Editing Dice (section)

==Applications==
[[File:Master Jean de Mauléon - Playing Dice - Walters W4492V (cropped).jpg|thumb|left|''Playing Dice'' by Master Jean de Mauléon (c. 1520)]]

Many board games use dice to randomize how far pieces move or to settle conflicts. Typically, this has meant that rolling higher numbers is better. Some games, such as ''[[Axis & Allies]]'', have inverted this system by making the lower values more potent. In the modern age,{{When|date=August 2021}}<!-- State since what year, decade or century this is referring to --> a few games and game designers have approached dice in a different way by making each side of the die similarly valuable. In ''[[Castles of Burgundy]]'', players spend their dice to take actions based on the die's value. In this game, a six is not better than a one, or vice versa. In ''[[Quarriors]]'' (and its descendant, ''[[Dice Masters]]''), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant the player useful actions.<ref>{{Cite web |date=2 October 2014 |title=Making better use of dice in games |url=http://boingboing.net/2014/10/02/making-better-use-of-dice-in-g.html}}</ref>

Dice can be used for [[divination]] and using dice for such a purpose is called [[cleromancy]]. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this [[Mo (divination)|method of divination]]. It is highly likely that the [[Pythagoreans]] used the [[Platonic solids]] as dice. They referred to such dice as "the dice of the gods" and they sought to understand the universe through an understanding of geometry in polyhedra.<ref>{{Cite book |last=Guthrie |first=Kenneth |title=The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy |publisher=Phanes Press |year=1988 |isbn=978-0-933999-50-3 |location=Grand Rapids, MI |oclc=255212063}}</ref>

[[File:Wuerfel5.jpg|thumb|Typical role-playing dice, showing a variety of colors and styles. Note the older hand-inked green 12-sided die (showing an 11), manufactured before pre-inked dice were common. Many players collect or acquire a large number of mixed and unmatching dice.]]
Polyhedral dice are commonly used in role-playing games. The fantasy role-playing game ''[[Dungeons & Dragons]]'' (''D&D'') is largely credited with popularizing dice in such games. Some games use only one type, like ''[[Exalted]]'' which uses only ten-sided dice. Others use numerous types for different game purposes, such as ''D&D'', which makes use of all common polyhedral dice. Dice are usually used to determine the outcome of events. Games typically determine results either as a total on one or more dice above or below a fixed number, or a certain number of rolls above a certain number on one or more dice. Due to circumstances or character skill, the initial roll may have a number added to or subtracted from the final result, or have the player roll extra or fewer dice. To keep track of rolls easily, [[dice notation]] is frequently used.

Astrological dice are a specialized set of three 12-sided dice for divination; the first die represents the planets, the Sun, the Moon, and the [[orbital node|nodes]] of the Moon, the second die represents the 12 [[Astrological sign|zodiac signs]], and the third represents the [[House (astrology)|12 houses]]. A specialized icosahedron die provides the answers of the [[Magic 8 Ball]], conventionally used to provide answers to yes-or-no questions.

Dice can be used to generate random numbers for use in [[password]]s and [[cryptography]] applications. The [[Electronic Frontier Foundation]] describes a method by which dice can be used to generate [[passphrase]]s.<ref>{{Cite news |date=12 May 2016 |title=EFF Dice-Generated Passphrases |language=en |work=Electronic Frontier Foundation |url=https://www.eff.org/dice |access-date=16 November 2018}}</ref> [[Diceware]] is a method recommended for generating secure but memorable passphrases, by repeatedly rolling five dice and picking the corresponding word from a pre-generated list.<ref>{{Cite web |date=19 July 2016 |title=EFF's New Wordlists for Random Passphrases |url=https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases |access-date=4 December 2016 |website=Electronic Frontier Foundation}}</ref>

===Notation===
{{Main|Dice notation}}
In many gaming contexts, especially tabletop role-playing games, shorthand notations are used to differentiate between different types of dice. The most commonly-used notation, considered the [[Dice notation|standard]], is written as {{math|''n''d''s''}}. In this expression, {{math|''s''}} is the number of sides on the dice and {{math|''n''}} is the number of rolls; if there is only one roll, the {{math|''n''}} is omitted. As an illustration, the d20 (twenty-sided dice) is to ''[[Dungeons & Dragons]]'' what the d6 (six-sided dice) is to many board games. ''[[Monopoly (game)|Monopoly]]'' uses 2d6 rolls (the total value of two six-sided dice) to determine player movement.

The notation also allows for adding or subtracting a constant amount ''c'' to the roll. When an amount is added, the notation is {{math|''n''d''s''+''c''}}. For example, "3d6+4" instructs the player to roll three six-sided dice, calculate the total, and add four to it. When an amount is to be subtracted, the notation is {{math|''n''d''s''−''c''}}. Thus, "3d6−4" instructs the player to subtract four from the total value of three six-sided dice. The notation {{math|''n''d''s''−L}} is also sometimes used, with the modifier "L" (or less commonly "H") representing the lowest amount (or highest amount) of each roll combined. For instance, 4d6−L instructs the player to sum up the total of four six-sided dice and subtract the lowest value. If the result of a modified dice roll is negative, it is often taken to be zero or one; for instance, when the dice roll determines the amount of damage to a creature.<ref>{{Cite book |last=Sim |first=Chris |title=Dungeons & Dragons Rules Compendium |collaboration= |year=2007 |isbn=9780786947256 |location=Renton, WA USA |pages=17}}</ref><ref>{{Cite web |last=Mearls |first=Mike |display-authors=etal |date=2016 |title=System Reference Document 5.1 |url=https://media.wizards.com/2016/downloads/DND/SRD-OGL_V5.1.pdf |access-date=September 12, 2024 |page=96}}</ref>

===Role-playing dice sets and percentile dice===
A role-playing dice set typically comprises seven dice: one each of d4, d6, d8, d12 and d20, and two d10s, one labeled from 0 to 9 and the other labeled in tens from 00 to 90. These last two, taken together, are called ''percentile dice''. In standard dice notation, a roll of percentile dice can be expressed as "d100", although "d%" is also seen.

A d100 roll is typically performed like a 2d10 roll, using both decahedral dice together. Adding the numbers shown gives a random number from 0 to 99 – although 0+00 is typically read as 100,<ref>https://www.dicedragons.co.uk/blogs/dice-advice/how-to-roll-a-d100</ref> for consistency with other dice notation.

The [[zocchihedron]] was invented as an alternative to percentile dice. Unlike percentile dice, the zocchihedron is a true d100 die, though no single die of 100 sides can be as consistently fair.<ref>https://rpggeek.com/blog/1051/blogpost/38414/interview-with-lou-zocchi-the-first-dice-idea-i-wa</ref>