There are six ways to roll a 7: 1 and 6, 2 and 5, 3 and 4, and each of those the other way round. That is why 7 comes up 16.67% of the time and 2 only 2.78%.
- 22.78%
- 35.56%
- 48.33%
- 511.11%
- 613.89%
- 716.67%
- 813.89%
- 911.11%
- 108.33%
- 115.56%
- 122.78%
| Result | Chance | Odds |
|---|---|---|
| 2 | 2.78% | 1 in 36 |
| 3 | 5.56% | 1 in 18 |
| 4 | 8.33% | 1 in 12 |
| 5 | 11.11% | 1 in 9 |
| 6 | 13.89% | 1 in 7.2 |
| 7 | 16.67% | 1 in 6 |
| 8 | 13.89% | 1 in 7.2 |
| 9 | 11.11% | 1 in 9 |
| 10 | 8.33% | 1 in 12 |
| 11 | 5.56% | 1 in 18 |
| 12 | 2.78% | 1 in 36 |
Three dice tighten it further
Add a third die and the peak sharpens again. 3d6 can still reach 3 or 18, but it does so about once in every 216 rolls, while the middle results take over almost everything.
- 30.46%
- 41.39%
- 52.78%
- 64.63%
- 76.94%
- 89.72%
- 911.57%
- 1012.5%
- 1112.5%
- 1211.57%
- 139.72%
- 146.94%
- 154.63%
- 162.78%
- 171.39%
- 180.46%
| Result | Chance | Odds |
|---|---|---|
| 3 | 0.46% | 1 in 216 |
| 4 | 1.39% | 1 in 72 |
| 5 | 2.78% | 1 in 36 |
| 6 | 4.63% | 1 in 21.6 |
| 7 | 6.94% | 1 in 14.4 |
| 8 | 9.72% | 1 in 10.3 |
| 9 | 11.57% | 1 in 8.6 |
| 10 | 12.5% | 1 in 8 |
| 11 | 12.5% | 1 in 8 |
| 12 | 11.57% | 1 in 8.6 |
| 13 | 9.72% | 1 in 10.3 |
| 14 | 6.94% | 1 in 14.4 |
| 15 | 4.63% | 1 in 21.6 |
| 16 | 2.78% | 1 in 36 |
| 17 | 1.39% | 1 in 72 |
| 18 | 0.46% | 1 in 216 |
Work out any sum
- Lowest
- 3
- Highest
- 18
- Average
- 10.5
- Most likely
- 10, 11
- 30.46%
- 41.39%
- 52.78%
- 64.63%
- 76.94%
- 89.72%
- 911.57%
- 1012.5%
- 1112.5%
- 1211.57%
- 139.72%
- 146.94%
- 154.63%
- 162.78%
- 171.39%
- 180.46%
| Result | Chance | Odds |
|---|---|---|
| 3 | 0.46% | 1 in 216 |
| 4 | 1.39% | 1 in 72 |
| 5 | 2.78% | 1 in 36 |
| 6 | 4.63% | 1 in 21.6 |
| 7 | 6.94% | 1 in 14.4 |
| 8 | 9.72% | 1 in 10.3 |
| 9 | 11.57% | 1 in 8.6 |
| 10 | 12.5% | 1 in 8 |
| 11 | 12.5% | 1 in 8 |
| 12 | 11.57% | 1 in 8.6 |
| 13 | 9.72% | 1 in 10.3 |
| 14 | 6.94% | 1 in 14.4 |
| 15 | 4.63% | 1 in 21.6 |
| 16 | 2.78% | 1 in 36 |
| 17 | 1.39% | 1 in 72 |
| 18 | 0.46% | 1 in 216 |
Odds against a target
Pick the number you need to hit.