Dice

A game cube ( usually simply called cube) is an object that occupies a distinct of several stable rest positions for a throw on a horizontal plane and serves as a random number generator in many games. This would include dice symbols, one of which occupies an excellent position after the throw. This symbol then displays the result of the throw.

By far the most common dice is numbered 1 to 6, or a corresponding number of points, the eyes, inscribed cube or hexahedron. In everyday life, by the term cube usually only these six pus meant and so the name was adopted for the geometric body. However, there are also many others, also described in the following dice. Regular users of different cube types refer to this often with the abbreviation W, or d for english dice, followed by the indication of the page number, so for example, D6 or D6 for a six-sided, W10, W20, W30 for ten, twenty and thirty -sided dice.

• 5.1 The standard cube
• 5.2 Other polyhedra
• 5.3 prisms
• 5.4 rollers
• 5.5 spindles
• 5.6 balls
• 5.7 Other

• 6.1 Numbers and eyes
• 6.2 Other prints

Use

In craps dice are the central element of the game, there are only the comparison of the results of cube itself or directly with them coherent tactics. Here usually are the classic six cubes or specially painted, but still six-sided dice are used. Many gambling fall into this category. Well-known examples in the leisure sector are about Yahtzee or tens of thousands, in each of which certain eye combinations different numbers of points are assigned. Used in casinos include craps and Sic Bo, is where to bet on the results of individual litters.

In addition cubes are significant to determine approximately the speed of movement of game characters or the outcome of random events in a variety of board games. Here are primarily six pus used. Find use dice in role-playing games, where in recent decades, the use of a variety of other cube has prevailed with other page numbers in order to make random decisions flexible and diverse. A rather rare, complete on cube translated as Game Materials principle is that of collecting dice games where you have to trading card games acquire Similarly, a large number of cubes for sale and tactically. The best known representative is Dragon Dice.

In all these areas there are in addition to the simple throw of a dice also occasions when multiple cubes are throwing at the same time. The results can be added ( a weapon in an RPG aimed at as much damage as two dice together show ) or be considered as an ensemble (many board games follow special actions when multiple dice show the same number, in a so-called Pasch ). To simplify the throwing multiple dice to avoid cheating by trick casts or conceal earnings before other players to come Dice Cup (also called Knobelbecher ) are used. High-quality copies have inside so-called lip to keep the dice jump while rolling out in every case. This is to make the dice roll regardless of the original location of the dice. Serves the same purpose of the dice tower. To avoid loud impact noise and rolling the dice, sometimes a padded and bordered detes board is ( Dice Board or Dice tray ) is hereby established.

Instead of rolling the dice with them, so to generate random results, cubes can also be selectively rotated to certain values ​​and so used to their display. The best known example is the doubling cube, with those in the backgammon rating a game is shown. Dice are also used in the game of skill Dice Stacking.

Main Features

Used as a random number generator, is usually expected of a cube equal distribution of possible outcomes. These are therefore equally often occur in the long run, if the throws are not aware of influences. Then you call the dice a fair, ideal or real dice or - after Pierre -Simon Laplace, who conducted research at the equal distribution - a Laplace dice. In the manufacture of the cube always occur deviations ( see Preparation ) by which the cube is not quite ideal. For high quality dice you can keep very low this though.

Leaving aside these differences, then ideality is a property of the design of the cube, ie, among others, its geometric shape. The blueprint is exactly ideal when the rest positions of the cube are only distinguishable by a label due to its symmetry. A die is designed mostly for a convex polyhedron. Such is exactly ideal when its surfaces all have the same shape and size, and if you can not discriminate on the basis of their relative position to the other faces two surfaces. This condition is met only the five Platonic solids, the Catalan body, and certain Distorted these two classes, as well as spindles and rollers. Besides these forms are perceived as particularly aesthetically because of its symmetry.

Other polyhedra have different types of possible landing areas, so that their land probabilities can differ. In some forms you can try to compensate for this by the right choice of size ratios, such as stretching of the side faces the adjacent prism as a seven -sided die. However, the landing probabilities in addition to the geometry may depend on other conditions, for example by the friction between die and substrate or - even unintentionally - by the throwing technique. If these conditions are not known in advance, or if they change, then an exact equalization is a priori impossible. Cubes that are based on such bodies, so can never really be ideal.

Other requirements are that the cube good - but not too long - rolls and that the rest positions have a certain stability. This shaping is further restricted; such as cubes are difficult to construct with a high number of rest positions. Often the corners and edges are rounded to improve roll stability and handling. In the casino game of craps as well as some role players but this is frowned upon, since uneven rounding may prefer certain land areas.

Occasionally, the probability distribution is also aware manipulated in favor of certain results, if possible without the cube to change visually to gain an advantage in the game. In this case, it is called the cube dovetailed. The possibilities include changing the weight distribution, different degrees rounded edges or corners and warped surfaces. Too strong loaded dice betrayed by a tottering rolling motion, but this is not noticeable when using a dice cup. Another possibility is to place the interior of the cube a permanent magnet in order to influence the roll of the dice by a second magnet, which is believed, for example, under the table plate when required. To complicate the tines, often transparent cubes are used in casinos.

History

Antiquity

The oldest known dice belong to an ancient Iranian board game that dates back to 3000 BC and is a possible precursor of the backgammon game. Other early finds come from Tepe Gawra (northern Iraq), early 3rd millennium BC, and Mohenjo -daro (Pakistan ), late 3rd millennium BC These finds have been the shape of a cube and are marked with eyes. Even from the other early history and antiquity of the Orient numerous six-sided dice are preserved.

In addition comes from the Sumerian city of Ur in about 2600 BC a dated game. Therein cubes were used to determine the movement distance. A party used quadrilateral rods, the other tetrahedron, which were labeled at two corners. These are the oldest known dice in the form of another regular polyhedron as the cube.

In the Egyptian game Senet several semicircular wooden sticks were used, which were marked on one side and could be read by their position after throwing. The first safe Fund to Senet is a grave painting, which dates back to 2686 BC. But there are game board finds, which date back to 3500 BC and probably also part of Senet. Thus, this game is a candidate for the first use of cube -like objects. In addition, Sprunggelenkknöchelchen of cloven-hoofed animals such as sheep or goats were used as dice in Egypt.

In Greek and Roman culture, these bones, Astragali were called, among other things, oracle purposes. Due to its angular shape they have four different possible rest positions, the probability of the results is differently high. In addition, modern cube shape were used. Even ancient authors had theories about their invention, among other things wrote Pliny the Elder they Palamedes during the Trojan War and Herodotus to the People of Lydians. It is likely, however, that they were taken from the Orient. This was in addition to six-sided dice already known with higher page numbers, among other things, there are finds of 12 -, 18 -, 20 - and 24 - sided dice. A wide range of materials has been handed down, including clay, metal, ivory, crystal, bone and glass. Also, there was already cubes with letters and words instead of numbers or eyes, which were used for divination or complex dice games.

Both dice and Astragali were used in addition to the divination for dice games. Here, there were games for children and women who were sometimes more skill throwing games, some dice games in the modern sense. The best known example is Astragaloi. To use dice and Astragali beyond gambling for money, was banned in the Roman Empire outside the Saturnalia and was regarded as a heavy truck, but was still widespread.

Another independent development of dice existed in India. Here existed since the Vedic period ritual and board games, in which the nuts of Vibhidaka tree ( Terminalia bellerica ) were used as five-sided dice. Later ( in the game Jataka ) developed four-sided prismatic cube (see below). Furthermore, it can be assumed that the dice related random decision of the coin toss will probably operated on since the invention of the coin. Coins can be used as two -sided dice interpret (see below), thus also is a form with a long history.

Middle Ages and Early Modern Times

By Roman legionnaires and colonists dice and dice games were brought to the rest of Europe. In the Middle Ages, the ankles were known under the name of humpback horns, but gradually sat down exclusively modern, regularly shaped cubes through. As in ancient times, the six-sided dice was clearly dominant, but still appeared also in some other page numbers on: 965 was designed by the French cleric Wibold a game that used a four-sided prism cube, and even a medieval eight -sided prism is known.

Dice games of various forms were popular in all European countries and in all layers, they are mentioned in numerous contemporary works. Early on, there was also a professional gambler, 1254 are in an ordinance of Louis IX. first mentioned special playhouses. There are many reports also loaded dice. Despite the wide spread social gambling with dice were still a vice and it has been made with secular and ecclesiastical prohibitions against them. In the French literature of the cube was branded partly as an invention of the devil.

Modern

Were mainly used in the past for pure dice games and rarely as backgammon as parts of other varieties dice, they came during the 20th century in a growing number of board games for use. On the mass market, this almost always limited to six-sided dice. Other forms first appeared with the rise of tabletop games in the 1960s on a larger scale. The first successful pen-and -paper role -playing game Dungeons & Dragons established then in 1974 the five Platonic solids plus the ten -sided die as widespread models. The growing variety of role-playing game systems and incipient gatherer is a need for ever more exotic dice, which was taken up in the economy through the creation of numerous companies emerged in the following decades.

Production

Today Most dice are made of plastic (ABS), is quite common even wood and occasionally other materials such as cork, horn, stone, metal, or cardboard can be used. The default cube has a diameter of about one and a half centimeters, but the market covers a wide range of sizes. Plastic cubes are usually cast, with a Einfüllpropfen remains, which is smoothed along with other irregularities by machine rolling. The labels are usually recesses in the ink is then filled printed frequently. Strictly speaking, these various arrangements of the pages is a light prongs, but the effect is minimal and negligible in practice.

For the dice and board game mass market, there are a number of producers, for the more exotic role playing dice, however, exists worldwide, only a small number of renowned manufacturers. Many of the dice in the following places are also exclusively manufactured by one of these companies, since some structures such as the Zocchihedron are even patented. Among these companies primarily, Koplow and Chessex Games the mass market, GameScience and Crystal Caste specializing in exclusive models and would be also partly from the manufacturing process; so inspired about GameScience the rolling of the production tracks, as this will damage the ideality of the cube more than the tracks themselves

Particularly complicated is the preparation of casino dice, also called precision dice. For the professional gambling highest demands are placed on the ideality of dies. These cellulose acetate is used instead of the usual plastics, the manufacture completely bubble- free and thus can be processed more accurately. The dice are not cast, but earlier with diamonds, today cut with lasers from larger blocks. Since the 1960s, cellulose acetate replaces the light burning and detachable cellulose nitrate. But even the more modern material has a weakness: it is temperature -, moisture and light sensitive and begins after some time to crystallize and become brittle. In addition to higher costs, this is one reason why such dice only come in casinos used where they are often exchanged, and not in private use, in which the useful life is usually much longer. The tolerances for the shape of the casino dice are in the range of 0.0005 and 0.0002 inches ( 0.0127 and 0.00508 mm).

In order not to endanger the balance of the dice results in casino dice also only color with the density of the cube material is used to fill the eyes. Depending on the game and casino are the edges and corners sharp ( razor edge ) or rounded ( ball cornered ) and the surface matt ( sanded ) or polished ( polished ). In the latter treatment, the die is transparent, whereby some zinc methods (see above) were identified. Safety features are also used in serial numbers, in the interior of visible signs or responsive to UV light, coatings.

Molding

The main distinguishing criterion is the number of cubes of their sides and thus the number range from which they can generate numbers. According to the usual terminology role players the dice corresponding to the number of the normal six-sided dice are hereinafter referred to as Wn n their pages, so as W6. Also widespread is the name of dn english dice. Ideal column indicates whether with a perfectly crafted representatives of a form, all the results in one units with the same probability ( see above).

The standard cube

The following six dice have evolved under the influence of Dungeons & Dragons as a standard assortment under role players and are thus by far the most common dice types. There are the five Platonic solids and a trapezohedron. All six are ideal due to their symmetrical shape.

Other polyhedra

These dice have the form of a highly symmetric, but not platonic polyhedron. Catalan or Archimedean bodies are suitable for this purpose particularly well, said the Catalan body, because of their identical faces than ideal, which does not apply to the Archimedean solids.

Prisms

Prisms or cube columns consist of two bases, and any, usually relatively small odd number of side faces. If a prism cube odd number area on one of its side faces, so has an edge upward. So here's the values ​​over the side edges extending, color demarcated points are displayed. Alternatively, the labeling is carried out as in a conventional W4, as in the possible rest positions of the side faces is not above.

Prism dice with more than two surfaces are difficult to produce as perfect cube, since the correct ratios of sides and base areas are difficult for a balanced probability distribution to calculate. GameScience are but at least supposedly ideal W5 and W7 succeeded - commonly but such forms are not considered ideal.

Roll

For rolling dice there are two different, but similar construction methods: For an n- sided prisms can be used, which are placed corresponding to n - sided pyramids on the broad surfaces. The other option are anti- prisms ( ie reciprocally displaced triangles as faces) with - sided pyramids on the top surfaces. In both cases, the pyramids ensure that neither the deck areas nor the pyramid surfaces can occur as a result, the values ​​thus distributed exclusively through the side surfaces. The prism principle allows any number of pages, but is rarely used. In an odd number of faces, the problem arises that there is no overhead for a union side, this can be solved by edge labels like prisms. In the anti- prism - variant only just page numbers are possible, it is the more common form of rolling dice, usually as an alternative to the standard dice. With four sides there is a tetrahedron, and the top surfaces degenerate into lines so that the patch pyramids omitted.

Spindles

There are two classes of geometric shapes that visually resemble spindles or rotors. These are firstly the bipyramids, which consist of two pyramids stuck together with the base, so that at the " equator" meet two surfaces. To perform labeling on the surfaces, each of the two pyramids must have an even number of pages, so that an area can be on top. This means that only dice with 4n sides possible, in other words, each half body must have an even surface number, because otherwise an edge would be on top. The other variety are trapezohedron that consist of dragon four corners. These are arranged so that at the " equator" of each surface and edge meet, he receives by a zigzag course. For surface labeling are here - for the same reason as above - only page numbers 4n 2 possible.

By Edge marking the other side numbers are possible, so bipyramids with 2n sides, n odd, and trapezohedron with 2n sides, n even. In practice, however, only the surface of labels may be used. The halves of both forms act as capped cone with high page numbers. In addition to those listed below exotic cubes includes two standard dice to this class: the W8 is a bipyramid, the W10 a trapezohedron. Also, the W6 can be construed as trapezohedron.

Roll

Ball cubes are a very unusual construction method. Also, just a valid reason of them, the Zocchihedron -W100, as a sort of culmination of role-playing or generally exotic dice.

Inside there is a cavity with hexahedron -shaped skeleton and a ball that comes to rest in one of the six wells. The ball thus has six stable states. This W6 is also ideal as a normal cube. Depending on the quality of production may lead to very long roll of time at this form.

Other

In addition to these families, there are some even more exotic models, these include polyhedral, but less regular body and completely isolated design principles.

Labeling

Numbers and eyes

Usually dice are labeled with numbers, as these are the most desired result of chance and allow using multiple cubes addition and other further processing. Instead Arabic numerals are sometimes, especially when W6, also round marks, the eyes used, which can be considered fully equivalent to the numbers.

Most cubes whose unique design principle includes opposite sides, it is customary to arrange the numbers so as to add two opposite sides of an n-sided cube. However, there are exceptions to this rule. And even if it is complied with, thus the precise arrangement of the figures is not yet clearly defined, because it usually gives several labels that meet this rule. For the W6 for example, two orientations are possible, which are also used both since antiquity. These two orientations of the digits in the cube are mirror images, see chirality in chemistry. The numbers 6 and 9 are identical except for rotation. For cubes, the number range used both digits, usually a feature is added for easier distinction. Usual, a point on the side which is to be read as below, or underlining it.

In China and partly in Japan, the standard eye -W6 are painted slightly differently than in Europe. Typically, a particularly large red eye for one, a red four and arrangement of the two eyes of the two are side by side instead of diagonally.

Other prints

A diverse field are also cubes with alternative labels. Halved cubes are used to simulate unusual page numbers with the more common forms, such as a W2, which is generated by the fact that a W4 with two ones and two twos is labeled. Tens cubes are variants of the W10, which takes 0-9 with 00-90, 000-900 or 0000-9000 or digits (according to the English notation with dot instead of comma) as .0 - .09 and - .9, .00. 000- 009 are labeled. These are diced in combination, and the results added together, so as to obtain results with more throwing tens. Spread is mainly the use of a W10 to 00-90 and 0-9 as a simulated W100 (also called W %) or W10 with a 00-90 and 1-10, in which the two numbers are added together. This can be achieved by two different colored W10 0-9, in which for example represents the red, the tens digit. Condensed cube are octahedra (usually 0 and 1) summarize the sum of several coin flips: The "W2" is four times each with the 0 and the 1 labeled. The " 2W2 " bears according to the probability each twice the 0 and 2, and four times the 1 The " 3W2 " has ever once the 0 and 3, and three times the 1 and 2 theory would be larger cube ( 1x0, 4x1, 6x2, 4x3, 1x4, etc.), but the number of required spaces would be 2n and would quickly become very large.

For some games dice with symbols that do not stand for numbers used. In the overwhelming number of cases, these are W6. Examples are cubes for Dice Poker, Chuck-a -Luck variants or various modern games. In role-playing dice are common with hit zones. Instead of symbols colors are sometimes also used simply. Combinations of Numeric and Symbol dice exist where about only a number for advertising purposes by a company logo or a game, is replaced by a symbol of a particularly important event.

Since there are many exactly counted categories in human culture, it makes sense to also cover these with matching cubes. So there W4 with the four basic arithmetic operations, W8 with the eight points of the compass, W12 with the calendar months and similar products.

Probability Theory

As everyday objects and easy to dice -looking systems are popular examples in probability. Conversely, the probability theory important insights for the use of dice in games.

The throw of a single ideal cube, no matter what page number n, is the classic example of a uniform distribution: each of the possible outcomes have exactly the same probability for long games so under the law of large numbers to be expected that the frequencies of numbers similar to be. The expected value of such litter is always on.

When used in many games simultaneous throw of two dice with the same adding the result of the probability plot takes contrast to the shape of a triangle, the result is the more frequent the closer it is to the mean of the result area. If we add more cubes, the curve completes, the distribution approaches more and more of a normal distribution.

Additionally, many games more complicated cube systems, which can also do probability calculations. Common problems are the probabilities for specific result classes (such as a Pasch, ie two of the same results, Monopoly ), exceeding or falling below a certain barrier by the overall result (in many RPG systems, called " About cubes " and " dice " ) or the risk assessment between different distributions (if you about in an RPG the choice between a weapon with a damage roll, according 2d10 or 1d20 with has ).

An amazing, by the calculus of probability but explainable magic trick is the dice snake.

Sicherman the cube, a pair of dice, one of which is labeled 1, 2, 2, 3, 3, 4 and the other with 1, 3, 4, 5, 6, 8. This is the only alternative way of labeling with positive integers such that every as frequently occurs with this pair of diced sum as with ordinary dice.

Are statistically interesting intransitive dice. For each of these differently labeled cube, there is another who wins against him in the long term, that is, frequently shows a higher than a lower number.

Other random

Roll is not the only method that is used in games of chance for generating results. Closely related with dice are the objects known as spinner or gambling tops. They consist of a cube-like body and a central axis to which they can be turned on and then behave like a top until they come to rest and like a cube View analogous a result; Example of this is the dreidel and the Nimmgib.

Another mechanical random generator is the Wheel of Fortune, in which a wheel turns with result labels below a pointer. It is also possible to let the random decision to perform directly from people. Approximately by the blind drawing straws or playing cards and playing rock, paper, scissors Nowadays, electronic random number may be used.

Quotes

• Alea est iacta. ( The dice is thrown. ) - Julius Caesar
• The old man does not play dice. - Albert Einstein
• God does not play dice with the universe, but sometimes throws the dice so that we can not see them. - Stephen Hawking