Dicenotation

Dicenotation is a formal notation used to express dice-based random variables and their combinations in probability, statistics, and game design. It provides a compact, machine-parsable way to specify how many dice are rolled, what faces they have, and how their results are combined or transformed.

The basic syntax commonly follows NdM, where N is the number of dice and M is the number of faces on each die. A single-die case is written dM. Constants may be added or subtracted after the dice expression, and parentheses can be used to group operations.

Examples include 3d6 for the sum of three six-sided dice, 2d8+5 for two eight-sided dice plus five, and 4d10-2 for four ten-sided dice minus two. Some variants introduce modifiers such as exploding dice (roll again on a maximum), rerolls, or keep/drop rules, which extend the basic syntax.

In analysis and simulation, dicenotation enables straightforward computation of probability distributions, expected values, and variances, and supports the implementation of dice-based models in software tools and educational settings.

Dicenotation intersects with traditional dice notation used in tabletop role-playing games and with formal notation for discrete random variables. Its goal is to improve clarity, interoperability, and automation in the description of dice-driven processes.

Related topics include dice notation, probability distributions, random variables, and game design.