Dice

Dice (singular die or dice; from Old French dé; from Latin datum "something which is given or played") are small throwable objects with multiple resting positions, used for generating random numbers. Dice are suitable as gambling devices for games like craps, and are also used in non-gambling tabletop games.

A traditional die is a rounded cube, with each of its six faces showing a different number of dots (pips) from 1 to 6. When thrown or rolled, the die comes to rest showing on its upper surface a random integer from one to six, each value 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.

A dice tray or a dice box is a piece of gaming equipment, a tray used to contain thrown dice, for gambling or board games. One traditional form used in Flemish dice games is an octagonal shaped wooden tray, lined with fabric. A dice tray can be used to play games on its own or as an add-on for other board games, in particular to allow dice throws which do not interfere with other game pieces.

History
Dice have been used since before recorded history, and it is uncertain where they originated. 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. Other excavations from ancient tombs in the Indus Valley civilization indicate a South Asian origin. Dicing is mentioned as an Indian game in the Rigveda, Atharvaveda and Buddha games list. 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 (or a related activity) was commonplace when the psalm was composed. 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 a frequent accompaniment to symposia.

Dice were originally made from the talus of hoofed animals, colloquially known as "knucklebones". These are approximately tetrahedral, leading to the nickname "bones" for dice. Modern Mongolians still use such bones as shagai for games and fortunetelling. Besides bone, materials like ivory, wood and plastics such as cellulose acetate have been used. Dice are hard to distinguish from knucklebones in literature 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 youths who wasted time on dicing instead of horse-chasing. Throwing dice for money was the cause of many special laws in Rome, one of which 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, and some of their loaded dice are preserved in museums. The public houses were the resorts of gamblers, and depictions of quarreling dicers can be seen on frescos. Twenty-sided dice date back to the 2nd century AD and late BC.

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 a favorite pastime of knights, who formed dicing schools and guilds. After the downfall of feudalism, the landsknechts established a reputation as the most notorious dicing gamblers of their time. In France dice were used by both knights and ladies, despite repeated legislation against gambling with dice, including interdictions on the part of St. Louis in 1254 and 1256. The markings on Chinese dominoes evolved from the markings on dice.

Usage
Dice are thrown onto a flat surface either from the hand or from a container designed for this (such as a dice cup). The face of the die that is uppermost when it comes to rest provides the value of the throw. One 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.

The result of a die roll is determined by the way it is thrown, according to the laws of classical mechanics. A die roll is made random by uncertainty in minor factors such as tiny movements in the thrower's hand; They are thus a crude form of hardware random number generator. Perhaps to militate against concerns that the pips on the faces of certain styles of dice cause a small bias, casinos use precision dice with flush markings.

Arrangement
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 dice are less common.) Opposite sides of a die traditionally add up to seven, implying that the 1, 2 and 3 faces share a vertex; 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 if those faces run clockwise, the die is called "left-handed". Western dice are normally right-handed, and Chinese dice are normally left-handed.

The pips on dice are arranged in specific patterns as shown. Asian style dice bear similar patterns to Western ones, but the pips are closer to the centre of the face; in addition, the pips are differently sized on Asian style dice, and the pips are colored red on the 1 and 4 sides. One possible explanation is that red fours are of Indian origin. In some older sets, the "one" pip is a colorless depression.

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 submerging 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.

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 center of gravity of the dice is as close to the geometric center as possible. All such dice are stamped with a serial number to prevent potential cheaters from substituting a die. Precision backgammon dice are made the same way; they tend to be slightly smaller and have rounded corners and edges, to allow better movement inside the dice cup and stop forceful rolls from damaging the playing surface.

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"; 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 to U+2685 or using decimal  to.

In many gaming contexts, especially tabletop role-playing games, it is common to see shorthand notations representing different dice rolls. A "d" or "D" is used to indicate a die with a specific number of sides,  indicating a four-sided die, for example. If several dice of the same type are to be rolled, this is indicated by a leading number specifying the number of dice. Hence,  means the player should roll six eight-sided dice. Modifiers to a die roll can also be indicated as desired. For example,  instructs the player to roll three six-sided dice, calculate the total, and add four to it.

Loaded dice
A loaded, weighted or crooked die is one that has been tampered with so that it will land with a specific side facing upwards more or less often than a fair die would. There are several methods for creating loaded dice, including round faces, off-square faces and 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.

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.

Non-numeric
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, playing card symbols for poker dice, and instructions for sexual acts using sex dice.

Non-cubic
Seven- and eight-sided dice are described in the 13th century Libro de los juegos as having been invented by Alfonso X in order to speed up play in chess variants. Around the end of the 1960s, non-cubical dice became popular among players of wargames, and since have been employed extensively in role-playing games and trading card games. Reciprocally symmetric numerals like 6 and 9 are distinguished with a dot or underline.

The other four Platonic solids are the most common non-cubical dice; these can have 4, 8, 12, and 20 faces. The only other common non-cubical die is the 10-sided die. The 4-sided platonic solid is difficult to roll, and a few games like Dayakattai and Daldøs use a 4-sided barrel die instead. Using these dice in various ways, games can closely approximate the real probability distributions of the events they simulate. For instance, 10-sided dice can be rolled in pairs to produce a uniform distribution of random percentages; and summing the values of multiple dice will produce approximations to normal distributions.

Unlike other common dice, a tetrahedral die does not have a side that faces upward when it is at rest on a surface, so it has to be read in a different way. Many such dice have the numbers printed around the points, so that when it settles, the numbers at the vertex pointing up are the same and the one counted. Less commonly, the numbers on a tetrahedral die 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 polyhedron 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. They are also sold frequently with a second 10-sided die of a complementary or contrasting color. Sometimes, dice are sold additionally with a die resembling the five Platonic solids, whose faces are regular polygons, or the pentagonal trapezohedron die, whose faces are ten kites, each with two different edge lengths, three different angles, and two different kinds of vertices.

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 a dice with 4 sides and dice with an odd-number of faces, this is simply not possible). Some dice, such as a dice with 10 sides, are usually numbered sequentially beginning with 0, in which case the opposite faces will add to one less than the number of faces.

Rarer variations
"Uniform fair dice" are dice where equal probability of the faces follow from the symmetry of the die (as it is face-transitive), and include:
 * 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 prisms, 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

Dice with an odd number of flat faces can be made as "rolling-pin style dice". 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.)

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

Dice are 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  or. 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 with use, which would gradually render them 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 and using dice for such a purpose is called cleromancy. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this method of divination. It is highly likely that the Pythagoreans used the Platonic solids as dice. They referred to such dice as "the dice of the gods" and they sought to understand the universe through an understanding of geometry in polyhedra.

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 answers to yes-or-no questions.