Dice notation
4d6 drop lowest
Roll 4d6 drop lowest and see where it lands on the real distribution. Range 3 to 18, averaging 12.24.
The shape of 4d6 drop lowest
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 3
- Highest
- 18
- Average
- 12.24
- Most likely
- 13
- Chance of 13
- 13.3%
- Possible totals
- 16
Peak at 13 (13.3%). Average 12.24. Range 3–18.
Dropping the lowest die pulls the average up from 14.00 to 12.24 and lifts the floor from 4 to 3. This is the standard way to roll ability scores, and the reason a rolled character usually beats the flat array.
Every total, with odds
Exact figures, enumerated rather than simulated.
| Total | Chance | Odds | This or higher |
|---|---|---|---|
| 3 | 0.077% | 1 in 1,296 | 100.0% |
| 4 | 0.309% | 1 in 324 | 99.9% |
| 5 | 0.772% | 1 in 130 | 99.6% |
| 6 | 1.62% | 1 in 62 | 98.8% |
| 7 | 2.93% | 1 in 34 | 97.2% |
| 8 | 4.78% | 1 in 21 | 94.3% |
| 9 | 7.02% | 1 in 14 | 89.5% |
| 10 | 9.41% | 1 in 11 | 82.5% |
| 11 | 11.4% | 1 in 9 | 73.1% |
| 12 | 12.9% | 1 in 8 | 61.7% |
| 13 | 13.3% | 1 in 8 | 48.8% |
| 14 | 12.3% | 1 in 8 | 35.5% |
| 15 | 10.1% | 1 in 10 | 23.1% |
| 16 | 7.25% | 1 in 14 | 13.0% |
| 17 | 4.17% | 1 in 24 | 5.79% |
| 18 | 1.62% | 1 in 62 | 1.62% |
Common questions about 4d6 drop lowest
What is the average of 4d6 drop lowest?
12.24. 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 4d6 drop lowest?
1.62%, or 1 in 62. The minimum of 3 is a different figure at 0.077%. Both extremes need every die to cooperate.
What is the most likely result of 4d6 drop lowest?
13, at 13.3%. There are 172 different combinations that add up to 13, against 21 for 18. That gap is what makes the curve.
Is 4d6 drop lowest 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. 4d6 drop lowest covers the same span with a hump in the middle: 13 lands 8 times more often than 18 does. Same range, completely different behaviour.