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Dice

2007 Schools Wikipedia Selection. Related subjects: Games

   Two standard six-sided pipped dice with rounded corners.
   Enlarge
   Two standard six-sided pipped dice with rounded corners.
   Japanese die, with its distinctive oversized pip.
   Enlarge
   Japanese die, with its distinctive oversized pip.
   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.
   Enlarge
   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.

   A die ( Old French de, from Latin datum "something given or played" )
   is a small polyhedral object, usually cubical, 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.

   Traditionally, a die is seldom seen alone, and is rather one of a pair
   of identical dice that are sized to be comfortably rolled or thrown,
   together, from a user's hand. Because of this, the singular word "die"
   is rare, but treating "dice" as interchangeably singular or plural is
   less common; the plural form "dices" is rarer still.

   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.

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

   Dice are thrown to provide random numbers for gambling and other games
   and thus are a type of hardware random number generator. However,
   because the numbers on toy 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.

   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 such as Backgammon.

History

   Knucklebone dice, made of Steatite
   Enlarge
   Knucklebone dice, made of Steatite

   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. Even today in English, dice are sometimes
   colloquially referred to as "bones", as in "shake them bones". Ivory,
   bone, wood, metal, and stone materials have been commonly used, though
   the use of plastics is now nearly universal. It is almost impossible to
   trace clearly the development of dice as distinguished from
   knucklebones, because ancient writers confused the two games. It is
   certain, however, that both were played in prehistoric times.
   A collection of historical dice from Asia
   Enlarge
   A collection of historical dice from Asia

   Dice have been used throughout Asia since time immemorial.

   The oldest known dice was 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, seem
   to further indicate a South Asian origin. Dicing is mentioned as an
   Indian game in the Rig Veda, Atharva Veda 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 banquets (symposia).

   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.

   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 favourite 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.

   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.

Materials

   Precision backgammon dice
   Enlarge
   Precision backgammon dice

   Dice have been made from a wide variety of materials throughout
   history, including stone, wood, and animal bones, and more recently,
   bakelite and plastic.

Precision dice

   Precision casino dice, used for the game of craps, are made from
   cellulose acetate. These dice 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
   specific gravity as the acetate, such that the dice remain in perfect
   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.

   Precision backgammon dice are also made from acetate, or a similar
   material, with the pips filled in as is done 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.

Polyhedral dice

   Metal dice, made of brass
   Enlarge
   Metal dice, made of brass

   It is unknown of what material the earliest polyhedral dice were made.
   A pair of icosahedral (20-sided) dice dating from Roman times are on
   display at the British Museum.

   Roughly cubical six-sided Roman dice made of wood, bone, ivory and lead
   have been discovered. It is possible that polyhedral dice were used by
   even earlier cultures.

   Polyhedral dice are usually made of plastic, though infrequently metal,
   wooden, 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. Modern
   polyhedral dice are typically made of high-impact plastic and can
   withstand years of use without visible wear.

   Polyhedral dice can be purchased at most hobby stores in numerous
   combinations. In the early days of role-playing games, most dice came
   with the numbers uninked and players took great care in painting their
   sets of dice. Some twenty-sided dice of this era came numbered zero
   through nine twice; half of the numbers had to be painted a contrasting
   colour to signify the "high" faces. Such a die could also double as a
   ten-sided die by ignoring the distinguishing coloring.

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" ; the others are the numbers 2–6 in old French.

Dice Notation

   Often the names of the dice appear in formulas for calculating game
   parameters: e.g., hit points. "6d8+10", for example, will yield a
   number between 16 (6×1+10) and 58 (6×8+10), as it means "Roll an
   eight-sided die six times and add ten to the total." Occasionally they
   may be written "1d6×10+20"; this means "Roll one six-sided die.
   Multiply it by ten and add twenty."

"Crooked" dice

   "Crooked dice" refers to dice that have been altered in some way to
   change the distribution of the dice's 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 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
   centre 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 centre 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.

   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.

   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.

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.

Variants

Dice with faces other than digit sequences

   As noted, the faces of most dice are labelled using an unbroken series
   of whole numbers, starting at one (or zero), expressed with either pips
   or digits. Common exceptions include:
     * colour 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
   Enlarge
   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 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.
     * 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 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.

Non-cubical dice

   Barrel Dice
   Enlarge
   Barrel Dice

   Some dice are polyhedra other than cubes in shape. They were once
   almost exclusively used by fortune-tellers and in other occult
   practices, but they have become popular lately (at least since 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).

   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 2, 5, 7, 10, 16,
   24, 30, 34, 50, or 100 sides, 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.
   20-sided die 10-sided die 4-sided die
   20-sided die 10-sided die 4-sided die

   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.

   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.

   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.)

Standard variations

   A matched Platonic-solids set of five dice, (from left) tetrahedron,
   cube, octahedron, dodecahedron and icosahedron.
   A matched Platonic-solids set of five dice, (from left) tetrahedron,
   cube, octahedron, dodecahedron and icosahedron.

   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.
   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 something like
   two Egyptian pyramids attached at the base. Usually, the sum of the
   opposite faces is 9.
   10 pentagonal trapezohedron 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 Dodecahedron Each face is a regular pentagon.
   20 icosahedron Icosahedron Faces are equilateral triangles. Typically,
   opposite faces add to twenty-one. A Roman icosahedron die from the 2nd
   century AD has been found, though the game it was used for is not
   known.

Rarer variations

   Sides Shape Notes
   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, it is usually referred to as such, and not as rolling
   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 essentially 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.
   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 "pyramid"'s top. 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 in the shape of a rhombus.
   14 heptagonal dipyramid Each face is in the shape of an isosceles
   triangle.
   16 octagonal dipyramid Each face is in the shape of an isosceles
   triangle.
   24 tetrakis hexahedron Each face is in the shape of an isosceles
   triangle.
   24 deltoidal icositetrahedron Each face is in the shape of a kite
   (geometry).
   30 rhombic triacontahedron Each face is in the shape of a rhombus
   (diamond-shaped).
   50 icosakaipentagonal dipyramid Just like the 14- and 16-sided dice,
   the faces of the 50-sided die are isosceles triangles, although very
   narrow.
   100 Dice of this sort are rare. See main article.

   The full geometric set of "uniform fair dice" (with all congruent
   sides) are:
     * 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)

   Rolling-pin style dice are usually made so that all the faces they may
   actually land on are congruent, so they are equally fair.

Probability

   For a single roll of an 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 a six-sided die, for example, the probability distribution
   is as follows:
   Probability distribution for the sum of two six-sided dice
   Enlarge
   Probability distribution for the sum of two six-sided dice

                                     Sum
                                      2
                                      3
                                      4
                                      5
                                      6
                                      7
                                      8
                                      9
                                     10
                                     11
                                     12
                                 Probability
                                   ^1/[36]
                                   ^2/[36]
                                   ^3/[36]
                                   ^4/[36]
                                   ^5/[36]
                                   ^6/[36]
                                   ^5/[36]
                                   ^4/[36]
                                   ^3/[36]
                                   ^2/[36]
                                   ^1/[36]
                          Probability (simplified)
                                   ^1/[36]
                                   ^1/[18]
                                   ^1/[12]
                                   ^1/[9]
                                   ^5/[36]
                                   ^1/[6]
                                   ^5/[36]
                                   ^1/[9]
                                   ^1/[12]
                                   ^1/[18]
                                   ^1/[36]

   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] for any number of s-sided dice i can be
   calculated as the repeated convolution of the single-die probability
   distribution with itself.

          F_{s,i}(k) = \sum_n {F_{s,1}(n) F_{s,i-1}(k - n)} \,

   where F_{s,1}(k) = \frac{1}{s} for all 1\leq k \leq s and 0 otherwise.

   For example, in the triangular curve described above,
   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) + \ldots + F_{6,1}(5)
   F_{6,1}(1)\,
   =5\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{5}{36}\approx0.14\,

   Equivalently, one can calculate the probability using combinations:

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

   The probability of rolling any exact sequence of numbers is simply
   \frac{1}{s^i} . For example, the chance of rolling 1, 2, and 3 in that
   order with three rolls of a six-sided die is \frac{1}{6^3} , or
   \frac{1}{216} . Rolling any single number i times in a row, regardless
   of which number, is s times more likely, at a \frac{s}{s^i} chance.

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

   The fantasy role-playing game Dungeons & Dragons introduced the use of
   polyhedral dice during modern times and paved the way for their use in
   other role-playing games, using 20-, 12-, 10-, 8- and 4-sided dice in
   addition to the traditional 6 sided die. Such dice are often sold in
   sets.

   Types of polyhedral dice are distinguished by prefixing a "d" to the
   number of faces; for example, a ten-sided die is a d10.

   Players use polyhedral dice together in a number of ways. For example,
   a d10 can be used in conjunction with a d6 instead of using a d20. If
   the d6 displays a 1, 2 or 3, the number on the d10 is resolved as 1–10.
   If the d6 displays a 4, 5 or 6, the number shown on the d10 is resolved
   to 11–20 ("1" is 11, "2" is 12, etc.). In cases like this, almost any
   sided die can be used as a "resolver".

   Two d10 are often used to generate a number between 1 and 100, with one
   die representing the tens position. The tens die may be distinguished
   by colour, by using a custom die marked with multiples of ten, or any
   other means the player can indicate. Similar methods can be used for
   additional digits.

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 generally used.

   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.

   Rune dice are a specialized set of dice for divination ( runecasting),
   using the symbols of the runes printed on the dice.

   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.

   Retrieved from " http://en.wikipedia.org/wiki/Dice"
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