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Dice

Dice (the plural of the word die, probably from the Latin dare: to give) are, in general, small polyhedral objects with the faces marked with numbers or other symbols, thrown in order to choose one of the faces randomly. The most common dice are small cubess 1-2 cm across, whose faces are numbered from one to six (usually by patterns of dots, with opposite sides totalling seven, and numbers 1, 2 and 3 set in counterclockwise direction).

In Unicode, the faces of common cubical dice are ⚀ ⚁ ⚂ ⚃ ⚄ ⚅

Dice are thrown to provide (supposedly uniformly distributed) random numbers for gambling and other games (and thus are a type of hardware random number generator).

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 spots on the two dice. They are also frequently used to randomize allowable moves in board games such as Backgammon.

"Loaded" or "gaffed" dice can be made in many ways to cheat at such games. Weights can be added, or some edges made round while others are sharp, or some faces made slightly off-square, to make some outcomes more likely than would be predicted by pure chance. Dice used in casinos are often transparent to make loading more difficult.

In cooking, to dice means to chop into small cubes, in allusion to the dice used in games.

Table of contents

1 History 2 Other kinds of dice 2.1 Non-cubical dice 2.2 Dice with other labels 3 References 4 External links

History

Dice probably evolved from knucklebones, which are approximately tetrahedral. Even today, dice are sometimes colloquially referred to as "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, on account of the confusing of the two games by the ancient writers. It is certain, however, that both were played in times antecedent to those of which we possess any written records.

The fact that dice have been used throughout the Orient from time immemorial, as has been proved by excavations from ancient tombs, seems to point clearly to an Asiatic origin. Dicing is mentioned as an Indian game in the Rig-veda. 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 (symposium).

The Romans were passionate gamblers, especially in the luxurious days of the Roman Empire, and dicing was a favourite form, though it was forbidden except during the Saturnalia. Horace derided the 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 Japan, China, Korea, India, 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.

Other kinds of dice

Non-cubical dice

Dice with non-cubical shapes were once almost exclusively used by fortune-tellers and in other occult practices, but they have become popular lately among players of roleplaying games and wargames.

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 10, 30, and other numbers of faces. (See Zocchihedron and polyhedral dice).

Dice with various numbers of faces are often described by their numbers of sides, with a d6 being a six-sided die, a d10 a ten-sided die, and so forth.

20, 10 and 4-sided dice

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.

Spherical dice also exist; these function like the plain cubic dice, but have some sort of internal cavity in which a weight moves which causes them to settle in one of six orientations when rolled.

Cowry shells or coins may be used as a kind of two-sided dice ("d2"). (In the case of cowries it is questionable if they yield a uniform distribution.)

Dice with other labels

Although most dice are labelled with numbers (starting at 1), all sorts of other symbols may be used. The most common ones include (probably among others):

• color dice (e.g., with the colors of the playing pieces used in a game)
• Poker dice, with the following labels somewhat reminiscent of the names of standard playing cards:
  • Nine (of spades; black)
  • Ten (of diamonds; red)
  • Jack (blue)
  • Queen (blue)
  • King (red)
  • Ace (of clubs; black)
• dice with letters (cf. Boggle)

References

• Persi Diaconis and Joseph B. Keller. "Fair Dice". The American Mathematical Monthly, 96(4):337-339, 1989. (Discussion of dice that are fair "by symmetry" and "by continuity".)

• Roman Board Games (See, in particular, Tali and Tesserae.)