Dice notation
3d12
Roll 3d12 and see where it lands on the real distribution. Range 3 to 36, averaging 19.50.
The shape of 3d12
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 3
- Highest
- 36
- Average
- 19.50
- Most likely
- 19
- Chance of 19
- 6.2%
- Possible totals
- 34
Peak at 19 (6.2%). Average 19.50. Range 3–36.
There is exactly one way to roll 3 and one way to roll 36, so each sits at 0.058%, or 1 in 1,728. There are 108 ways to make 19, 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 | 0.058% | 1 in 1,728 | 100.0% |
| 4 | 0.174% | 1 in 576 | 99.9% |
| 5 | 0.347% | 1 in 288 | 99.8% |
| 6 | 0.579% | 1 in 173 | 99.4% |
| 7 | 0.868% | 1 in 115 | 98.8% |
| 8 | 1.22% | 1 in 82 | 98.0% |
| 9 | 1.62% | 1 in 62 | 96.8% |
| 10 | 2.08% | 1 in 48 | 95.1% |
| 11 | 2.60% | 1 in 38 | 93.1% |
| 12 | 3.18% | 1 in 31 | 90.5% |
| 13 | 3.82% | 1 in 26 | 87.3% |
| 14 | 4.51% | 1 in 22 | 83.4% |
| 15 | 5.09% | 1 in 20 | 78.9% |
| 16 | 5.56% | 1 in 18 | 73.8% |
| 17 | 5.90% | 1 in 17 | 68.3% |
| 18 | 6.13% | 1 in 16 | 62.4% |
| 19 | 6.25% | 1 in 16 | 56.2% |
| 20 | 6.25% | 1 in 16 | 50.0% |
| 21 | 6.13% | 1 in 16 | 43.8% |
| 22 | 5.90% | 1 in 17 | 37.6% |
| 23 | 5.56% | 1 in 18 | 31.7% |
| 24 | 5.09% | 1 in 20 | 26.2% |
| 25 | 4.51% | 1 in 22 | 21.1% |
| 26 | 3.82% | 1 in 26 | 16.6% |
| 27 | 3.18% | 1 in 31 | 12.7% |
| 28 | 2.60% | 1 in 38 | 9.55% |
| 29 | 2.08% | 1 in 48 | 6.94% |
| 30 | 1.62% | 1 in 62 | 4.86% |
| 31 | 1.22% | 1 in 82 | 3.24% |
| 32 | 0.868% | 1 in 115 | 2.03% |
| 33 | 0.579% | 1 in 173 | 1.16% |
| 34 | 0.347% | 1 in 288 | 0.579% |
| 35 | 0.174% | 1 in 576 | 0.231% |
| 36 | 0.058% | 1 in 1,728 | 0.058% |
Common questions about 3d12
What is the average of 3d12?
19.50. The range runs 3 to 36, 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 36 on 3d12?
0.058%, or 1 in 1,728. The minimum of 3 is equally rare at 0.058%. Both extremes need every die to cooperate.
What is the most likely result of 3d12?
19, at 6.2%. There are 108 different combinations that add up to 19, against 1 for 36. That gap is what makes the curve.
Is 3d12 the same as picking a number between 3 and 36?
No, and this is the most useful thing to understand about dice. Picking at random from 3 to 36 gives every one of those 34 results an equal 2.94% chance. 3d12 covers the same span with a hump in the middle: 19 lands 108 times more often than 36 does. Same range, completely different behaviour.