Dice notation

Dice notation (also known as dice algebra, common dice notation, RPG dice notation, and several other titles) is a system to represent different combinations of dice in role-playing games using simple algebra-like notation such as 2d6+12.

In most role-playing games, die rolls required by the system are given in the form AdX. A and X are variables, separated by the letter "d", which stands for die or dice. The letter "d" is most commonly lower-case, but some notation uses upper-case "D" (non-English texts can use the equivalent form of the first letter of the given language's word for "dice", but also often use the English "d").

If the final number is omitted, it is typically assumed to be a six, but in some contexts, other defaults are used.

For example, if a game would call for a roll of d4 or 1d4 this would mean, "roll one 4-sided die."

3d6 would mean, "roll three six-sided dice." Commonly, these dice are added together, but some systems could direct the player use them in some other way, such as choosing the best die rolled.

To this basic notation, an additive modifier can be appended, yielding expressions of the form, AdX+B. The plus is sometimes replaced by a minus sign ("−") to indicate subtraction. B is a number to be added to the sum of the rolls. So, 1d20-10 would indicate a roll of a single 20-sided die with 10 being subtracted from the result. These expressions can also be chained (e.g. 2d6+1d8), though this usage is less common. Additionally, notation such as AdX-L is not uncommon, the "L" (or "H", less commonly) being used to represent "the lowest result" (or "the highest result"). For instance, 4d6-L means a roll of 4 six-sided dice, dropping the lowest result. This application skews the probability curve towards the higher numbers, as a result a roll of 3 can only occur when all four dice come up 1 (probability 1/1296), while a roll of 18 results if any three dice are 6 (probability 21/1296 = 7/432).

Rolling three or more dice gives a probability distribution that is approximately Gaussian, in accordance with the central limit theorem.

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