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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 wargames and tabletop role-playing games using simple algebra-like notation such as d8+2.
In most tabletop role-playing games, die rolls required by the system are given in the form nds. n and s are variables, separated by the letter d, which stands for die or dice. The letter d is most commonly lower-case, but some forms of notation use 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").
For example, if a game calls for a roll of d4 or 1d4, it means "roll one 4-sided die."
If the final number is omitted, it is typically assumed to be a d6, but in some contexts, other defaults are used.
3d6 would mean "roll three six-sided dice." Commonly, these dice are added together, but some systems direct the choice of the best result rolled, or some other action.
To this basic notation, an additive modifier can be appended, yielding expressions of the form nds+c. The plus sign is sometimes replaced by a minus sign ("−") to indicate subtraction. c is a number to be added to the sum of the rolls. Therefore, 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 nds-L is not uncommon. In this case, the "L" is used to represent the lowest result; it is sometimes replaced by an "H" to represent 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 1/1,296), while a roll of 18 results if any three dice are 6 (probability 21/1,296 = 7/432).
Rolling three or more dice gives a probability distribution that is approximately Gaussian, in accordance with the central limit theorem.
Miniatures wargamers began using dice in the shape of Platonic solids in the late 1960s and early 1970s, to obtain results that could not easily be produced on a conventional six-sided die. Dungeons & Dragons emerged in this milieu, and was the first game with widespread commercial availability to use such dice. In its earliest edition (1974), D&D had no standardized way to call for polyhedral die rolls or to refer to the results of such rolls. In some places the text gives a verbal instruction; in others, it only implies the roll to be made by describing the range of its results. For example, the spell sticks to snakes says, "From 2–16 snakes can be conjured (roll two eight-sided dice)." When only a range is listed, the exact method of rolling can be ambiguous. For example, a typical random wilderness encounter might be a village of "30–300" orcs. A number in that range might be generated by rolling 3d10×10, or alternately by rolling 30d10.
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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 wargames and tabletop role-playing games using simple algebra-like notation such as d8+2.
In most tabletop role-playing games, die rolls required by the system are given in the form nds. n and s are variables, separated by the letter d, which stands for die or dice. The letter d is most commonly lower-case, but some forms of notation use 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").
For example, if a game calls for a roll of d4 or 1d4, it means "roll one 4-sided die."
If the final number is omitted, it is typically assumed to be a d6, but in some contexts, other defaults are used.
3d6 would mean "roll three six-sided dice." Commonly, these dice are added together, but some systems direct the choice of the best result rolled, or some other action.
To this basic notation, an additive modifier can be appended, yielding expressions of the form nds+c. The plus sign is sometimes replaced by a minus sign ("−") to indicate subtraction. c is a number to be added to the sum of the rolls. Therefore, 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 nds-L is not uncommon. In this case, the "L" is used to represent the lowest result; it is sometimes replaced by an "H" to represent 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 1/1,296), while a roll of 18 results if any three dice are 6 (probability 21/1,296 = 7/432).
Rolling three or more dice gives a probability distribution that is approximately Gaussian, in accordance with the central limit theorem.
Miniatures wargamers began using dice in the shape of Platonic solids in the late 1960s and early 1970s, to obtain results that could not easily be produced on a conventional six-sided die. Dungeons & Dragons emerged in this milieu, and was the first game with widespread commercial availability to use such dice. In its earliest edition (1974), D&D had no standardized way to call for polyhedral die rolls or to refer to the results of such rolls. In some places the text gives a verbal instruction; in others, it only implies the roll to be made by describing the range of its results. For example, the spell sticks to snakes says, "From 2–16 snakes can be conjured (roll two eight-sided dice)." When only a range is listed, the exact method of rolling can be ambiguous. For example, a typical random wilderness encounter might be a village of "30–300" orcs. A number in that range might be generated by rolling 3d10×10, or alternately by rolling 30d10.