Dice notation
Roll 3d6
The classic ability score roll, and the closest thing to a bell curve you can make with three dice.
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.
Three dice and the birth of the bell curve
Three six sided dice is the oldest character generation method in tabletop roleplaying: roll 3d6 six times in order and live with what you get. It survives because the numbers work out to something recognisably human. The average is 10.5, which the rules treat as unremarkable, and 18 turns up once in 216 rolls, which makes it rare enough to be worth a story. Rolling six scores, your chance of seeing at least one 18 is about 2.7%.
The shape is why this feels different from a flat roll. Totals of 10 and 11 each come up 12.5% of the time, so a quarter of all rolls land on one of those two numbers, and about two thirds of rolls land between 8 and 13. If you have ever felt that rolled characters come out stubbornly average, that is the distribution doing exactly what it is built to do, and it is the reason 4d6 drop lowest was invented as an alternative that pushes the whole curve upward by about 1.7 points.
3d6 is also a complete resolution system on its own. Games that roll under a target on three dice get a much steeper competence gradient than a d20 system: the difference between a target of 10 and a target of 13 is 50% versus 84%, so a few points of skill matter enormously. Compare a flat d20, where the same three points buys you a uniform 15%.
Every total on 3d6, with odds
Exact figures, enumerated rather than simulated.
| Total | Chance | Odds | This or higher | This or lower |
|---|---|---|---|---|
| 3 | 0.463% | 1 in 216 | 100.0% | 0.463% |
| 4 | 1.39% | 1 in 72 | 99.5% | 1.85% |
| 5 | 2.78% | 1 in 36 | 98.1% | 4.63% |
| 6 | 4.63% | 1 in 22 | 95.4% | 9.26% |
| 7 | 6.94% | 1 in 14 | 90.7% | 16.2% |
| 8 | 9.72% | 1 in 10 | 83.8% | 25.9% |
| 9 | 11.6% | 1 in 9 | 74.1% | 37.5% |
| 10 | 12.5% | 1 in 8 | 62.5% | 50.0% |
| 11 | 12.5% | 1 in 8 | 50.0% | 62.5% |
| 12 | 11.6% | 1 in 9 | 37.5% | 74.1% |
| 13 | 9.72% | 1 in 10 | 25.9% | 83.8% |
| 14 | 6.94% | 1 in 14 | 16.2% | 90.7% |
| 15 | 4.63% | 1 in 22 | 9.26% | 95.4% |
| 16 | 2.78% | 1 in 36 | 4.63% | 98.1% |
| 17 | 1.39% | 1 in 72 | 1.85% | 99.5% |
| 18 | 0.463% | 1 in 216 | 0.463% | 100.0% |
Common questions about 3d6
What are the odds of rolling 18 on 3d6?
The odds of rolling 18 on 3d6 are 1 in 216, or 0.463%, because all three dice have to show a 6 and there are 216 equally likely combinations of three dice. Rolling six ability scores this way, your chance of getting at least one 18 among them is about 2.7%.
Is 3d6 better than 4d6 drop lowest for stats?
3d6 produces noticeably lower ability scores than 4d6 drop lowest: an average of 10.50 against 12.24, and a much lower chance of high scores. Neither is better in the abstract. 3d6 in order is the old school option and produces flawed, memorable characters; 4d6 drop lowest produces capable ones. The stat rolling methods page compares both against point buy and the standard array.
What is the most likely result of 3d6?
The most likely result of 3d6 is 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, 3d6 is not the same as picking a random number from 3 to 18, and this is the most useful thing to understand about dice. A random pick 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.