Dice notation
3d6
Roll 3d6 and see where it lands on the real distribution. Range 3 to 18, averaging 10.50.
The shape of 3d6
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 3
- Highest
- 18
- Average
- 10.50
- Most likely
- 10
- Chance of 10
- 12.5%
- Possible totals
- 16
Peak at 10 (12.5%). Average 10.50. Range 3–18.
There is exactly one way to roll 3 and one way to roll 18, so each sits at 0.463%, or 1 in 216. There are 27 ways to make 10, which is why the middle of the range dominates. Rolling 3 dice instead of one trades range for reliability.
Every total, with odds
Exact figures, enumerated rather than simulated.
| Total | Chance | Odds | This or higher |
|---|---|---|---|
| 3 | 0.463% | 1 in 216 | 100.0% |
| 4 | 1.39% | 1 in 72 | 99.5% |
| 5 | 2.78% | 1 in 36 | 98.1% |
| 6 | 4.63% | 1 in 22 | 95.4% |
| 7 | 6.94% | 1 in 14 | 90.7% |
| 8 | 9.72% | 1 in 10 | 83.8% |
| 9 | 11.6% | 1 in 9 | 74.1% |
| 10 | 12.5% | 1 in 8 | 62.5% |
| 11 | 12.5% | 1 in 8 | 50.0% |
| 12 | 11.6% | 1 in 9 | 37.5% |
| 13 | 9.72% | 1 in 10 | 25.9% |
| 14 | 6.94% | 1 in 14 | 16.2% |
| 15 | 4.63% | 1 in 22 | 9.26% |
| 16 | 2.78% | 1 in 36 | 4.63% |
| 17 | 1.39% | 1 in 72 | 1.85% |
| 18 | 0.463% | 1 in 216 | 0.463% |
Common questions about 3d6
What is the average of 3d6?
10.50. The range runs 3 to 18, but the average sits in the middle because there are far more ways to land near the centre than at either end.
What are the odds of rolling 18 on 3d6?
0.463%, or 1 in 216. The minimum of 3 is equally rare at 0.463%. Both extremes need every die to cooperate.
What is the most likely result of 3d6?
10, at 12.5%. There are 27 different combinations that add up to 10, against 1 for 18. That gap is what makes the curve.
Is 3d6 the same as picking a number between 3 and 18?
No, and this is the most useful thing to understand about dice. Picking at random from 3 to 18 gives every one of those 16 results an equal 6.25% chance. 3d6 covers the same span with a hump in the middle: 10 lands 27 times more often than 18 does. Same range, completely different behaviour.