Dice notation
3d10
Roll 3d10 and see where it lands on the real distribution. Range 3 to 30, averaging 16.50.
The shape of 3d10
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 3
- Highest
- 30
- Average
- 16.50
- Most likely
- 16
- Chance of 16
- 7.5%
- Possible totals
- 28
Peak at 16 (7.5%). Average 16.50. Range 3–30.
There is exactly one way to roll 3 and one way to roll 30, so each sits at 0.100%, or 1 in 1,000. There are 75 ways to make 16, 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 | 0.100% | 1 in 1,000 | 100.0% |
| 4 | 0.300% | 1 in 333 | 99.9% |
| 5 | 0.600% | 1 in 167 | 99.6% |
| 6 | 1.00% | 1 in 100 | 99.0% |
| 7 | 1.50% | 1 in 67 | 98.0% |
| 8 | 2.10% | 1 in 48 | 96.5% |
| 9 | 2.80% | 1 in 36 | 94.4% |
| 10 | 3.60% | 1 in 28 | 91.6% |
| 11 | 4.50% | 1 in 22 | 88.0% |
| 12 | 5.50% | 1 in 18 | 83.5% |
| 13 | 6.30% | 1 in 16 | 78.0% |
| 14 | 6.90% | 1 in 14 | 71.7% |
| 15 | 7.30% | 1 in 14 | 64.8% |
| 16 | 7.50% | 1 in 13 | 57.5% |
| 17 | 7.50% | 1 in 13 | 50.0% |
| 18 | 7.30% | 1 in 14 | 42.5% |
| 19 | 6.90% | 1 in 14 | 35.2% |
| 20 | 6.30% | 1 in 16 | 28.3% |
| 21 | 5.50% | 1 in 18 | 22.0% |
| 22 | 4.50% | 1 in 22 | 16.5% |
| 23 | 3.60% | 1 in 28 | 12.0% |
| 24 | 2.80% | 1 in 36 | 8.40% |
| 25 | 2.10% | 1 in 48 | 5.60% |
| 26 | 1.50% | 1 in 67 | 3.50% |
| 27 | 1.00% | 1 in 100 | 2.00% |
| 28 | 0.600% | 1 in 167 | 1.00% |
| 29 | 0.300% | 1 in 333 | 0.400% |
| 30 | 0.100% | 1 in 1,000 | 0.100% |
Common questions about 3d10
What is the average of 3d10?
16.50. The range runs 3 to 30, 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 30 on 3d10?
0.100%, or 1 in 1,000. The minimum of 3 is equally rare at 0.100%. Both extremes need every die to cooperate.
What is the most likely result of 3d10?
16, at 7.5%. There are 75 different combinations that add up to 16, against 1 for 30. That gap is what makes the curve.
Is 3d10 the same as picking a number between 3 and 30?
No, and this is the most useful thing to understand about dice. Picking at random from 3 to 30 gives every one of those 28 results an equal 3.57% chance. 3d10 covers the same span with a hump in the middle: 16 lands 75 times more often than 30 does. Same range, completely different behaviour.