Dice notation
3d8
Roll 3d8 and see where it lands on the real distribution. Range 3 to 24, averaging 13.50.
The shape of 3d8
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 3
- Highest
- 24
- Average
- 13.50
- Most likely
- 13
- Chance of 13
- 9.4%
- Possible totals
- 22
Peak at 13 (9.4%). Average 13.50. Range 3–24.
There is exactly one way to roll 3 and one way to roll 24, so each sits at 0.195%, or 1 in 512. There are 48 ways to make 13, 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 | 0.195% | 1 in 512 | 100.0% |
| 4 | 0.586% | 1 in 171 | 99.8% |
| 5 | 1.17% | 1 in 85 | 99.2% |
| 6 | 1.95% | 1 in 51 | 98.0% |
| 7 | 2.93% | 1 in 34 | 96.1% |
| 8 | 4.10% | 1 in 24 | 93.2% |
| 9 | 5.47% | 1 in 18 | 89.1% |
| 10 | 7.03% | 1 in 14 | 83.6% |
| 11 | 8.20% | 1 in 12 | 76.6% |
| 12 | 8.98% | 1 in 11 | 68.4% |
| 13 | 9.38% | 1 in 11 | 59.4% |
| 14 | 9.38% | 1 in 11 | 50.0% |
| 15 | 8.98% | 1 in 11 | 40.6% |
| 16 | 8.20% | 1 in 12 | 31.6% |
| 17 | 7.03% | 1 in 14 | 23.4% |
| 18 | 5.47% | 1 in 18 | 16.4% |
| 19 | 4.10% | 1 in 24 | 10.9% |
| 20 | 2.93% | 1 in 34 | 6.84% |
| 21 | 1.95% | 1 in 51 | 3.91% |
| 22 | 1.17% | 1 in 85 | 1.95% |
| 23 | 0.586% | 1 in 171 | 0.781% |
| 24 | 0.195% | 1 in 512 | 0.195% |
Common questions about 3d8
What is the average of 3d8?
13.50. The range runs 3 to 24, 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 24 on 3d8?
0.195%, or 1 in 512. The minimum of 3 is equally rare at 0.195%. Both extremes need every die to cooperate.
What is the most likely result of 3d8?
13, at 9.4%. There are 48 different combinations that add up to 13, against 1 for 24. That gap is what makes the curve.
Is 3d8 the same as picking a number between 3 and 24?
No, and this is the most useful thing to understand about dice. Picking at random from 3 to 24 gives every one of those 22 results an equal 4.55% chance. 3d8 covers the same span with a hump in the middle: 13 lands 48 times more often than 24 does. Same range, completely different behaviour.