dice

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(dīs) pronunciation
n.
  1. Plural of die2 (sense 3).
  2. pl., dice, also dices.
    1. A small cube, as of food.
    2. A dish of diced food.

v., diced, dic·ing, dic·es.

v.intr.
To play or gamble with dice.

v.tr.
  1. To win or lose (money) by gambling with dice.
  2. To cut (food) into small cubes.
  3. To decorate with dicelike figures.

[Pl. of DIE2 .]



is in origin the plural of die (as in the die is cast, meaning 'the decisive step has been taken'). Dice are also the small cubes bearing 1 to 6 spots on each face, used in games of chance; this form is also used for the singular (He had a dice in his pocket).

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Set of small cubes (each called a die) marked on each face with from one to six spots and used in gambling and in various social games by being shaken and thrown down to come to rest at random on a flat surface. The combined number of the spots on the topmost surface of the tossed dice decides, according to the rules of the game being played, whether the thrower (or shooter) wins, loses, or continues to throw. In numerous board games the thrown dice determine the player's moves. Dice, which may be traced back to prehistory, were in many cultures magical devices used for the casting of lots to divine the future. In the modern era they became associated with the playing of games of chance, including craps.

For more information on dice, visit Britannica.com.

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Background

Dice are implements used for generating random numbers in a variety of social and gambling games. Known since antiquity, dice have been called the oldest gaming instruments. They are typically cube-shaped and marked with one to six dots on each face. The most common method of dice manufacture involves injection molding of plastic followed by painting.

History

Dice have been used for gaming and divination purposes for thousands of years. Evidence found in Egyptian tombs has suggested that this civilization used them as early as 2000 B.C. Other data shows that primitive civilizations throughout the Americas also used dice. These dice were composed of ankle bones from various animals. Marked on four faces, they were likely used as magical devices that could predict the future. The ancient Greeks and Romans used dice made of bone and ivory. The dice of most of these early cultures were made in numerous shapes and sizes. The modern day cubical dice originated in China and have been dated back as early as 600 B.C. They were most likely introduced to Europe by Marco Polo during the fourteenth century.

Dice were typically handcrafted and produced on a small scale up until the twentieth century. As plastic technology emerged, methods for applying it to dice manufacture were developed. This allowed manufacturers to produce mass quantities of dice in a cost effective manner. Over the years a variety of patents for improved methods of dice manufacture have been granted.

Design

The standard die is a six-sided, plastic cube. Each side is typically marked with one to six spots, or dots. These dots are arranged such that opposite sides always total seven. For example, the one dot side is opposite the six dot side and the three dot side is opposite the four dot side. In a two dice game, the dice are shaken and thrown on a surface. The rolled amount is indicated by the sides of the dice that are face up. If the dice are well-balanced and fair, each side has an equal chance of landing face up. Depending on the game, the player will either move her piece or collect money based on this rolled amount. Some popular gambling games that use dice include craps, chuck-a-luck, and poker dice. Board games such as backgammon, Monopoly, and Parcheesi also use dice.

Standard dice are available in a wide variety of sizes and colors. For board games a pair of 12 mm dice are typically used. These dice are considered imperfect because they have rounded corners, which reduce randomness. Since these dice are often used in children's games, they must be designed to meet certain toy safety standards. Casinos use perfect dice that may be hand made. They are generally larger than board game dice with a side measuring 33 mm. These are red, translucent dice which have precision-edges and corners and white dots. With this construction, rolls with these dice have the greatest probability of being fair.

Specialty dice are produced for many different applications. In some cases, the spots on a standard cube die are replaced by words, pictures, or symbols. Divining dice, which are used to predict future events, have different predictive messages on each face. Poker dice have card faces printed on each side. For blind people, Braille dice are available. Some games require dice that have a different number of sides and can provide a greater number of outcomes than standard dice. These polydice can have anywhere from three to 20 sides. They are used extensively in fantasy role playing games.

The key design element of dice manufacture is the mold. A mold is a cavity carved in steel that has the shape of the product that it forms. Typically, a mold is made up of two pieces which are forced together to form the cavity. When a plastic is injected into this mold, it takes on the mold's shape as it hardens. Since dice are solid cubes, using a standard mold is not practical because they would take too long to cool. For mass production of dice a special mold design is used. This mold is made up of separate chambers, which create individual elements of the die. As the individual pieces cool, they can be forced together to create a unified single object. The mold is then opened and the die is ejected. Special release agents are used to help make the plastic easier to remove from the mold. This mold design saves time because the smaller pieces can cool more rapidly.

Raw Materials

Numerous materials have been forged into dice throughout history. This includes such things as bones, glass, wood, seeds, and metals. Today, the most widely used base material for dice manufacture is plastic. Plastics are high molecular weight polymers that are produced through a variety of chemical reactions. For a plastic to be suitable in dice manufacture it must have good impact strength, be easily colored, and heat stable. It is also desirable that it be clear, colorless, and transparent. Most dice are made with a thermoset plastic. One plastic that meets all of these requirements is polymethyl methacrylate (PMMA). Cellulose based plastics are also used.

Since the polymer, which makes up the bulk of the plastic is typically colorless, colorants are added to make the dice more appealing. These may be soluble dyes or comminuted pigments. To produce a white color, an inorganic material such as titanium dioxide may be used. Other inorganic materials such as iron oxides can be used to produce yellow, red, black, brown and tan dice. Organic dyes such as pyrazolone reds, quinacridone violet, and flavanthrone yellow may also be utilized.

A host of other filler materials are added to the plastics to produce a durable, high quality set of dice. To increase the workability and flexibility of the polymer, a plasticizer is included. Plasticizers are nonvolatile solvents and include things such as paraffinic oils or glycerol. To improve the overall properties of the plastic, reinforcement materials such as fiberglass are added. During production the plastic is typically heated. For this reason, stabilizers must be added to protect the plastic from breaking down. Unsaturated oils such as soybean oil may be used as heat stabilizers. Other protective materials that are added include ultraviolet (UV) protectors such as benzophenones to prevent UV degradation and antioxidants such as aliphatic thiols to alleviate environmental oxidation. Finally, compounds are also used during manufacture to aid in processing. This generally includes materials like ethoxylated fatty acids, silicones, or metal stearates, which help with the removal of the plastic from the mold.

The Manufacturing
Process

The exact manufacturing process for any type of die depends on the base raw materials used. For mass production of imperfect standard dice an injection molding process is used followed by painting and packaging.

Forming

  • At the beginning of a dice manufacturing line, plastic pellets are transformed into dice via injection molding. The pellets are plastic beads that have all the colorants and fillers already added. They are placed into a large bin known as a hopper and passed through a hydraulically controlled screw. As they travel through the screw, they are heated and melted. At the end of this screw is a spreader which injects the molten material into a cool, closed two-piece mold.
  • The mold is made up of several chambers, which create multiple plastic parts. Inside the mold, the plastic is held under pressure and then allowed to cool. As it cools, the plastic pieces harden. The mold is then opened. When the mold is opened, the individual pieces are forced together to form a single solid cube. Because the mold was appropriately designed, this cube has indentations that will become the dots on each side. The cube is then ejected from the mold, coated and passed to the next phase of production via conveyor. Meanwhile, the two piece mold closes again making it ready to create the next die.

Painting and labeling

  • To complete the production of the die, they may be washed and dried before the final decorations are applied. First, the spots are appropriately painted. For specialty dice, words may be printed or images may be applied to each side. Company logos or other advertising may also be applied. These can be stickers or coatings. The coatings used during this step are specially formulated to adhere to the plastic and dry quickly.

Packaging

  • Depending on the final use of the dice, they may be bulk packaged for use in board games, or individually wrapped for consumer sale. For board games, the dice are packed up into boxes and shipped to game manufacturers just like any other component material. When they are sold directly to consumers, dice are typically put into plastic blister packs with a cardboard backing. This package has the dual purpose of protecting the dice during shipping and advertising the product. The finished dice are then placed in cases and shipped by truck to distributors.

Quality Control

To ensure that each die produced meets specified quality standards, a number of quality control measures are taken. Prior to manufacturing, certain physical and chemical properties of the incoming plastic raw materials are checked. This includes things such as molecular weight determinations, chemical composition studies, and visual inspection of the appearance. More rigorous testing may also be done. For example, stress-strain testing can be performed to determine the strength of the plastic. Impact tests help determine the toughness of the plastic. During manufacture, line inspectors are stationed at various points on the production line. Here, they visually check the plastic parts to make sure they are shaped, sized and colored correctly. They also check the integrity of the final packaging. If any defective dice are found, they are removed from the production line and set aside for reforming. Computers are also used to control plastic use, mold retention time, and line speed.

The Future

In the future, dice manufacturers will concentrate on increasing sales and improving the production process. To increase sales, dice marketers will be involved in developing new games that utilize different types of dice. These games will require new types of dice that may have different shapes, sizes, and plastic compositions. From a production standpoint, future improvements will focus on increasing manufacturing speeds, minimizing chemical waste, and reducing overall costs.

Where to Learn More

Books

Beasley, John. The Mathematics of Games. Oxford: Oxford University Press, 1990.

Chabot, J. The Development of Plastics Processing Machinery and Methods. Brookfield, IL: Society of Plastics Engineers, 1992.

Scarne, John. Scarne on Dice. Wilshire Book Co., 1992.

Seymour, R. and C. Carraher. Polymer Chemistry. New York: Marcel Dekker, Inc., 1992.

Periodicals

Chabot, J. and R. Malloy. "A History of Thermoplastics Injection Molding. Part I: The Birth of an Industry." Journal of Injection Molding Technology (March 1997).

Other

U.S. Patent #4,012,827, 1977.

[Article by: Perry Romanowski]


To cut food into tiny (about 1⁄8- to 1⁄4-inch) cubes.

dice [plural of die], small cubes used in games. They are usually made of ivory, bone, wood, plastic, or similar materials. The six sides are numbered by dots from 1 to 6, so placed that the sum of the dots on opposite sides equals 7. Dice much like those used today were found in ancient Egyptian tombs and in the ruins of Babylon. The playing of dice was popular in Greece and even more so in Rome, and dice were used throughout the Middle Ages. In the simplest form of play with dice each player throws, or shoots, for the highest sum. The most popular dice game in the United States is called craps. It is played with two dice; the underlying principle of the game is the fact that the most probable throw is a 7. On the first throw, if a player shoots 7 or 11 (called a natural) he wins and throws again, but if he shoots 2, 3, or 12 (called craps) he loses. If he shoots 4, 5, 6, 8, 9, or 10 that number becomes his point, and he continues to shoot until he makes his point, in which case he wins and retains the dice, or until he shoots a 7, in which case he loses and relinquishes the dice to the next player. Bets may be placed against the thrower or, in side bets, in favor of him. In gambling halls all bets are made with the house either for or against. There are numerous other dice games.

Bibliography

See studies by J. Scarne and C. Rawson (rev. ed. 1962) and H. A. Heritage (1969).


Dice fall under the meaning of the broader category of gambling because they are symbols of chance and even of fate (e.g., "the roll of the dice").


noun
noun, orig US

1:
no dice (It is or was) useless, hopeless, unsuccessful, profitless, etc. (1931 —) .
M. Pugh Nothing doing. I'm not going. No dice (1959). verb trans.

2:
Austral To reject; to leave alone, abandon. (1943 —) .
F. Hardy No bastard puts my daughter in the family way then dices her...and gets away with it (1963).

[Verb from earlier sense, to gamble away by playing dice.]


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abbr. for differentiation control element; a nucleotide sequence in the 3′ untranslated region of mRNA for 15-lipoxygenase. In erythroid precursor cells DICE binds and is repressed by the hnRN proteins K and E1. The repression is removed in the terminal stages of erythrocyte differentiation and the encoded lipoxygenase mediates mitochondrial breakdown.

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categories related to 'dice'

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Random House Word Menu by Stephen Glazier
For a list of words related to dice, see:

  See crossword solutions for the clue Dice.
Four coloured dice showing all six possible sides (on a right-handed, 6-sided die with pips)

A die (plural dice, from Old French , from Latin datum "something which is given or played")[1] is a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

A traditional die is an often rounded cube, with each of its six faces showing a different number (pips) from 1–6. The design as a whole is aimed at the die providing a randomly determined integer from one to six, each of those values being equally likely. A variety of similar devices are also described as dice; such specialized dice may have polyhedral or irregular shapes and may have faces marked with symbols instead of numbers. They may be used to produce results other than one through six. Loaded and crooked dice are designed to favor some results over others for purposes of cheating or amusement.

Contents

History

Bone die found at Cantonment Clinch (1823–1834), an American fort used in the American Civil War by both Confederate and Union forces at separate times.

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, an archeological site in south-eastern Iran.[2] Other excavations from ancient tombs in the Indus Valley civilization indicate a South Asian origin.[3] Dicing is mentioned as an Indian game in the Rigveda, Atharvaveda and Buddha games list;[4] it also plays a critical role in the great Hindu epic Mahabharata, where Yudhisthira plays a game of dice against the Kauravas for the northern kingdom of Hastinapura, which becomes the trigger for a war. There are several biblical references to "casting lots", as in Psalm 22, indicating that dicing was commonplace in the region during King David's reign. Knucklebones was a skill game played by women and children; a derivative form had the four sides of the bone receive different values and count as modern dice. Gambling with two or three dice was a very popular form of amusement in Greece, especially with the upper classes, and an invariable accompaniment to symposia.

Knucklebones die, made of steatite.

Dice were originally made from the talus of hoofed animals, colloquially known as "knucklebones". These are approximately tetrahedral, giving the term "bones" used for dice. Modern Mongolians still use such bones as shagai, for games and fortunetelling. Besides bone, materials like ivory, wood and recently plastics like cellulose acetate have been used. Dice are hard to differentiate from knucklebones because ancient writers confused the two, but both were used in prehistoric times.

The Romans were passionate gamblers, especially at the peak of the Roman Empire, and dicing was common though forbidden except during the Saturnalia. Horace derided what he thought as a typical youth of the period, who wasted time on dicing instead of horse-chasing. Throwing dice for money was the cause of many special laws in Rome; one of these stated that no lawsuit could be filed by a person who allowed gambling in his house, even if he had been cheated or assaulted. Professional gamblers were common; some of their loaded dice are preserved in museums. The public houses were the resorts of gamblers, and frescos exist showing two quarrelling dicers being ejected by the host. Twenty-sided dice date back to the 2nd century AD.[5]

A collection of historical dice from Asia.

Tacitus stated that the Germans were passionately fond of dicing, so much that they would stake their personal liberty when bankrupt. During the Middle Ages, dicing became the favorite pastime of the knights, with dicing schools and guilds. After the downfall of feudalism, the landsknechts established a reputation as the most notorious dicing gamblers of their time; many of the dice then were curiously carved in the images of men and beasts. In France, dicing was played by both knights and ladies, despite repeated legislation, including interdictions on the part of St. Louis in 1254 and 1256. The markings on Chinese dominoes evolved from the markings on dice.

Construction

Western, Asian and casino dice.

Common dice are small cubes most commonly 1.6 cm across, whose faces are numbered from one to six, usually by patterns of round dots called pips. (While the use of Hindu-Arabic numerals is occasionally seen, such as in the game Pop-O-Matic Trouble, the ambigrammatic properties of the digits (for instance, 6 can look like a 9 upside down) make such dice uncommon.) Traditionally, opposite sides of a die add up to seven, implying that the 1, 2 and 3 faces share a vertex;[6] these faces may be placed clockwise or counterclockwise about this vertex. If the 1, 2 and 3 faces run counterclockwise, the die is called right-handed and vice versa. Western dice are normally right-handed and Chinese dice are normally left-handed.[7]

Typical facets of an Asian-style (top) and a Western-style die (bottom). The pips on the Asian-style facets are arranged more compactly than the Western-style facets.

The pips on dice are arranged in specific patterns as shown in the picture to the left. Asian style dice bear similar patterns to Western ones, but the pips are closer to the centre of the face; the one's pip is larger than the others, with that and the four's pips coloured red. In some older sets, the "one" pip is a colorless depression. It is suggested[who?] that an entirely black and white color combination on the one's and four's sides would be unlucky; red, a lucky color in Chinese culture, would counteract this. The word for four in Chinese is a homophone of the word for death and is considered unlucky; it is probable that red fours are of Indian origin.[7][8]

The result of a die roll is determined by the way it is thrown, according to the laws of classical mechanics; they are made random by uncertainty due to factors like movements in the thrower's hand. Thus, they are a type of hardware random number generator. Some people[who?] claim that the pips on the faces of certain styles of dice cause a small bias, but there is no research to support this claim; this is reduced somewhat in the Asian die with its oversized single pip.[citation needed] Casino dice have flush markings, offering the assurance that this brings them very close to providing true uniformly distributed random numbers.[citation needed]

Dice are thrown, singly or in groups, from the hand or from a container designed for this, onto a flat surface; the face of the die that is uppermost when it comes to rest provides the value of the throw. A typical dice game today is craps, where two dice are thrown at a time and wagers are made on the total value of the two dice. Dice are frequently used to randomize moves in board games, usually by deciding the distance through which a piece will move along the board; examples of this are backgammon and Monopoly.

Clones of board games must use computer generated dice; the values are usually determined by a pseudorandom number generator, then displayed as a visual representation of a die. The reverse is also possible, with bar coded dice shuffling as a source of true random data for computers.[9]

Manufacturing

Non-precision dice are manufactured via the plastic injection molding process. The pips or numbers on the dice are a part of the mold. The coloring for numbering is achieved by submersing the dice entirely in paint, which is allowed to dry and then polished via a tumble finishing 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 creates the smoother, rounded edges on the dice.[10]

Precision 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 as the material used for the dice, such that the dice are as close to perfectly cubical as possible. All such dice are stamped with a serial number to prevent potential cheaters from substituting a die.[citation needed] 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.

Terms

While the terms ace, deuce, trey, cater, cinque and sice have been made obsolete by one to six, they are still used by some professional gamblers to designate different sides of the dice. Ace is from the Latin as, meaning "a unit";[11] the others are 2 to 6 in old French.

Notation

Using Unicode characters, the faces ⚀ ⚁ ⚂ ⚃ ⚄ ⚅, can be shown in text using the range U+2680–U+2685 or using decimal &9856;–&9861;.[12]

In many gaming contexts, especially tabletop RPGs, the count and number of sides of dice to be rolled at any given time is reduced to a common set of notations; typically these involve the letter "d" for dice. Hence, 6d8 means six eight-sided dice and 2d6 two common dice. Various arithmetic operations are often added at the end; 3d6+4 is three six-sided dice plus four to the outcome.

Loaded dice

A loaded, weighted or crooked die is one that has been tampered with to land with a specific side facing upwards more often than it normally would. There are several methods for creating loaded dice; these include round and off-square faces and (if not transparent) weights. Tappers have a mercury drop in a reservoir at the center, with a capillary tube leading to another reservoir at a side; the load is activated by tapping the die so that the mercury travels to the side.

Another type of loaded die is hollow with a small weight and a semi-solid substance inside whose melting point is just lower than the temperature of the human body, allowing the cheater to change the loading of the die by applying body heat, causing the semi-solid to melt and the weight to drift down, making the chosen opposite face more likely to land up. A less common type of loaded die can be made by inserting a magnet into the die and embedding a coil of wire in the game table; running current through the coil increases the likelihood of a certain side landing on the bottom, depending on the direction of the current. Transparent acetate dice, used in all reputable casinos, are harder to tamper with than other dice.

Shaved dice

A Boggle game requires dice with letters on them to create a field for players to search for words.

A die may be shaved on one side, making it slightly shorter in one dimension, thus affecting its outcome. One countermeasure employed by casinos against shaved dice is to measure the dice with a micrometer before playing.[13]

Variants

Dice with faces other than digit sequences

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, and instructions for sexual acts using sex dice.

Non-cubic dice

A Platonic solids set of five dice.
10-sided dice are used for games requiring percentages.

Seven- and eight-sided dice are stated in the 13th century Libro de los juegos to have been invented by Alfonso X in order to speed up play in chess variants.[14][15] Around the early 1950s,[citation needed] such non-cubical dice became popular among players of wargames, and since have been employed extensively in RPGs and TCGs. Although these are relative novelties now, ancient cultures appear to have used them in games, as evidenced by the discovery of two icosahedral dice dating from ancient Rome, currently on display in the British Museum. Reciprocally symmetric numerals are distinguished with a dot or by being underlined.

The Platonic solids are the most common non-cubical dice; these can make for 4, 8, 12, and 20 faces. The only other common non-cubical die is the 10-sided die. More uncommon dice include 3, 5, 7, 14, 16, 18, 24, 30, 50, and the 100 sided Zocchihedron. Using these dice in various ways, like 10-sided dice in pairs to produce a uniform distribution of random percentages and summing multiple dice to produce approximations to normal distributions, games can closely approximate the real probability distributions of the events they simulate.

The tetrahedral die can be marked in one of two ways – either the numbers are printed around the points, so that when it settles, the numbers at the vertex pointing up are the same and the one counted; or, the numbers can be placed at the middle of the edges, in which case the numbers around the base are read.

A die can be constructed in the shape of a sphere, with the addition of an internal cavity in the shape of the dual polygon 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.

Standard variations

Dice are often sold in sets, matching in color, of five or six different shapes: the five Platonic solids, whose faces are regular polygons, and optionally the pentagonal trapezohedron, whose faces are ten kites, each with two different edge lengths and three different angles; the die's vertices also are of two different kinds.

Normally, the faces on a die will be numbered sequentially beginning with 1, and opposite faces will thus add up to one more than the number of faces (but in the case of the d4 and dice with an odd-number of faces, this is simply not possible). Some dice, such as d10, are usually numbered sequentially beginning with 0, in which case the opposite faces will add to one less than the number of faces.

Sides Shape Notes
4 tetrahedron 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 Cube A common die. The sum of the numbers on opposite faces is seven.
8 octahedron Octahedron Each face is triangular; looks like two square pyramids attached base-to-base. Usually, the sum of the opposite faces is 9.
10 pentagonal trapezohedron Pentagonal trapezohedron Each face is a kite. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet. The ten faces usually bear numbers from zero to nine, rather than one to ten (zero being read as "ten" in many applications). Often all odd numbered faces converge at one sharp corner, and the even ones at the other. The sum of the numbers on opposite faces is usually 9 (numbered 0–9) or 11 (number 1–10).
12 dodecahedron Dodecahedron Each face is a regular pentagon. The sum of the numbers on opposite faces is usually 13.
20 icosahedron Icosahedron Faces are equilateral triangles. A 2nd century AD Roman icosahedron die is in the collection of the British Museum, though the game for which it was used is not known.[16] These are sometimes numbered 0–9 twice as an alternative to 10-sided dice. The sum of the numbers on opposite faces is 21 if numbered 1–20.

Rarer variations

Sides Shape Notes
1 sphere Most commonly a joke die,[citation needed] this is just a sphere with a 1 marked on it. About spherical dice that may produce more than one result, see the section non-cubical dice above. See also Monostatic polytope, Gömböc.
2 cylinder This is nothing more than a coin shape with 1 marked on one side and 2 on the other. While some tasks in roleplaying require flipping a coin, the game rules usually simply call for the use of a coin rather than requiring the use of a two-sided die. It is possible, however, to find dice of this sort for purchase, but they are rare, and can typically be found among other joke dice.
3 Rounded-off triangular prism This is a rounded-off triangular prism, intended to be rolled like a rolling-pin style die. The die is rounded-off at the edges to make it impossible for it to somehow land on the triangular sides, which makes it look a bit like a jewel. When the die is rolled, one edge (rather than a side) appears facing upwards. On either side of each edge the same number is printed (from 1 to 3). The numbers on either side of the up-facing edge are read as the result of the die roll. Another possible shape is the "American Football" or "Rugby ball" shape, where the ends are pointed (with rounded points) rather than just rounded. A third variety features faces that resemble warped squares.
5 Triangular prism This is a prism that is thin enough to land either on its "edge" or "face". When landing on an edge, the result is displayed by digits (2–4) close to the prism's top edge. The triangular faces are labeled with the digits 1 and 5.
7 Pentagonal prism Similar in constitution to the 5-sided die. When landing on an edge, the topmost edge has pips for 1–5. The pentagonal faces are labeled with the digits 6 and 7. This kind of die is particularly odd since it has pips for five of its results and digits for two of them. Seven-sided dice are used in a seven-player variant of backgammon. Some variants have heptagonal ends and rectangular faces.
12 rhombic dodecahedron Each face is a rhombus.
14 heptagonal trapezohedron Each face is a kite.
16 octagonal dipyramid Each face is an isosceles triangle.
24 tetrakis hexahedron Each face is an isosceles triangle.
24 deltoidal icositetrahedron Each face is a kite.
30 rhombic triacontahedron Each face is a rhombus. Although not included in most dice kits, it can be found in most hobby and game stores.
34 heptadecagonal trapezohedron Each face is a kite.
50 icosakaipentagonal trapezohedron The faces of the 50-sided die are kites, although very narrow.
100 Zocchihedron 100-sided dice can be found in hobby and game stores. They are not, however, a true polyhedron. A 100-sided die is made by flattening 100 facets on a sphere.

The full geometric set of "uniform fair dice" (face-transitive) are:

  • Platonic solids, the five regular polyhedra: 4, 6, 8, 12, 20 sides
  • Catalan solids, the duals of the 13 Archimedean solids: 12, 24, 30, 48, 60, 120 sides
  • Bipyramids, the duals of the infinite set of prism, with triangle faces: any even number above 4
  • Trapezohedrons, the duals of the infinite set of antiprisms, with kite faces: any even number above 4
  • Disphenoids, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides
  • "Rolling-pin style dice" are the only way to make dice with an odd number of flat faces.[17] 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 die never actually rests on those faces.)

Probability

Probability density function, p(S), for the sum of two fair six-sided dice, S.

For a single roll of a fair s-sided die, the probability of rolling each value is exactly 1/s; this is an example of a discrete uniform distribution. For n multiple rolls, with a s-sided die the possibility space is equal to sn. So, for n rolls of an s-sided die the probability of any result is 1/sn.

However, if we are rolling two dice and adding the result together, as in the game craps, the total is distributed in a triangular curve; the case for common dice follows:

Sum 2 3 4 5 6 7 8 9 10 11 12
Probability 1/36
 
2/36
=1/18
3/36
=1/12
4/36
=1/9
5/36
 
6/36
=1/6
5/36
 
4/36
=1/9
3/36
=1/12
2/36
=1/18
1/36
 
Comparison of probability density functions, p(k) for the sum of n fair 6-sided dice to show their convergence to a normal distribution with increasing n, in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve).

As the number of dice increases, the distribution of the sum of all numbers tends to normal distribution by the central limit theorem; the exact value F_{s,n}(k) of a sum of n s-sided dice, k, is

F_{s,n}(k) = \sum_{i=1}^{k-n+1} {F_{s,1}(i) F_{s,n-1}(k - i)} \,

where Fs,1(k) = 1/s for 1 ≤ k ≤ s and 0 otherwise.

A faster algorithm would adapt the exponentiation by squaring algorithm:

F_{s,x+y}(k) = \sum_i {F_{s,x}(i) F_{s,y}(k - i)} \,.

In the triangular curve described above,


\begin{align}
F_{6,2}(6) & =\sum_n {F_{6,1}(n) F_{6,1}(6 - n)} \\
& =F_{6,1}(1) F_{6,1}(5) + F_{6,1}(2) F_{6,1}(4) + \\
& \qquad \cdots + F_{6,1}(5) F_{6,1}(1) \\[6pt]
& = 5\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{5}{36}\approx0.14
\end{align}

Equivalently, the probability can be calculated using combinations:

F_{s,n}(k)=\frac{1}{s^n}\sum_{i=0}^{\left \lfloor \frac{k-n}{s} \right \rfloor} (-1)^i {n \choose i} {k-si-1 \choose n-1}

where \lfloor {x} \rfloor is the floor function. The probability of rolling an exact sequence of numbers is 1/sn.

Application in role-playing games

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.

The fantasy role-playing game Dungeons & Dragons (D&D) is largely credited with popularizing dice in such games. Some games use only one type, like Exalted which uses only ten-sided dice. Others use numerous types for different game purposes, such as D&D, which makes use of all common polyhedral dice.

Dice are used to determine the outcome of events; such usage is called a check. 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.

A common special case is percentile rolls, referred to as 1d100 or 1d%. Since actual hundred-sided dice are large, almost spherical, and difficult to read, percentile rolls are instead 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. Some sets of percentile dice explicitly mark one die in tens and the other in units to avoid ambiguity.

Dice for role-playing games are usually plastic; early polyhedral dice from the 1970s and 1980s were made of a soft plastic that would easily wear as the die was used, and wear would gradually render the die unusable. Many early dice were unmarked, and players took great care in painting them. Some twenty-sided dice then were numbered zero through nine twice; half of the numbers had to be painted a contrasting color to differentiate faces. These could double as a ten-sided die by ignoring the distinguishing coloring.

Application in divination

Dice can be used for divination; using dice for such a purpose is called cleromancy. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this method of divination. It is highly likely that the Pythagoreans used the Platonic solids as dice;[citation needed] 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.[18]

Astrological dice are a specialized set of three 12-sided dice for divination; the first die represents 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. An icosahedron provides the answers of the Magic 8-Ball, conventionally used to provide advice on yes-or-no questions.

See also

Notes

  1. ^ AskOxford: die
  2. ^ presstv.ir
  3. ^ Possehl, Gregory. "Meluhha". In: J. Reade (ed.) The Indian Ocean in Antiquity. London: Kegan Paul Intl. 1996a, 133–208
  4. ^ 2.3, 4.38, 6.118, 7.52, 7.109
  5. ^ christies.com
  6. ^ Cf. Greek Anthology Book 14, §8: "The Opposite Pairs of Numbers on a Die. The numbers on a die run so: six one, five two, three four."
  7. ^ a b Standard Dice from dice-play
  8. ^ Chinese Dice from the Elliott Avedon Museum & Archive of Games
  9. ^ Bar Coded Dice for Digital Entropy Collection
  10. ^ How Dice Are Made from Awesome Dice
  11. ^ AskOxford: ace<
  12. ^ "Dice faces in block Miscellaneous Symbols". The Unicode standard. http://www.unicode.org/charts/PDF/U2600.pdf. 
  13. ^ fullbooks.com
  14. ^ games.rengeekcentral.com
  15. ^ wwmat.mat.fc.ul.pt
  16. ^ Thompson, Clive (December 2, 2003). "Ancient Roman dungeonmastering". Collision Detection. http://www.collisiondetection.net/mt/archives/2003/12/ancient_roman_d.html. Retrieved 2006-06-26. 
  17. ^ Properties of Dice
  18. ^ Guthrie, Kenneth (1988). The Pythagorean sourcebook and library : an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Grand Rapids, Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 255212063. 

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, and others. Psychometrika, Vol. 36, No. 1, March 1971
  • Knizia, Reiner (1999). Dice Games Properly Explained. Elliot Right Way Books. ISBN 0-7160-2112-9.

External links

 This article incorporates text from a publication now in the public domainChisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press. 


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Dansk (Danish)
n. - terninger, terningspil, rafling
v. intr. - rafle, spille hasard
v. tr. - spille, skære i terninger, kassere, tegne tern på

idioms:

  • dice away    spille op
  • no dice    den går ikke

Nederlands (Dutch)
dobbelstenen (ook enkelvoud), dobbelen, in dobbelsteentjes snijden

Français (French)
n. - dé (à jouer)
v. intr. - jouer aux dés, couper qch en cubes
v. tr. - couper en dés/en cubes

idioms:

  • dice away    couper en cubes
  • dice with death    jouer avec la mort
  • no dice    pas question, pas de chance

Deutsch (German)
v. - würfeln, Würfel spielen
n. - Würfel, Würfelspiel

idioms:

  • dice away    etwas beim Würfeln verlieren
  • dice with death    Würfeln mit dem Tot
  • no dice    (fig)(ugs) kommt nicht in frage!

Ελληνική (Greek)
n. pl. - κύβος ή κύβοι (κυβοπαιξίας), ζάρι(α)
v. - παίζω ζάρια, προσδίδω ή κόβω σε σχήμα κύβου, κυβοποιώ

idioms:

  • dice away    χάνω στα ζάρια
  • no dice    ανώφελο

Italiano (Italian)
giocare ai dadi, dado

idioms:

  • load the dice against    tramare contro

Português (Portuguese)
n. pl. - dados (m)
v. - jogar dados, cortar em cubos

idioms:

  • dice away    fatiar
  • load the dice against    forçar os resultados
  • no dice    inútil

Русский (Russian)
резать кубиками, кубики, игральные кости

idioms:

  • dice away    проигрывать
  • load the dice against    все уже настроено против него
  • no dice    Нет!

Español (Spanish)
n. - dado
v. intr. - jugar a los dados, arriesgarse
v. tr. - cortar en cubos, adornar con cuadros

idioms:

  • dice away    perder por apostar
  • dice with death    jugar con la vida
  • no dice    inútil

Svenska (Swedish)
n. pl. - tärningar
v. - spela tärning, kok. skära i bitar, göra rutig

中文(简体)(Chinese (Simplified))
骰子, 掷骰子, 切成方块

idioms:

  • dice away    赌输掉...
  • no dice    不行

中文(繁體)(Chinese (Traditional))
n. - 骰子
v. intr. - 擲骰子
v. tr. - 切成方塊

idioms:

  • dice away    賭輸掉...
  • no dice    不行

한국어 (Korean)
n. - 주사위, 내기, 작은 입방체
v. intr. - 내기하다, 주사위놀이 하다, (자동차 시합에서) 유리한 자리를 경쟁하다
v. tr. - 내기해서 탕진하다, 주사위 모양으로 자르다, 거부하다

idioms:

  • dice away    ~를 노름으로 날리다

日本語 (Japanese)
n. - さいころ, ばくち, 位置のせり合い, 小立方体, さい
v. - 賭博で失う, さいころで遊ぶ, 位置をせり合う, さいの目に切る, さいの目形にする, さいころ遊びをする, ばくちで失う

idioms:

  • dice away    博打で失う
  • no dice    だめ, うまくいかない

العربيه (Arabic)
‏(الجمع) حجارة النرد ( مكعب صغير من الخشب أو البلاستيك يستخدم في ألعاب الحظ مثل طاوله الزهر), أي لعبه تلعب برمي حجر النرد (فعل) يقعط اللحوم والخضار مثلا الى مكعبات صغيرة‏

עברית (Hebrew)
n. - ‮קובייה, קוביות‬
v. intr. - ‮שיחק בקוביות, הימר‬
v. tr. - ‮חתך (מזון) לקוביות, קצץ, הימר, סימן בריבועים‬


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