Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of

"Fair Dice"

, ''The American Mathematical Monthly'', 96(4):337–339, 1989 (Discussion of dice that are fair "by symmetry" and "by continuity".) * Iverson, G. R.; Longcour, W. H.; et al.; ''Bias and Runs in Dice Throwing and Recording: A Few Million Throws'', Psychometrika, vol. 36, no. 1, March 1971 * Knizia, Reiner, ''Dice Games Properly Explained'', Elliot Right Way Books, 1999,

tabletop game
Tabletop games or tabletops are games that are normally played on a table or other flat surface, such as board games, card games, dice games, miniature wargames, or tile-based games.
Classification according to equipment used
Tabletop games ...

s, including dice games, board game
Board games are tabletop games that typically use . These pieces are moved or placed on a pre-marked board (playing surface) and often include elements of table, card, role-playing, and miniatures games as well.
Many board games feature a co ...

s, role-playing game
A role-playing game (sometimes spelled roleplaying game, RPG) is a game in which players assume the roles of characters in a fictional setting. Players take responsibility for acting out these roles within a narrative, either through literal ...

s, and games of chance.
A traditional die is a cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the onl ...

with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material
Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geologi ...

of the dice instead of marked on it. Loaded dice are designed to favor some results over others for cheating
Cheating generally describes various actions designed to subvert rules in order to obtain unfair advantages. This includes acts of bribery, cronyism and nepotism in any situation where individuals are given preference using inappropriate crit ...

or entertainment.
History

Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the practice of fortune-telling with the talus of hoofed animals, colloquially known asknucklebones
Knucklebones, also known as scatter jacks, snobs, astragalus, tali, dibs, fivestones, jacks, or jackstones, among many other names, is a game of dexterity played with a number of small objects that are thrown up, caught, and manipulated in var ...

. The Egyptian game of senet
Senet or senat ( egy, znt, translation=passing; cf. Coptic ⲥⲓⲛⲉ /sinə/ "passing, afternoon") is a board game from ancient Egypt. The earliest representation of senet is dated to E from the Mastaba of Hesy-Re, while similar boards an ...

was played with flat two-sided throwsticks which indicated the number of squares a player could move, and thus functioned as a form of dice. Senet was played before 3000 BCE and up to the 2nd century CE. Perhaps the oldest known dice were excavated as part of a backgammon
Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back nearly 5,000 years to the regions of Mesopotamia and P ...

-like game set at the Burnt City
Shahr-e Sukhteh ( fa, شهر سوخته, meaning " heBurnt City"), c. 3200–2350 BCE,
also spelled as ''Shahr-e Sūkhté'' and ''Shahr-i Sōkhta'', is an archaeological site of a sizable Bronze Age urban settlement, associated with the Helmand ...

, an archeological site in south-eastern Iran
Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Tur ...

, estimated to be from between 2800 and 2500 BCE. Bone dice from Skara Brae
Skara Brae is a stone-built Neolithic settlement, located on the Bay of Skaill on the west coast of Mainland, the largest island in the Orkney archipelago of Scotland. Consisting of ten clustered houses, made of flagstones, in earthen dams t ...

, Scotland have been dated to 3100–2400 BCE. Excavations from graves at Mohenjo-daro
Mohenjo-daro (; sd, موئن جو دڙو'', ''meaning 'Mound of the Dead Men';Indus Valley civilization
The Indus Valley Civilisation (IVC), also known as the Indus Civilisation was a Bronze Age civilisation in the northwestern regions of South Asia, lasting from 3300 BCE to 1300 BCE, and in its mature form 2600 BCE to 1900&n ...

settlement, unearthed terracotta dice dating to 2500–1900 BCE.
Games involving dice are mentioned in the ancient Indian ''Rigveda
The ''Rigveda'' or ''Rig Veda'' ( ', from ' "praise" and ' "knowledge") is an ancient Indian collection of Vedic Sanskrit hymns (''sūktas''). It is one of the four sacred canonical Hindu texts ('' śruti'') known as the Vedas. Only one ...

'', '' Atharvaveda,'' ''Mahabharata
The ''Mahābhārata'' ( ; sa, महाभारतम्, ', ) is one of the two major Sanskrit epics of ancient India in Hinduism, the other being the ''Rāmāyaṇa''. It narrates the struggle between two groups of cousins in the Kuru ...

'' and Buddhist games list. There are several biblical
The Bible (from Koine Greek , , 'the books') is a collection of religious texts or scriptures that are held to be sacred in Christianity, Judaism, Samaritanism, and many other religions. The Bible is an anthologya compilation of texts of a v ...

references to "casting lots" ( ''yappîlū ḡōrāl''), as in Psalm
The Book of Psalms ( or ; he, תְּהִלִּים, , lit. "praises"), also known as the Psalms, or the Psalter, is the first book of the ("Writings"), the third section of the Tanakh, and a book of the Old Testament. The title is derived ...

22, indicating that dicing (or a related activity) was commonplace when the psalm was composed. Knucklebones was a game of skill played in ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...

; a derivative form had the four sides of bones receive different values like modern dice.
Although gambling was illegal, many Romans were passionate gamblers who enjoyed dicing, which was known as ''aleam ludere'' ("to play at dice"). There were two sizes of Roman dice. ''Tali'' were large dice inscribed with one, three, four, and six on four sides. ''Tesserae'' were smaller dice with sides numbered from one to six. Twenty-sided dice date back to the 2nd century CE and from Ptolemaic Egypt as early as the 2nd century BCE.
Dominoes
Dominoes is a family of tile-based games played with gaming pieces, commonly known as dominoes. Each domino is a rectangular tile, usually with a line dividing its face into two square ''ends''. Each end is marked with a number of spots (also c ...

and playing cards originated in China as developments from dice. The transition from dice to playing cards occurred in China around the Tang dynasty (618–907 CE), and coincides with the technological transition from rolls of manuscripts to block printed books. In Japan, dice were used to play a popular game called sugoroku
(literally 'double six') refers to two different forms of a Japanese board game: ''ban-sugoroku'' (盤双六, 'board-sugoroku') which is similar to western tables games like Backgammon, and ''e-sugoroku'' (絵双六, 'picture-sugoroku') which ...

. There are two types of sugoroku. ''Ban-sugoroku'' is similar to backgammon
Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back nearly 5,000 years to the regions of Mesopotamia and P ...

and dates to the Heian period
The is the last division of classical Japanese history, running from 794 to 1185. It followed the Nara period, beginning when the 50th emperor, Emperor Kanmu, moved the capital of Japan to Heian-kyō (modern Kyoto). means "peace" in Japanes ...

(794–1185 CE), while ''e-sugoroku'' is a racing game
Racing games are a video game genre in which the player participates in a racing competition. They may be based on anything from real-world racing leagues to fantastical settings. They are distributed along a spectrum between more realistic r ...

.
Use

Dice are thrown onto a surface either from the hand or from a container designed for this (such as a cup or tray). The face of the die that is uppermost when it comes to rest provides the value of the throw. The result of a die roll is determined by the way it is thrown, according to the laws ofclassical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mec ...

. A die roll is made random
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rando ...

by uncertainty in minor factors such as tiny movements in the thrower's hand; they are thus a crude form of hardware random number generator.
One typical contemporary dice game is craps
Craps is a dice game in which players bet on the outcomes of the roll of a pair of dice. Players can wager money against each other (playing "street craps") or against a bank (" casino craps"). Because it requires little equipment, "street ...

, where two dice are thrown simultaneously and wagers are made on the total value of the two dice. Dice are frequently used to introduce randomness into board game
Board games are tabletop games that typically use . These pieces are moved or placed on a pre-marked board (playing surface) and often include elements of table, card, role-playing, and miniatures games as well.
Many board games feature a co ...

s, where they are often used to decide the distance through which a piece will move along the board (as in backgammon
Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back nearly 5,000 years to the regions of Mesopotamia and P ...

and ''Monopoly
A monopoly (from Greek el, μόνος, mónos, single, alone, label=none and el, πωλεῖν, pōleîn, to sell, label=none), as described by Irving Fisher, is a market with the "absence of competition", creating a situation where a spec ...

'').
Construction

Arrangement

Common dice are smallcube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the onl ...

s, most often across, whose faces are numbered from one to six, usually by patterns of round dots called pips. (While the use of Arabic numerals
Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such as ...

is occasionally seen, such dice are less common.)
Opposite sides of a modern die traditionally add up to seven, requiring the 1, 2, and 3 faces to share a vertex. The faces of a die may be placed clockwise or counterclockwise about this vertex. If the 1, 2, and 3 faces run counterclockwise, the die is called "right-handed". If those faces run clockwise, the die is called "left-handed". Western dice are normally right-handed, and Chinese dice are normally left-handed.
The pips on standard six-sided dice are arranged in specific patterns as shown. Asian style dice bear similar patterns to Western ones, but the pips are closer to the center of the face; in addition, the pips are differently sized on Asian style dice, and the pips are colored red on the 1 and 4 sides. Red fours may be of Indian origin.
Manufacturing

Non-precision dice are manufactured via the plasticinjection molding
Injection moulding (U.S. spelling: injection molding) is a manufacturing process for producing parts by injecting molten material into a mould, or mold. Injection moulding can be performed with a host of materials mainly including metals (for ...

process, often made of polymethyl methacrylate (PMMA). The pips or numbers on the die are a part of the mold. Different pigments can be added to the dice to make them opaque or transparent, or multiple pigments may be added to make the dice speckled or marbled.
The coloring for numbering is achieved by submerging the die entirely in paint, which is allowed to dry. The die is then polished via a tumble finishing
Tumble finishing, also known as tumbling or rumbling, is a technique for smoothing and polishing a rough surface on relatively small parts. In the field of metalworking, a similar process called barreling, or barrel finishing,Degarmo, p. 781. wo ...

process similar to rock polishing. The abrasive agent scrapes off all of the paint except for the indents of the numbering. A finer abrasive is then used to polish the die. This process also produces the smoother, rounded edges on the dice.
Precision casino dice may have a polished or sand finish, making them transparent or translucent respectively. Casino dice have their pips drilled, then filled flush with a paint of the same density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...

as the material used for the dice, such that the center of gravity of the dice is as close to the geometric center as possible. This mitigates concerns that the pips will cause a small bias. All such dice are stamped with a serial number
A serial number is a unique identifier assigned incrementally or sequentially to an item, to ''uniquely'' identify it.
Serial numbers need not be strictly numerical. They may contain letters and other typographical symbols, or may consist ent ...

to prevent potential cheaters from substituting a die. Precision backgammon dice are made the same way; they tend to be slightly smaller and have rounded corners and edges, to allow better movement inside the dice cup and stop forceful rolls from damaging the playing surface.
Etymology and terms

The word die comes from Old French '' dé''; fromLatin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of t ...

'' datum'' "something which is given or played".
While the terms '' ace'', ''deuce'', ''trey'', ''cater'', ''cinque'' and ''sice'' are generally obsolete, with the names of the numbers preferred, they are still used by some professional gamblers to designate different sides of the dice. ''Ace'' is from the Latin ''as'', meaning "a unit"; the others are 2 to 6 in Old French.
When rolling two dice, certain combinations have slang names. The term ''snake eyes'' is a roll of one pip on each die. The '' Online Etymology Dictionary'' traces use of the term as far back as 1919.
The US term ''boxcars'', also known as ''midnight'', is a roll of six pips on each die. The pair of six pips resembles a pair of boxcar
A boxcar is the North American (AAR) term for a railroad car that is enclosed and generally used to carry freight. The boxcar, while not the simplest freight car design, is considered one of the most versatile since it can carry most loa ...

s on a freight train. Many rolls have names in the game of craps.
Unicode representation

⚀ ⚁ ⚂ ⚃ ⚄ ⚅ Using Unicode characters, the faces can be shown in text using the range U+2680 to U+2685 or using decimal`⚀`

to `⚅`

.
Loaded dice

A loaded, weighted, cheat, or crooked die is one that has been tampered with so that it will land with a specific side facing upwards more or less often than a fair die would. There are several methods for making loaded dice, including rounded faces, off-square faces, and weights. Casinos and gambling halls frequently use transparent cellulose acetate dice as tampering is easier to detect than with opaque dice.Variants

Polyhedral dice

Various shapes like two-sided or four-sided dice are documented in archaeological findings; for example, from Ancient Egypt and the Middle East. While the cubical six-sided die became the most common type in many parts of the world, other shapes were always known, like 20-sided dice in Ptolemaic and Roman times. The modern tradition of using ''sets'' of polyhedral dice started around the end of the 1960s when non-cubical dice became popular among players of wargames, and since have been employed extensively inrole-playing game
A role-playing game (sometimes spelled roleplaying game, RPG) is a game in which players assume the roles of characters in a fictional setting. Players take responsibility for acting out these roles within a narrative, either through literal ...

s and trading card games. Dice using both the numerals 6 and 9, which are reciprocally symmetric through rotation, typically distinguish them with a dot or underline.
Common variations

Dice are often sold in sets, matching in color, of six different shapes. Five of the dice are shaped like thePlatonic solid
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges ...

s, whose faces are regular polygons. Aside from the cube, the other four Platonic solids have 4, 8, 12, and 20 faces, allowing for those number ranges to be generated. The only other common non-cubical die is the 10-sided die, a pentagonal trapezohedron
In geometry, a pentagonal trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites.
It can b ...

die, whose faces are ten kites
A kite is a tethered heavier-than-air or lighter-than-air craft with wing surfaces that react against the air to create lift and drag forces. A kite consists of wings, tethers and anchors. Kites often have a bridle and tail to guide the face ...

, each with two different edge lengths, three different angles, and two different kinds of vertices. Such sets frequently include a second 10-sided die either of contrasting color or numbered by tens, allowing the pair of 10-sided dice to be combined to generate numbers between 1 and 100.
Using these dice in various ways, games can closely approximate a variety of probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...

s. For instance, 10-sided dice can be rolled in pairs to produce a uniform distribution of random percentages, and summing the values of multiple dice will produce approximations to normal distributions.
Unlike other common dice, a four-sided (tetrahedral) die does not have a side that faces upward when it is at rest on a surface, so it must be read in a different way. On some four-sided dice, each face features multiple numbers, with the same number printed near each vertex on all sides. In this case, the number around the vertex pointing up is used. Alternatively, the numbers on a tetrahedral die can be placed at the middles of the edges, in which case the numbers around the base are used.
Normally, the faces on a die will be placed so opposite faces will add up to one more than the number of faces. (This is not possible with 4-sided dice and dice with an odd-number of faces.) Some dice, such as those with 10 sides, are usually numbered sequentially beginning with 0, in which case the opposite faces will add to one less than the number of faces.
Some twenty-sided dice have a different arrangement used for the purpose of keeping track of an integer that counts down, such as health points. These ''spindown dice'' are arranged such that adjacent integers appear on adjacent faces, allowing the user to easily find the next lower number. They are commonly used with collectible card game
A collectible card game (CCG), also called a trading card game (TCG) among other names, is a type of card game that mixes strategic deck building elements with features of trading cards, introduced with '' Magic: The Gathering'' in 1993.
Genera ...

s.
Rarer variations

"Uniform fair dice" are dice where all faces have equal probability of outcome due to the symmetry of the die as it isface-transitive
In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congru ...

. In addition to the Platonic solids, these theoretically include:
* Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. There are 13 Catalan solids. They are named for the Belgian mathematician Eugène Catalan, who first described them in 1865.
The Catalan ...

s, the duals
''Duals'' is a compilation album by the Irish rock band U2. It was released in April 2011 to u2.com subscribers.
Track listing
:* "Where the Streets Have No Name" and "Amazing Grace" are studio mix of U2's performance at the Rose Bowl, Pas ...

of the 13 Archimedean solids: 12, 24, 30, 48, 60, 120 sides
* Trapezohedra
In geometry, an trapezohedron, -trapezohedron, -antidipyramid, -antibipyramid, or -deltohedron is the dual polyhedron of an antiprism. The faces of an are congruent and symmetrically staggered; they are called ''twisted kites''. With a h ...

, the duals of the infinite set of antiprism
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .
Antiprisms are a subcla ...

s, with kite faces: any even number not divisible by 4 (so that a face will face up), starting from 6
* Bipyramid
A (symmetric) -gonal bipyramid or dipyramid is a polyhedron formed by joining an -gonal pyramid and its mirror image base-to-base. An -gonal bipyramid has triangle faces, edges, and vertices.
The "-gonal" in the name of a bipyramid does n ...

s, the duals of the infinite set of prisms, with triangle faces: any multiple of 4 (so that a face will face up), starting from 8
* Disphenoids, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides. This is a less symmetric tetrahedron than the Platonic tetrahedron, but still sufficiently symmetrical to be face-transitive. Similarly, pyritohedra and tetartoids are less symmetrical but still face-transitive dodecahedra: 12 sides.
Two other types of polyhedra are technically not face-transitive, but are still fair dice due to symmetry:
* antiprism
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .
Antiprisms are a subcla ...

s: the basis of barrel dice
* prisms: the basis of long dice and teetotums
Long dice and teetotums can in principle be made with any number of faces, including odd numbers. Long dice are based on the infinite set of prisms. All the rectangular faces are mutually face-transitive, so they are equally probable. The two ends of the prism may be rounded or capped with a pyramid, designed so that the die cannot rest on those faces. 4-sided long dice are easier to roll than tetrahedra, and are used in the traditional board games dayakattai and daldøs.
Non-numeric dice

The faces of most dice are labelled using sequences of whole numbers, usually starting at one, expressed with either pips or digits. However, there are some applications that require results other than numbers. Examples include letters for Boggle, directions for '' Warhammer Fantasy Battle'', Fudge dice, playing card symbols for poker dice, and instructions for sexual acts using sex dice.Alternatively-numbered dice

Dice may have numbers that do not form a counting sequence starting at one. One variation on the standard die is known as the "average" die. These are six-sided dice with sides numbered`2, 3, 3, 4, 4, 5`

, which have the same arithmetic mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...

as a standard die (3.5 for a single die, 7 for a pair of dice), but have a narrower range of possible values (2 through 5 for one, 4 through 10 for a pair). They are used in some table-top wargames, where a narrower range of numbers is required. Other numbered variations include Sicherman dice and intransitive dice
A set of dice is intransitive (or nontransitive) if it contains three dice, ''A'', ''B'', and ''C'', with the property that ''A'' rolls higher than ''B'' more than half the time, and ''B'' rolls higher than ''C'' more than half the time, but it is ...

.
Spherical dice

A die can be constructed in the shape of a sphere, with the addition of an internal cavity in the shape of thedual polyhedron
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other ...

of the desired die shape and an internal weight. The weight will settle in one of the points of the internal cavity, causing it to settle with one of the numbers uppermost. For instance, a sphere with an octahedral cavity and a small internal weight will settle with one of the 6 points of the cavity held downwards by the weight.
Applications

Polyhedral dice are commonly used in role-playing games. The fantasy role-playing game ''Dungeons & Dragons
''Dungeons & Dragons'' (commonly abbreviated as ''D&D'' or ''DnD'') is a fantasy tabletop role-playing game (RPG) originally designed by Gary Gygax and Dave Arneson. The game was first published in 1974 by Tactical Studies Rules, Inc. (TSR ...

'' (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.
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
''Axis & Allies'' is a series of World War II strategy board games. The first version was initially published in 1981 and a second edition known colloquially as ''Axis & Allies: Classic'' was published in 1984. Played on a board depicting a Spr ...

'', have inverted this system by making the lower values more potent. In the modern age, 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, '' Dicemasters''), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant the player useful actions.
Dice can be used for divination
Divination (from Latin ''divinare'', 'to foresee, to foretell, to predict, to prophesy') is the attempt to gain insight into a question or situation by way of an occultic, standardized process or ritual. Used in various forms throughout histor ...

and using dice for such a purpose is called cleromancy
Cleromancy is a form of sortition (casting of lots) in which an outcome is determined by means that normally would be considered random, such as the rolling of dice, but that are sometimes believed to reveal the will of a deity.
In classical ci ...

. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this method of divination. It is highly likely that the Pythagoreans
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, ...

used the Platonic solids
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges ...

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.
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 nodes of the Moon, the second die represents the 12 zodiac signs, and the third represents the 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
A password, sometimes called a passcode (for example in Apple devices), is secret data, typically a string of characters, usually used to confirm a user's identity. Traditionally, passwords were expected to be memorized, but the large number of ...

s and cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

applications. The Electronic Frontier Foundation
The Electronic Frontier Foundation (EFF) is an international non-profit digital rights group based in San Francisco, California. The foundation was formed on 10 July 1990 by John Gilmore, John Perry Barlow and Mitch Kapor to promote Internet ...

describes a method by which dice can be used to generate passphrase
A passphrase is a sequence of words or other text used to control access to a computer system, program or data. It is similar to a password in usage, but a passphrase is generally longer for added security. Passphrases are often used to control ...

s. Diceware
Diceware is a method for creating passphrases, passwords, and other cryptographic variables using ordinary dice as a hardware random number generator. For each word in the passphrase, five rolls of a six-sided die are required. The numbers from ...

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.
Notation

In many gaming contexts, especially tabletop role-playing games, shorthand notations representing different dice rolls are used. A "d" or "D" is used to indicate a die with a specific number of sides; for example,`d4`

denotes a four-sided die. If several dice of the same type are to be rolled, this is indicated by a leading number specifying the number of dice. Hence,`6d8`

means the player should roll six eight-sided dice and add the results. Modifiers to a die roll can also be indicated as desired. For example, `3d6+4`

instructs the player to roll three six-sided dice, calculate the total, and add four to it.
See also

* Crown and Anchor * d20 System *Dreidel
A dreidel, also dreidle or dreidl ( ; yi, דרײדל, dreydl, plural: ''dreydlech''; he, סביבון, sevivon) is a four-sided spinning top, played during the Jewish holiday of Hanukkah. The dreidel is a Jewish variant on the teetotum, a ga ...

* Fuzzy dice
* '' Musikalisches Würfelspiel''
* Dice throw (review)
* Intransitive dice
A set of dice is intransitive (or nontransitive) if it contains three dice, ''A'', ''B'', and ''C'', with the property that ''A'' rolls higher than ''B'' more than half the time, and ''B'' rolls higher than ''C'' more than half the time, but it is ...

* Quincunx
A quincunx () is a geometric pattern consisting of five points arranged in a cross, with four of them forming a square or rectangle and a fifth at its center. The same pattern has other names, including "in saltire" or "in cross" in heraldry (dep ...

* Teetotum
* Urim and Thummim
In the Hebrew Bible, the Urim ( he, ''ʾŪrīm'', "lights") and the Thummim ( he, ''Tummīm'', meaning uncertain, possibly "perfections") are elements of the ''hoshen'', the breastplate worn by the High Priest attached to the ephod. They are ...

References

Bibliography

* Diaconis, Persi; and Keller, Joseph B."Fair Dice"

, ''The American Mathematical Monthly'', 96(4):337–339, 1989 (Discussion of dice that are fair "by symmetry" and "by continuity".) * Iverson, G. R.; Longcour, W. H.; et al.; ''Bias and Runs in Dice Throwing and Recording: A Few Million Throws'', Psychometrika, vol. 36, no. 1, March 1971 * Knizia, Reiner, ''Dice Games Properly Explained'', Elliot Right Way Books, 1999,

External links

* analysis of dice probabilities, also featuring Uspenski's work on rolling multiple dice {{Authority control Gaming devices