Dice notation

In most tabletop role-playing games, die rolls required by the system are given in the form AdX.

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.

For instance, 4d6−L means a roll of 4 six-sided dice, dropping the lowest result.

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 ’70s, 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 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.

D&D player Ted Johnstone introduced standard dice notation as a way to discuss probability distribution in an article, "Dice as Random Number Generators", in the inaugural issue of fanzine Alarums & Excursions (1975).

[3] The notation was also used by another writer, Barry Gold, in the same issue, and quickly spread throughout the fan community.

[3] Eventually, standard dice notation became so deeply ingrained in D&D fan culture that Gary Gygax would adopt it as a commonplace in the first edition of Advanced Dungeons & Dragons (1977-1979).

[3][6] The close association between D&D fandom and standard dice notation is reflected in the name of the Open Game version of the D&D rules: the "d20 System."

In some games, the above notation is expanded to allow for a multiplier, as in AdX×C or C×dX, where: For example, Multiplication can also mean repeating throws of similar setup (usually represented by the letter "x", rather than the multiplication symbol): Often, the variable X in the above notation will be 100, alternatively written "%".

(Half could be given a distinct color, indicating the addition of ten, for use when randomizing numbers from 1 to 20.)

Whether the dice omitted are the highest, lowest, or the player's choice depends on the game in question; "k" can be replaced with "kh", "kl", or "kc", respectively, to represent this, which also allows for combining them.

, which means "roll A dice with X sides each, keeping the H highest, the L lowest, and C of the player's choice".

Just as "B" is normally not shown when it is 0, terms where you would keep all of the dice are normally omitted for ease of reading.

7th Sea and Legend of the Five Rings use only 10-sided dice, so it omits the number of sides, using notation of the form

For example, Vampire: the Requiem has players roll a pool of ten-sided dice and note the number that come up as 8 or higher as "successes".

Some companies produce custom dice, marked with successes and failures, for use in games which use this mechanic.

Various Games Workshop systems such as Necromunda and Mordheim use an anomalously-named D66 roll, meaning d6×10+d6.

The D66 is generally a combination of two six-sided dice, often made distinguishable from each other by color, or simply one die rolled twice.

Blood Bowl, also a Games Workshop product, introduces the block die with special notation Xdb, which is shorthand for

Planet Mercenary calls its variation d6³, to indicate that in addition to using the conventional sum of 3d6 to check for success or failure, various secondary effects are determined via comparison of the individual numbers rolled.

The Cyborg Commando role-playing game by Gary Gygax uses a dice mechanic called d10x.

This is equivalent to d10×d10 and gives a non-linear distribution, with most results concentrated at the lower end of the range.

Notational shorthand for exploding dice is to suffix the roll with an exclamation point: AdX!