Two standard six-sided pipped dice with rounded corners.

Dice (the plural of die, from Old French dé, from Latin datum "something given or played"^[1]) are small polyhedral objects, usually cubic, used for generating random numbers or other symbols. This makes dice suitable as gambling devices, especially for craps or sic bo, or for use in non-gambling tabletop games. Feature image for Dice article File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Feature image for Dice article File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Look up plural in Wiktionary, the free dictionary. ... Old French was the Romance dialect continuum spoken in territories corresponding roughly to the northern half of modern France and parts of modern Belgium and Switzerland from around 1000 to 1300. ... For other uses, see Latins and Latin (disambiguation). ... For the game magazine, see Polyhedron (magazine). ... A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal die roll, or the digits of Pi (as far as we can tell) exhibit statistical randomness. ... Gamble redirects here. ... Craps (previously known as crabs[1]) is a casino dice game. ... A Sic bo table Sic bo (骰寶), also known as tai sai (大細), dai siu (大小), big and small or hi-lo, is an unequal game of chance played with three dice, and of ancient Chinese origin. ... Tabletop game is a general term used to refer to card games, board games, parlor games, role-playing games, miniature wargames, tile-based games and other games that are normally played on a table or other flat surface. ...

A traditional die is a cube (often with corners slightly rounded), marked on each of its six faces with a different number of circular patches or pits called pips. All of these pips have the same appearance within a pair, or larger set of dice, and are sized for ease of recognizing the pattern the pips on one face form. The design as a whole is aimed at each die providing one randomly determined integer, in the range from one to six, with each of those values being equally likely. Three dimensions A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. ... Not to be confused with Natural number. ...

More generally, a variety of analogous devices are often described as dice, but necessarily in a context, or with a word or two preceding "die" or "dice", that avoids the assumption that traditional dice are intended. Such specialized dice may have cubical or other polyhedral shapes, with faces marked with various collections of symbols, and be used to produce other random results than one through six. There are also "loaded" or "crooked" dice (especially otherwise traditional ones), meant to produce skewed or even predictable results, for purposes of deception or amusement.

Ordinary dice

European-style, Asian-style, and casino dice.

The common dice are small cubes 1 to 2 cm along an edge (16mm being the standard), whose faces are numbered from one to six (usually by patterns of dots called pips). It is traditional to assign pairs of numbers that total seven to opposite faces (it has been since at least classical antiquity); this implies that at one vertex the faces 1, 2 and 3 intersect. It leaves one other abstract design choice: the faces representing 1, 2 and 3 respectively can be placed in either clockwise or counterclockwise order about this vertex. American, Chinese, and casino dice File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Three dimensions A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. ... Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, which begins roughly with the earliest-recorded Greek poetry of Homer (7th century BC), and continues through the rise of Christianity and the fall of the Western Roman Empire (5th century AD... In geometry, a vertex (plural vertices) is a special kind of point, usually a corner of a polygon, polyhedron, or higher dimensional polytope. ... A clockwise motion is one that proceeds like the clocks hands: from the top to the right, then down and then to the left, and back to the top. ...

The pips on traditional European-style dice are arranged in specific patterns. The face with two usually has the dots in opposite corners, with the third face containing one between these two. The fourth face has one in each corner, and the fifth adds one in the center, forming a quincunx. The final face has two rows of three pips along opposite edges of the face. Five dots forming a quincunx A quincunx is the arrangement of five units in the pattern corresponding to the five-spot on dice, playing cards, or dominoes. ...

Typical facets of an Asian-style (top) and a European-style die (bottom). Note the compactedness of the pips in the Asian-style die compared to those of the European-style one.

Dice are thrown to provide random numbers for gambling and other games, and thus are a type of hardware random number generator. The result of a die roll is random in the sense of lacking predictability, not lacking cause. Exactly how dice are thrown determines how they will land according to the laws of classical mechanics. However, dice also can exhibit sensitive dependence on initial conditions, making it difficult to predict the outcome of a die roll even with good information about exactly how it is thrown. Also, because the numbers on typical dice are marked with small indentations, slightly more material is removed from the higher numbered faces. This results in a small bias, and they do not provide fair (uniform) random numbers. The bias is reduced somewhat in the Japanese die with its oversized single pip (pictured). Casino dice have markings that are flush with the surface and come very close to providing true uniformly distributed random numbers. Random redirects here. ... Gamble redirects here. ... For other uses, see Game (disambiguation). ... In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Point attractors in 2D phase space. ...

Dice are thrown, singly or in groups, from the hand or from a cup or box designed for the purpose, onto a flat surface. The face of each die that is uppermost when it comes to rest provides the value of the throw. A typical dice game today is craps, wherein two dice are thrown at a time, and wagers are made on the total value of up-facing pips on the two dice. They are also frequently used to randomize allowable moves in board games, usually by deciding the distance through which a piece will move along the board; examples of this are ludo and backgammon. ... Craps (previously known as crabs[1]) is a casino dice game. ... A shelf of board games. ... This article does not cite any references or sources. ... Backgammon is a board game for two players in which the playing pieces[1] are moved according to the roll of dice. ...

Another unique feature about Asian dice aside from the oversized single pip is the fact that the pips for both "one" and "four" are colored red. Why this is so is unknown. But it is suggested that an entirely black and white color combination on the one side would be unlucky and red (a lucky color in Chinese culture) would counteract this. Several legends also mention that the "four" side is colored red because a Chinese emperor (one legend said it was a Ming dynasty emperor, while another stated it was Chung Tsung) ordered it as "fours" helped him win a dice game (sugoroku) against his empress. This story, however, is questionable at best, as it is also probable that "red fours" are also of common Indian origin.^[2][3] For other uses, see Ming. ... Zhongzong (656-710) was fourth and seventh Emperor of the Tang Dynasty of China, ruling briefly in 684 and again from 705 to 710. ... Sugoroku (双六) refers to two different forms of Japanese board game, one similar to western backgammon and the other similar to western Snakes and Ladders. ...

Precision dice

Precision casino dice, used for the game of craps, may have a polished finish, making them transparent, or a sand finish, making them translucent. Casino dice have their pips drilled, and then filled flush with a paint of the same density as the acetate used for the dice, such that the dice remain in balance. In casino play, a stick of 5 dice are used, all stamped with a matching serial number to prevent a cheat from substituting a die. For other uses, see Density (disambiguation). ... For other uses, see Acetate (disambiguation). ...

Precision backgammon dice are also made with the pips filled in as with casino dice. While casino dice are noticeably larger than common dice, with sharp edges and corners, precision backgammon dice tend to be somewhat smaller. Their corners and edges are beveled to allow greater movement inside the dice cup and prevent chaotic rolls from damaging the playing surface. Backgammon is a board game for two players in which the playing pieces[1] are moved according to the roll of dice. ...

History

Bone die found at Cantonment Clinch (1823 - 1834), an American fort used in the Civil War by both Confederate and Union troops at separate times. The fort was also used in 1898 in the Spanish-American War.

Knucklebone die, made of Steatite

A collection of historical dice from Asia

Dice were probably originally made from the ankle bones (specifically the talus or "astragalus") of hoofed animals (such as oxen), colloquially known as "knucklebones", which are approximately tetrahedral. Modern Mongolians still use such bones, known as shagai, for games and fortunetelling. In addition to bone, ivory, wood, metal, and stone materials have been commonly used. Recently, the use of plastics, including cellulose acetate and bakelite, is nearly universal. It is almost impossible to trace clearly the development of dice as distinguished from knucklebones, because ancient writers confused the two. It is certain, however, that both were used in prehistoric times. Image File history File links Metadata Size of this preview: 800 × 575 pixelsFull resolution (1428 × 1027 pixel, file size: 948 KB, MIME type: image/jpeg) author: Kolby Kirk. ... Image File history File links Metadata Size of this preview: 800 × 575 pixelsFull resolution (1428 × 1027 pixel, file size: 948 KB, MIME type: image/jpeg) author: Kolby Kirk. ... Image File history File links Knuck_dice_Steatite_37x27x21_mm. ... Image File history File links Knuck_dice_Steatite_37x27x21_mm. ... An Egyptian carved and glazed steatite scarab amulet. ... Download high resolution version (911x1163, 196 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (911x1163, 196 KB) Wikipedia does not have an article with this exact name. ... See talus for other meanings of the word The talus bone or astragalus of the ankle joint connects the leg to the foot. ... Binomial name Bos taurus Linnaeus, 1758 Cattle are domesticated ungulates, a member of the subfamily Bovinae of the family Bovidae. ... Roman statue of girl playing astragaloi Knucklebones also known as hucklebones, dibs, jackstones, chuckstones or five-stones, is a game of very ancient origin, played with five small objects, originally the knucklebones of a sheep, which are thrown up and caught in various ways. ... For the academic journal, see Tetrahedron (journal). ... Honorary guard of Mongolia. ... Shagai (Mongolian: Шагай) is the Mongolian word for the cuboid bone of the ankle of a sheep. ... Gypsies fortune-telling. ... This article is about the skeletal organs. ... This article or section does not cite its references or sources. ... For other uses, see Wood (disambiguation). ... This article is about metallic materials. ... This article is about the geological substance. ... For other uses, see Plastic (disambiguation). ... Cellulose acetate, first prepared in 1865, is the acetate ester of cellulose. ... Bakelite is a material based on the thermosetting phenol formaldehyde resin, polyoxybenzylmethylenglycolanhydride developed in 1907–1909 by Belgian-American Dr. Leo Baekeland. ...

Dice have been used throughout Asia since before recorded history.

The oldest known dice were excavated as part of a 5000-year-old backgammon set, at the Burnt City archeological site in south-eastern Iran. Excavations from ancient tombs in the Harappan civilization,^[4] seem to further indicate a South Asian origin. Dicing is mentioned as an Indian game in the Rig Veda, Atharva Veda^[5] and Buddha games list. It is also mentioned in the great Hindu epic, the Mahabharata, where Yudhisthira plays a game of dice against the Kauravas for the northern kingdom of Hastinapura. In its primitive form knucklebones was essentially a game of skill played by women and children. In a derivative form of knucklebones, the four sides of the bones received different values and were counted as with modern dice. Gambling with three or sometimes two dice was a very popular form of amusement in Greece, especially with the upper classes, and was an almost invariable accompaniment to symposia. Backgammon is a board game for two players in which the playing pieces[1] are moved according to the roll of dice. ... Shahr-i Sokhta or Shahr-e Sukhteh (literally Burnt City) is a Bronze Age urban settlement in the southeast of Iran, in Sistan. ... Excavated ruins of Mohenjo-daro. ... Map of South Asia (see note on Kashmir). ... The History of India begins with the Indus Valley Civilization, which flourished in the north-western part of the Indian subcontinent from 3300 to 1700 BCE. This Bronze Age civilization was followed by the Iron Age Vedic period, which witnessed the rise of major kingdoms known as the Mahajanapadas. ... Rig veda is the oldest text in the world. ... The Atharvaveda (Sanskrit: अथर्ववेद, , a tatpurusha compound of , a type of priest, and meaning knowledge) is a sacred text of Hinduism, and one of the four Vedas, often called the fourth Veda. According to tradition, the Atharvaveda was mainly composed by two groups of rishis known as the Bhrigus and the... The Buddha games list is a list of games which it is reputed that Gautama Buddha said that he would not play. ... This article discusses the adherents of Hinduism. ... For the film by Peter Brook, see The Mahabharata (1989 film). ... In the great Hindu epic Mahabharata, Yudhisthira (Sanskrit: युधिष्ठिर, yudhiṣṭhira) was the eldest son of King Pandu and Queen Kunti, king of Hastinapura and Indraprastha, and World Emperor. ... The term Kaurava is a Sanskrit term, that means the descendants of Kuru, a legendary king who is the ancestor of many of the characters of the Mahabharata. ... In the Hindu epic Mahabharata, Hastinapura is the capital and the kingdom of the Kauravas, the descendants of Kuru, which include the Pandavas. ... A game of skill is a game where the outcome is determined mainly by mental and/or physical skill, rather than by pure chance. ... Symposium originally referred to a drinking party (the Greek verb sympotein means to drink together) but has since come to refer to any academic conference, whether or not drinking takes place. ...

The Romans were passionate gamblers, especially in the luxurious days of the Roman Empire, and dicing was a favorite form, though it was forbidden except during the Saturnalia. Horace derided what he presented as a typical youth of the period, who wasted his time amid the dangers of dicing instead of taming his charger and giving himself up to the hardships of the chase. Throwing dice for money was the cause of many special laws in Rome. One of these stated that no suit could be brought by a person who allowed gambling in his house, even if he had been cheated or assaulted. Professional gamblers were common, and some of their loaded dice are preserved in museums. The common public-houses were the resorts of gamblers, and a fresco is extant showing two quarrelling dicers being ejected by the indignant host. Julius Caesar, from the bust in the British Museum, in Cassells History of England (1902). ... For other uses, see Roman Empire (disambiguation). ... For other uses, see Saturnalia (disambiguation). ... For other people named Horace, see Horace (disambiguation). ... For other uses, see Youth (disambiguation) Youth is defined by Websters New World Dictionary as, The time of life when one is young; especially: a: the period between childhood and maturity b: the early period of existence, growth, or development. ... Binomial name Equus caballus Linnaeus, 1758 The horse (Equus caballus, sometimes seen as a subspecies of the Wild Horse, Equus ferus caballus) is a large odd-toed ungulate mammal, one of ten modern species of the genus Equus. ... For other uses, see Law (disambiguation). ... For other uses, see Rome (disambiguation). ... Civil action redirects here. ... For other uses, see Museum (disambiguation). ... For other uses, see Fresco (disambiguation). ...

Tacitus states that the Germans were passionately fond of dicing, so much so, indeed, that, having lost everything, they would even stake their personal liberty. Centuries later, during the Middle Ages, dicing became the favorite pastime of the knights, and both dicing schools and guilds of dicers existed. After the downfall of feudalism the famous German mercenaries called landsknechts established a reputation as the most notorious dicing gamblers of their time. Many of the dice of the period were curiously carved in the images of men and beasts. In France both knights and ladies were given to dicing. This persisted through repeated legislation, including interdictions on the part of St. Louis in 1254 and 1256. Gaius Cornelius Tacitus Publius or Gaius Cornelius Tacitus (c. ... The term Germanic tribes (or Teutonic tribes) applies to the ancient Germanic peoples of Europe. ... Knights Dueling, by Eugène Delacroix For other uses, see Knight (disambiguation) or Knights (disambiguation). ... Roland pledges his fealty to Charlemagne; from a manuscript of a chanson de geste Feudalism, a term first used in the early modern period (17th century), in its most classic sense refers to a Medieval European political system comprised of a set of reciprocal legal and military obligations among the... For other uses, see Mercenary (disambiguation). ... Landsknecht. ... Louis IX (25 April 1215 – 25 August 1270), commonly Saint Louis, was King of France from 1226 to his death. ...

In China, India, Japan, Korea, and other Asiatic countries, dice have always been popular and are so still. The markings on Chinese dominoes evolved from the markings on dice, taken two at a time. This article is about the Korean civilization. ... A set of Chinese dominoes Chinese dominoes are used in several tile-based games, namely, Tien Gow, Pai Gow, Gwat Pai, Che Deng, Tiu U, Kap Tai Shap. ...

Terms

While the terms ace, deuce, trey, cater, cinque and sice are hardly common today having been replaced with the ordinary names of the numbers one to six, they are still used by some professional gamblers to describe the different sides of the dice. Ace is from the Latin as, meaning "a unit" [1]; the others are the numbers 2–6 in old French. (The dice game marketed as Kismet uses ace, deuce, and trey.) This article does not cite any references or sources. ... Kismet is the trademarked name of a commercial dice game introduced in 1964. ...

Notation

Main article: Dice notation

In many modern gaming contexts, the count and number of sides of dice to be rolled at any given time is reduced to a common set of notations. Typically this involves the lower-case letter "d", preceded by a die count and followed by (optionally) the number of sides of the dice. For example, 6d8 or 2d6; the former meaning "six eight-sided dice," and the latter meaning "two six-sided dice." Addition or various other arithmetic operations are often added at the end as well, e.g. 3d6+4 "three six-sided dice plus four to the outcome thereof". A brass dice set. ...

Crooked dice

"Crooked dice" refers to dice that have been altered in some way to change the distribution of their outcome.

Loaded dice

A loaded or gaffed die is a die that has been tampered with to land with a selected side facing upwards more often than it otherwise would simply by chance. There are methods of creating loaded dice, including having some edges round and other sharp and slightly off square faces. If the dice are not transparent, weights can be added to one side or the other. They can be modified to produce winners ("passers") or losers ("miss-outs"). "Tappers" have a drop of mercury in a reservoir at the center of the cube, with a capillary tube leading to another mercury reservoir at the side of the cube. The load is activated by tapping the die on the table so that the mercury leaves the center and travels to the side. Often one can see the circle of the cut used to remove the face and bury the weight. In a professional die, the weight is inserted in manufacture; in the case of a wooden die, this can be done by carving the die around a heavy inclusion, like a pebble around which a tree has grown. Probability is the likelihood that something is the case or will happen. ... This article is about the element. ... Capillary Flow Experiment to investigate capillary flows and phenomena onboard the International Space Station Capillary action, capillarity, capillary motion, or wicking is the ability of a substance to draw another substance into it. ... Sea wave polishing pebbles into rounded corners Pebbles For other uses, see Pebble (disambiguation). ...

A variable loaded die is hollow with a small weight and a semi-solid substance inside, usually wax, whose melting point is just lower than the temperature of the human body. This allows the cheater to change the loading of the die by breathing on it or holding it firmly in hand, causing the wax to melt and the weight to drift down, making the chosen opposite face more likely to land up. A less common type of variable die can be made by inserting a magnet into the die and embedding a coil of wire in the game table. Then, either leave the current off and let the die roll unchanged or run current through the coil to increase the likelihood that the north side or the south side will land on the bottom depending on the direction of the current. candle wax This page is about the substance. ... The melting point of a solid is the temperature range at which it changes state from solid to liquid. ... For other uses, see Magnet (disambiguation). ...

Plastic dice can be biased to roll a certain number by heating them (for example in an oven) with the desired face upward, so that the plastic will soften slightly and "pool" at the opposite (bottom) side of the die without showing much, if any, visible distortion.

Transparent acetate dice, used in all reputable casinos, are harder to tamper with. For other uses, see Acetate (disambiguation). ... This article or section does not adequately cite its references or sources. ...

Cheat dice

Cheat dice (see below) are often sold as loaded dice but usually are not technically loaded.

Shaved dice

A die can be "shaved" on one side i.e. slightly shorter in one dimension, making it slightly rectangular and thus affecting its outcome. One countermeasure employed by casinos against shaved dice is to measure the dice with a micrometer. Outside, inside, and depth micrometers A micrometer, also known as a micrometer screw gauge, is a widely used device in mechanical engineering for precisely measuring thickness of blocks, outer and inner diameters of shafts and depths of slots. ...

Variants

Dice with faces other than digit sequences

As noted, the faces of most dice are labeled using an unbroken series of whole numbers, starting at one (rarely zero), expressed with either pips or digits. Common exceptions include: Look up zero in Wiktionary, the free dictionary. ...

• color dice (e.g., with the colors of the playing pieces used in a game)
• Poker dice, with labels reminiscent of playing cards. Several varieties exist, but the most common contain the following pattern: 9♣, 10♦, Jack (blue), Queen (green), King (red), A♠
• dice with letters (e.g. in Boggle)
• average dice (2, 3, 3, 4, 4, 5) (In some war games, units are identified as regulars or irregulars. Because regulars are more predictable, the strength of a regular unit is multiplied by an average die. For this reason, average dice are jocularly called regular dice.)
• cheat dice, such as:
  • one face each with two through five, and two with sixes, or
  • for craps, a pair of dice in which one die has five on each face, and its mate has a mixture of twos and sixes, guaranteeing rolls of seven or 11.
• dice with a single sequence of markings repeated multiple times, for example:
  • a cubical die numbered twice from 1 to 3, or thrice from 1 to 2.
  • icosahedral dice numbered twice from 1 to 10 (commonly used in Dungeons & Dragons before the popularization of ten-sided dice).
  • Fudge dice, numbered twice from −1 to 1, represented as −, blank, +.

Doubling cube

• random direction dice, also known as scatter dice. The dice have arrows on each side; the outcome of a roll is a random direction. Scatter dice are used in tabletop wargames such as Warhammer Fantasy Battle to determine random movements of troops, wind direction or direction of misfired arms. Note that this is an unusual case where the majority of the time the die is read not according to which symbol is shown on its uppermost face, but its compass orientation.
• A doubling cube with the numbers 2, 4, 8, 16, 32, and 64 is used in backgammon and some other boardgames. This die is not actually rolled; it is used to denote the current stakes of the game. There is also a doubling octahedron with 1, 2, 4, 8, 16, 32, 64, and 128.
• Some board games use dice with positive and negative numbers for use in gain or loss of something.
• Sicherman dice, a pair having the same odds of rolling a given sum as a pair of standard six-sided dice, but with different markings: one die has 1, 3, 4, 5, 6, and 8, and the other has 1, 2, 2, 3, 3, and 4. Sicherman dice are the only such alternative arrangement if positive whole numbers are used.
• I Ching dice such as
  • Eight-sided dice bearing the eight trigrams
  • Six-sided dice bearing yin and yang twice each, and old yin and old yang once each
• "Projector dice" which are clear and marked only on one of each pair of opposing faces. For a "six"-sided die, e.g., a clear twelve sided-shape is used. Rolled on an overhead projector such a die will have the top or bottom marking equally readable.

Poker Room at the Trump Taj Mahal, Atlantic City, New Jersey Poker is a card game, the most popular of a class of games called vying games, in which players with fully or partially concealed cards make wagers into a central pot, which is awarded to the player or players... For the Russian group of artists, see Jack of Diamonds (artists). ... Typical game contents and scoring example. ... Irregular soldiers in Beauharnois, Quebec, 19th century. ... Craps (previously known as crabs[1]) is a casino dice game. ... This article is about the role-playing game. ... Fudge is a generic role-playing game system for use in freeform role-playing games. ... Image File history File linksMetadata Download high-resolution version (705x671, 132 KB) Summary Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Dice Metadata This file contains additional information, probably added from the digital camera or scanner used... Image File history File linksMetadata Download high-resolution version (705x671, 132 KB) Summary Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Dice Metadata This file contains additional information, probably added from the digital camera or scanner used... Wargaming can be one of number of ways of exploring the effects of warfare without actual combat. ... It has been suggested that Armies of warhammer be merged into this article or section. ... Backgammon is a board game for two players in which the playing pieces[1] are moved according to the roll of dice. ... A board game is any game played with a premarked surface, with counters or pieces that are moved across the board. ... This article belongs in one or more categories. ... Alternative meaning: I Ching (monk) The I Ching (Traditional Chinese: 易經, pinyin y jīng; Cantonese IPA: jɪk6gɪŋ1; Cantonese Jyutping: jik6ging1; alternative romanizations include I Jing, Yi Ching, Yi King) is the oldest of the Chinese classic texts. ... An overhead projector is a display system that is used to display images to an audience. ...

Non-cubical dice

Barrel Dice

Some dice are polyhedral other than cubical in shape. They became popular around the early 1950s among players of wargames, trading card games, German-style board games, and role-playing games. Although polyhedral dice are a relative novelty during modern times, some ancient cultures appear to have used them in games (as evidenced by the presence of two icosahedral dice dating from the days of ancient Rome on display in the British Museum). Such dice are typically plastic, and have faces bearing numerals rather than patterns of dots. Reciprocally symmetric numerals are distinguished with a dot in the lower right corner (6. vs 9.) or by being underlined (6 vs 9). Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... There are very few or no other articles that link to this one. ... For the game magazine, see Polyhedron (magazine). ... Wargaming is the play of simulated military operations in the form of games known as wargames. ... Collectible card games (CCGs), also called customizable card games or trading card games, are played using specially designed sets of cards. ... Puerto Rico, a popular German-style board game German-style board games are a broad class of games that feature simple rules, modest length, and attractive components. ... This article is about games in which one plays the role of a character. ... Ancient Rome was a civilization that grew from a small agricultural community founded on the Italian Peninsula circa the 9th century BC to a massive empire straddling the Mediterranean Sea. ... London museum | name = British Museum | image = British Museum from NE 2. ...

The platonic solids are commonly used to make dice of 4, 6, 8, 12, and 20 faces. Other shapes can be found to make dice with other numbers of faces, but other than the 10 sided, they are rarely used. (See Zocchihedron.) The 4 sided platonic solid is difficult to roll, and a few games like Daldøs use a 4 sided rolling pin instead. In geometry, a Platonic solid is a convex regular polyhedron. ... The Zocchihedron (approx. ... Daldøs [daldøs] is a board game of the tâb family only known from a few coastal locations in Scandinavia, where its history can be traced back to around 1800. ...

A large number of different probability distributions can be obtained using these dice in various ways; for example, 10-sided dice (or 20-sided dice labeled with single digits) are often used in pairs to produce a linearly-distributed random percentage. Summing multiple dice approximates a normal distribution (a "bell curve"), while eliminating high or low throws can be used to skew the distribution in various ways. Using these techniques, games can closely approximate the real probability distributions of the events they simulate. A probability distribution describes the values and probabilities that a random event can take place. ... (Redirected from 10-sided dice) Ten-sided dice are often used in role-playing games, such as Dungeons and Dragons, to get random decimal numbers, such as percentages. ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ...

There is some controversy over whether manufacturing processes create genuinely "fair" dice (dice that roll with even distributions over their number span). Casino dice are legally required to be fair; those used by others hold no such requirement. This article or section does not adequately cite its references or sources. ...

Spherical dice also exist; these function like the plain cubic dice, but have an octahedral internal cavity in which a weight moves which causes them to settle in one of six orientations when rolled. However, these dice are somewhat awkward in use because they require a flat and level surface to roll properly — an uneven surface often causes them to stop partway between two numbers, while a sloped surface will obviously cause the dice to keep rolling.

Cowry shells or coins may be used as a kind of two-sided dice. (Because of their shape, cowry shells probably do not yield a uniform distribution.) Species See text. ... This article is about monetary coins. ... In probability theory and statistics, the discrete uniform distribution is a discrete probability distribution that can be characterized by saying that all values of a finite set of possible values are equally probable. ...

Standard variations

A matched Platonic-solids set of five dice, (from left) tetrahedron (4 sides), cube (6), octahedron (8), dodecahedron (12), and icosahedron (20).

The most common non-cubical dice — often sold in sets of five or six that are each differently shaped but with the same pair of background and marking colors — include one each of the five Platonic solids, which are highly symmetrical. The six-die versions add the pentagonal trapezohedron, in which the faces (identical to one another as to angles and edge lengths) each have two different lengths of side, and three different sizes of angle; the corners at which multiple faces meet are also of two different kinds. Dice sold in sets are often identically colored, with matching die and marking colors. ... In geometry, a Platonic solid is a convex regular polyhedron. ... The trapezohedron is the dual polyhedron of the corresponding antiprism. ...

Sides	Shape		Notes
4	tetrahedron		Each face has three numbers: they are arranged such that the upright number (which counts) is the same on all three visible faces. Alternatively, all of the sides have the same number in the lowest edge and no number on the top. This die does not roll well and thus it is usually thrown into the air instead.
6	cube		A common die. The sum of the numbers on opposite faces is seven.
8	octahedron		Each face is triangular; looks something like two Egyptian pyramids attached at the base. Usually, the sum of the opposite faces is 9.
10	pentagonal trapezohedron		Each face is kite-shaped; five of them meet at the same sharp corner (as at the top of the diagram in this row), and five at another equally sharp one; about halfway between them, a different group of three faces converges at each of ten blunter corners. The ten faces usually bear numbers from zero to nine, rather than one to ten (zero being read as "ten" in many applications), and often all odd numbered faces converge at the same sharp corner, and the even ones at the other.
12	dodecahedron		Each face is a regular pentagon.
20	icosahedron		Faces are equilateral triangles. Typically, opposite faces add to twenty-one. A 2nd century CE Roman icosahedron die is in the collection of the British Museum, though the game it was used for is not known.[6]

A 4-sided die resting on its 1 face Four-sided dice are often used in role-playing games, such as Dungeons and Dragons, to get small numbers for things such as damage or character statistic increases. ... For the academic journal, see Tetrahedron (journal). ... Image File history File links Download high-resolution version (1000x1000, 187 KB)See: Stella (software) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Three dimensions A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. ... Hexahedron (sometimes called cube), rendered by Java applet I wrote. ... An octahedron (plural: octahedra) is a polyhedron with eight faces. ... Image File history File links Download high-resolution version (1000x1000, 201 KB)See: Stella (software) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... For other meanings, see pyramid (disambiguation). ... Ten-sided dice are often used in role-playing games, such as Dungeons and Dragons, to get random decimal numbers, such as percentages. ... The pentagonal trapezohedron or deltohedron is the third in an infinite series of face-uniform polyhedra which are dual polyhedron to the antiprisms. ... Download high resolution version (452x773, 37 KB)Pentagonal antiprism, made by me using POV-Ray, see image:poly. ... A kite showing its equal sides and its inscribed circle. ... In mathematics, any integer (whole number) is either even or odd. ... In mathematics, any integer (whole number) is either even or odd. ... A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ... Image File history File links Size of this preview: 600 × 600 pixel Image in higher resolution (1000 × 1000 pixel, file size: 211 KB, MIME type: image/png)image for Dodecahedron See: Stella (software) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to... [Etymology: 16th century: from Greek eikosaedron, from eikosi twenty + -edron -hedron], icosahedral adjective An icosahedron noun (plural: -drons, -dra ) is any polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangles as faces. ... Image File history File links Size of this preview: 600 × 600 pixel Image in higher resolution (1000 × 1000 pixel, file size: 252 KB, MIME type: image/png)See: Stella (software) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... London museum | name = British Museum | image = British Museum from NE 2. ...

Rarer variations

The full geometric set of "uniform fair dice" (face-transitive) are: For other uses, see Sphere (disambiguation). ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... For the optical prism, see Triangular prism (optics). ... United States simply as football, is a competitive team sport that is both fast-paced and strategic. ... Argentina-France Rugby Union match Rugby football refers to sports descended from a common form of football developed at Rugby School. ... For the optical prism, see Triangular prism (optics). ... In geometry, the pentagonal prism is the third in an infinite set of prisms formed by square sides and two regular polygon caps. ... The original reference to seven-sided backgammon appears to be from the Alfonso manuscript as compiled in the 13th century. ... Backgammon is a board game for two players in which the playing pieces[1] are moved according to the roll of dice. ... In geometry, a heptagon is a polygon with seven sides and seven angles. ... The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. ... For other uses, see Rhombus (disambiguation). ... In geometry, a heptagon is a polygon with seven sides and seven angles. ... The trapezohedron is the dual polyhedron of the corresponding antiprism. ... A kite showing its equal sides and its inscribed circle. ... For other uses, see Octagon (disambiguation). ... A bipyramid is a polyhedron formed by joining two identical pyramids base-to-base. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... A tetrakis hexahedron is an Archimedean dual solid, or a Catalan solid. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... A deltoidal icositetrahedron (or trapezoidal icositetrahedron) is a catalan solid which looks a bit like an overinflated cube. ... A kite showing its equal sides and its inscribed circle. ... The Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. ... For other uses, see Rhombus (disambiguation). ... Look up polygon in Wiktionary, the free dictionary. ... The trapezohedron is the dual polyhedron of the corresponding antiprism. ... A kite showing its equal sides and its inscribed circle. ... Look up polygon in Wiktionary, the free dictionary. ... The trapezohedron is the dual polyhedron of the corresponding antiprism. ... A kite showing its equal sides and its inscribed circle. ... The Zocchihedron (approx. ... In geometry, a polyhedron is isohedral or face-transitive when all its faces are the same. ...

• Platonic solids: 5 regular polyhedra: (4, 6, 8, 12, 20 sides)
• Catalan solids: 13 Archimedean duals: (12, 24, 30, 48, 60, 120 sides)
• Bipyramids: infinite set of prism duals, triangle faces: (6, 8, 10, 12, ... sides)
• Trapezohedrons: infinite set of antiprism duals, kite faces: (6, 8, 10, 12, ... sides)
• Disphenoids: infinite set of tetrahedra made from congruent non-regular triangles (4 sides)
• "Rolling-pin style dice" (also called "rolling logs" [2]) are the only way to make dice with an odd number of faces[3]. They are based on an infinite set of prisms. All the (rectangular) faces they may actually land on are congruent, so they are equally fair. (The other 2 sides of the prism are rounded or capped with a pyramid, designed so that the dice never actually rests on those faces.)

In geometry, a Platonic solid is a convex regular polyhedron. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... A bipyramid is a polyhedron formed by joining two identical pyramids base-to-base. ... In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. ... The trapezohedron is the dual polyhedron of the corresponding antiprism. ... An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles. ... Disphenoid tetrahedron inside a square cuboid A disphenoid is a polyhedron whose four faces are identical isosceles or scalene triangles. ... In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. ...

Probability

For a single roll of a fair s-sided die, the probability of rolling each value, 1 through s, is exactly ¹/_s. This is an example of a discrete uniform distribution. For a double roll, however, the total of both rolls is not evenly distributed, but is distributed in a triangular curve. For two six-sided dice, for example, the probability distribution is as follows: In probability theory and statistics, the discrete uniform distribution is a discrete probability distribution that can be characterized by saying that all values of a finite set of possible values are equally probable. ...

Probability distribution for the sum of two six-sided dice

For three or more die rolls, the curve becomes more bell-shaped with each additional die (according to the central limit theorem). The exact probability distribution F_s,i of a sum of i s-sided dice can be calculated as the repeated convolution of the single-die probability distribution with itself. Image File history File links Dice_Distribution_(bar). ... Image File history File links Dice_Distribution_(bar). ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ... A central limit theorem is any of a set of weak-convergence results in probability theory. ... In mathematics and, in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. ...

where for all and 0 otherwise.

A fastest algorithm would adapt the exponentiation by squaring algorithm, using . Exponentiating by squaring is an algorithm used for the fast computation of large integer powers of a number. ...

For example, in the triangular curve described above,

Equivalently, one can calculate the probability using combinations: In mathematics, particularly in combinatorics, a binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+1)n. ...

The probability of rolling any exact sequence of numbers is simply . For example, the chance of rolling 1, 2, and 3 in that order with three rolls of a six-sided die is , or .

The article Sampling equiprobably with dice describes the probabilities of sampling with dice from any range. An illustrative example of how to compute with the probabilities associated to dice, as well as the analysis of algorithms, is the following problem. ...

Application in role-playing games

Full set of matching dice used in roleplaying: a d4, d6, d8, d12, d20, and two d10s for percentile: ones and tens.

While polyhedral dice had previously been used in teaching basic arithmetic, the fantasy role-playing game Dungeons & Dragons is largely credited with popularizing their use in roleplaying games. Some games use only one type, such as Exalted which uses only ten sided dice, while others use numerous types for different game purposes, such as Dungeons & Dragons, which make use of 20-, 12-, 10-, 8- and 4-sided dice in addition to the traditional 6 sided die. Unlike the common six sided die, these dice often have the numbers engraved on them rather than a series of dots. Download high resolution version (2121x375, 61 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (2121x375, 61 KB) Wikipedia does not have an article with this exact name. ... For other uses, see Fantasy (disambiguation). ... This article is about games in which one plays the role of a character. ... This article is about the role-playing game. ... Exalted is a role-playing game published by White Wolf Publishing. ... This article is about the role-playing game. ...

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.

Roleplaying games generally use dice to determine the outcome of events, such as the success or failure of actions which are difficult to perform. A player may have to roll dice for combat, skill use, or magic use, amongst other things. This is generally considered fairer than decision by game master fiat, since success and failure are decided randomly based on a flat probability. Games typically determine success as either a total on one or more dice above (Dungeons & Dragons third edition) or below (Call of Cthulhu) a target number, or a certain number of rolls above a certain number (such as 8 or higher on a d10) on one or more dice (White Wolf's World of Darkness series). The player may gain a bonus or penalty due to circumstances or character skill, usually either by a number added to or subtracted from the final result, or by having the player roll extra or fewer dice. Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... In role-playing games, the game master or GM is the organizer, storyteller, and arbitrator. ...

Dice can also be used by a game master for other purposes, such as to randomly generate game content or to make arbitrary decisions. Some games use dice to determine what attributes the player's character has when created, such as how strong he or she is.

In Dungeons & Dragons and some other roleplaying games which use many types of dice, a dice notation is used. For example, a six-sided die is referred to as a d6, while two such dice rolled with the results totaled would be called 2d6. A bonus or penalty applied to the final result is referred to like 2d6+4 or 2d6-2. Games which use only one type of dice rarely require complex dice notation. A brass dice set. ...

A common special case is percentile rolls, referred to in dice notation as 1d100 or 1d%. Since actual hundred-sided dice are large, almost spherical, and difficult to read, percentile rolls are generally handled by rolling two ten-sided dice together, using one as the "tens" and the other as the "units". A roll of ten or zero on either die is taken as a zero, unless both are zeros or tens, in which case this is 100 (rather than zero). To avoid this confusion, sets of percentile dice exist where one is marked in tens (00, 10, 20... up to 90) and the other from 0 to 9.

Dice for role-playing games are usually made of plastic, though infrequently metal, wood, and semi-precious stone dice can be found. Early polyhedral dice from the 1970s and 1980s were made of a soft plastic that would easily wear as the die was used. Typical wear and tear would gradually round the corners and edges of the die until it was unusable. Many early dice were unmarked and players took great care in painting their sets of dice. Some twenty-sided dice of this era were numbered zero through nine twice; half of the numbers had to be painted a contrasting color to signify the "high" faces. Such a die could also double as a ten-sided die by ignoring the distinguishing coloring.

Use of dice for divination

Some people believe that dice can be used for divination. Using dice for such a purpose is called cleromancy. A pair of standard 6-sided dice is usual though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this method of divination. For other uses, see Divination (disambiguation). ... Cleromancy, sortilege, casting lots or casting bones is a form of divination in which an outcome is determined by random means, such as the rolling of a die. ...

It is uncertain if the Pythagoreans used the "Platonic Solids" as dice, but it is highly likely. They referred to these perfect geometries as "The Dice of the Gods". Julia E. Diggins, writer of "String, Straightedge, and Shadow" (Viking Press, New York, 1965) writes how the Pythagorean Brotherhood sought to understand the mysteries of the Universe through an understanding of geometry in polyhedra. It is recorded that the dodecahedron (12 sided platonic solid) was discovered by Pythagoras. (Guthrie: The Pythagorean Sourcebook) A Platonic solid is a convex polyhedron whose faces all use the same regular polygon and such that the same number of faces meet at all its vertices. ...

Astrological dice are a specialized set of three 12-sided dice for divination, using the concepts of astrology and containing astrological symbols for the planets, the zodiac signs and the astrological houses. The first die represents planets, the Sun, the Moon, and two nodes (North Node and South Node). The second die represents the 12 zodiac signs, and the third represents the 12 houses. In simplified terms, the planets, etc. could represent the 'actor'; the zodiac signs could represent the 'role' being played by the actor; and the house could represent the 'scene' in which the actor plays. Hand-coloured version of the anonymous Flammarion woodcut (1888). ... A planet (from the Greek πλανήτης, planetes or wanderers) is a body of considerable mass that orbits a star and that produces very little or no energy through nuclear fusion. ... For other uses, see Zodiac (disambiguation). ... Most astrological systems divide the astrological chart (or natal chart) into twelve houses, which depend more on the time and place of birth (or initiation) than on the date. ... Sol redirects here. ... This article is about Earths moon. ...

Rune dice are a specialized set of dice for divination (runecasting), using the symbols of the runes printed on the dice. This article or section does not cite its references or sources. ... Technical note: Due to technical limitations, some web browsers may not display some special characters in this article. ...

An icosahedron is used to provide the answers of a Magic 8-Ball, which is conventionally used to provide advice on yes-or-no questions. The standard face of a Magic 8-Ball The Magic 8-Ball, manufactured by Mattel, is a toy used for fortune-telling. ...

See also

• Fuzzy dice - car accessory
• Craps - on the casino game.
• Liar's dice - dice gambling game.
• Mia - a very old dice game.
• Mexico - dice gambling game.
• Pig - dice gambling game.
• Threes - street dice game.
• Yahtzee - modern dice game.
• Barrel Dice - uncommon type of polyhedral dice
• Nontransitive dice

This does not cite any references or sources. ... Craps (previously known as crabs[1]) is a casino dice game. ... This article or section does not cite any references or sources. ... It has been suggested that Kuriki be merged into this article or section. ... Pig is a simple folk jeopardy dice game first described in print by John Scarne in 1945 (Scarne, John. ... Threes (or 3s) is a gambling game, played with five dice where the goal is to get the lowest score in any given round. ... This article is about the game. ... There are very few or no other articles that link to this one. ... A set of nontransitive dice is a set of dice for which the relation is more likely to roll a higher number is not transitive. ...

References

• Persi Diaconis and Joseph B. Keller. "Fair Dice". The American Mathematical Monthly, 96(4):337-339, 1989. (Discussion of dice that are fair "by symmetry" and "by continuity".)
• Bias and Runs in Dice Throwing and Recording: A Few Million Throws. G. R. Iverson. W. H. Longcour, et al. Psychometrika, Vol. 36, No. 1, March 1971
• Knizia, Reiner (1999). Dice Games Properly Explained. Elliot Right Way Books. ISBN 0-7160-2112-9.

Gregory Possehl is a Professor of Anthropology at the University of Pennsylvania. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 177th day of the year (178th in leap years) in the Gregorian calendar. ... Reiner Knizia is a prolific German-style board game designer. ...

External links

Wikimedia Commons has media related to:

Dice

• Wolfram MathWorld: Dice Analysis of dice probabilities, also features Uspenski's work on rolling multiple dice.
• mathematically "Fair Dice"
  • Fair Dice is an illustrated Math Games column about all the possible fair dice, and the mathematical reasons why other shapes are not fair.
  • a complete list of all possible Fair Dice which has nice illustrations
  • "Properties of Dice" describes all solids that make for provably fair dice, and gives more details about all possible Fair Dice
  • The Bone Rollers' Guide to Polyhedral Solids describes how to design a fair dice and lists some ways to "stretch" dice in ways that are still fair.
• World's Largest Dice Collection Links, Photos, Information about dice
• Computer Simulation of Irregular Dice
• nontransitive dice
• A Pair Of Dice Which Never Roll 7
• A Brief History of Dice (in Dungeons & Dragons games)
• Divinity Dice Dice and Dice Divination history, with games and interpretations.
• The Dicer – Nice virtual hexahedron dice machine.

This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain. This article is about the role-playing game. ... Encyclopædia Britannica, the eleventh edition The Encyclopædia Britannica Eleventh Edition (1910–1911) is perhaps the most famous edition of the Encyclopædia Britannica. ... The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...