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Dice (the objects, usually cubical, used for generating Random Number s or other Symbol s. This makes dice suitable as Gambling devices, especially for Craps or Sic Bo , or for use in non-gambling Tabletop Game s. 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. 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 The common dice are small order about this vertex. Dice are thrown to provide Random numbers for Gambling and other Game s, and thus are a type of Hardware Random Number Generator . The result of a die roll is random in the sense of lacking predictability, not lacking cause. Exactly how dice are thrown determines how they will land according to the laws of Classical Mechanics . The unpredictability of the result is a demonstration of the Chaos Theory . However, because the numbers on typical dice are marked with small indentations, slightly more material is removed from the higher numbered faces. This results in a small bias, and they do not provide fair (uniform) random numbers. The bias is reduced somewhat in the Japanese die with its oversized single pip (pictured). Casino dice have markings that are flush with the surface and come very close to providing true uniformly distributed random numbers. 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 Game s, usually by deciding the distance through which a piece will move along the board; examples of this are Ludo and Backgammon . HISTORY ]] 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 Plastic s 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. Dice have been used throughout Asia since before recorded history. The oldest known dice were excavated as part of a 5000-year-old Backgammon set, at the Burnt City archeological site in south-eastern Iran . Excavations from ancient tombs in the n origin. Dicing is mentioned as an Indian game in the '' Rig Veda '', '' Atharva Veda ''2.3, 4.38, 6.118, 7.52, 7.109 and Buddha Games List . It is also mentioned in the great Hindu epic, the Mahabharata , where Yudhisthira plays a game of dice against the Kauravas for the northern kingdom of Hastinapura . In its primitive form knucklebones was essentially a Game Of Skill played by women and children. In a derivative form of knucklebones, the four sides of the bones received different values and were counted as with modern dice. Gambling with three or sometimes two dice was a very popular form of amusement in Greece , especially with the upper classes, and was an almost invariable accompaniment to Symposia . 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 Law s 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 Museum s. 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 favorite pastime of the Knight s, and both dicing schools and guilds of dicers existed. After the downfall of Feudalism the famous German Mercenaries called Landsknecht s 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 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 Density 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 Nearly all dice are polyhedral (that is, they have flat sides that meet at straight edges), but in common usage the term "polyhedral dice" typically indicates a mix of dice shapes used in a variety of modern games. By contrast, a round coin could be considered a non-polyhedral, two-sided die. 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 .1 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 , Wood , and semi-precious stone dice can be found. Early polyhedral dice from the 1970s and 1980s were made of a soft plastic that would easily wear as the die was used. Typical wear and tear would gradually round the corners and edges of the die until it was unusable. 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 Game s, most dice came with the numbers unmarked 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 color 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" {Link without Title} ; the others are the numbers 2–6 in old French. Dice notation See Also: Dice notation
In many modern gaming contexts, the count and number of sides of dice to be rolled at any given time is reduced to a common set of notations. Typically this involves the lower-case letter "d", preceded by a die count and followed by (optionally) the number of sides of the dice. For example, 6d8 or 2d6; the former meaning "six eight-sided dice," and the latter meaning "two six-sided dice." Addition or various other arithmetic operations are often added at the end as well, e.g. 3d6+4 "three six-sided dice plus four to the outcome thereof".
"Crooked" dice "Crooked dice" refers to dice that have been altered in some way to change the distribution of the dices' 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 center of the cube, with a Capillary Tube leading to another mercury reservoir at the side of the cube. The load is activated by tapping the die on the table so that the mercury leaves the center and travels to the side. Often one can see the circle of the cut used to remove the face and bury the weight. In a professional die, the weight is inserted in manufacture; in the case of a wooden die, this can be done by carving the die around a heavy inclusion, like a Pebble around which a tree has grown. 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 Casino s, 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 labeled using an unbroken series of whole numbers, starting at one (or zero), expressed with either pips or digits. Common exceptions include:
Non-cubical dice ]] Some dice are Polyhedra other than cubes in shape. They have become popular lately (at least since the early 1950s) among players of Wargame s, Trading Card Game s, German-style Board Game s, and Role-playing Game s. Some family style games use these non-traditional dice, such as Killer Bunnies And The Quest For The Magic Carrot . 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 Solid s 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, 14, 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. A large number of different Probability Distribution s 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 Coin s 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 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 Solid s, 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. Rarer variations The full geometric set of "uniform fair dice" (with all congruent sides) are:
PROBABILITY For a single roll of an -sided die, the probability of rolling each value, 1 through , is exactly 1/''s''. This is an example of a Discrete Uniform Distribution . For a double roll, however, the total of both rolls is not evenly distributed, but is distributed in a triangular curve. For two six-sided dice, for example, the probability distribution is as follows: 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 of a sum of ''i'' ''s''-sided dice can be calculated as the repeated Convolution of the single-die probability distribution with itself. : where for all and otherwise. A fastest algorithm would adapt the Exponentiation By Squaring algorithm, using . For example, in the triangular curve described above, Equivalently, one can calculate the probability using Combinations : The probability of rolling any exact sequence of numbers is simply . For example, the chance of rolling 1, 2, and 3 in that order with three rolls of a six-sided die is , or . The article Sampling Equiprobably With Dice describes the probabilities of sampling with dice from any range. APPLICATION IN ROLE-PLAYING GAMES While polyhedral dice had previously been used in teaching basic arithmetic, the Fantasy Role-playing Game '' Dungeons & Dragons '' is largely credited with popularizing their use in roleplaying games. Some games use only one type, such as '' Exalted '' which uses only ten sided dice, while others use numerous types for different game purposes, such as '' Dungeons & Dragons '', which make use of 20-, 12-, 10-, 8- and 4-sided dice in addition to the traditional 6 sided die. Roleplaying games generally use dice to determine the outcome of events, such as the success or failure of actions which are difficult to perform. A player may have to roll dice for combat, skill use, or magic use, amongst other things. This is generally considered fairer than decision by Game Master fiat, since success and failure are decided randomly based on a flat probability. Games typically determine success as either a total on one or more dice above (''Dungeons & Dragons'' third edition) or below (''Call of Cthulhu'') a target number, or a certain number of rolls above a certain number (such as 4 or higher on a d6) on one or more dice (''Exalted''). The player may gain a bonus or penalty due to circumstances or character skill, usually either by a number added to or subtracted from the final result, or by having the player roll extra or fewer dice. Dice can also be used by a game master for other purposes, such as to randomly generate game content or to make arbitrary decisions. Some games use dice to determine what attributes the player's character has when created, such as how strong he or she is. In ''Dungeons & Dragons'' and some other roleplaying games which use many types of dice, a Dice Notation is used. For example, a six-sided die is referred to as a d6, while two such dice rolled with the results totaled would be called 2d6. A bonus or penalty applied to the final result is referred to like 2d6+4 or 2d6-2. Games which use only one type of dice rarely require complex dice notation.A common special case is percentile rolls, referred to in dice notation as 1d100 or 1d%. Since an actual hundred-sided die would be large, almost spherical and difficult to read, percentile rolls are generally handled by rolling two ten-sided dice together, using one as the "tens" and the other as the "units". A roll of ten or zero on either die is taken as a zero, unless both are zeros or tens, in which case this is 100 (rather than zero). To avoid this confusion, sets of percentile dice exist where one is marked in tens (00, 10, 20... up to 90) and the other from 0 to 9.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. SEE ALSO
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