Common RPG dice notation

Standard notation: NdS+M where N is the number of dice, S is the number of sides, and M is an optional modifier (positive or negative). For example, 4d6+2 means roll four 6-sided dice and add 2 to the result.

2d6 probability distribution

Two six-sided dice produce a bell-curve distribution, not a flat one. The result 7 is six times more likely than either extreme (2 or 12) because there are six combinations that sum to 7 but only one each for 2 and 12. This is why 7 is the most important number in many board games and why the house edge in craps is built around it.

Total	Combinations	Probability
2	1	2.8%
3	2	5.6%
4	3	8.3%
5	4	11.1%
6	5	13.9%
7	6	16.7%
8	5	13.9%
9	4	11.1%
10	3	8.3%
11	2	5.6%
12	1	2.8%

D&D ability scores: 4d6 drop lowest

The standard D&D 5e method for generating ability scores rolls four d6 and discards the lowest result. This produces a range of 3–18 with a mean around 12.2, compared to a straight 3d6 mean of 10.5. Dropping the lowest die skews the distribution toward higher values, creating characters that feel heroic rather than average. The probability of rolling an 18 (three 6s after the drop) is about 1.6%, versus 0.46% on a straight 3d6.

Advantage and disadvantage (d20)

Rolling with advantage means rolling two d20s and taking the higher result; disadvantage takes the lower. This mechanic has a larger effect in the middle of the range than at the extremes. For example, the probability of rolling 15 or higher on a single d20 is 30%. With advantage it rises to 51%; with disadvantage it falls to 9%. Near the center of the range (rolling 11+), advantage raises the probability from 50% to 75%. The effective bonus is roughly equivalent to a flat +3 to +5 modifier depending on the target number.