Dice are a popular source of randomness in board games (especially the game of the same name). The Anglicism "dice" is also common among role-players. In Central Asia and the Caucasus they are called zars (zariks); Singular — zarik. The common name is "kubik".

A dice is a small object that, when dropped on a flat surface, occupies one of several possible stable positions. A traditional dice is a dice with numbers from 1 to 6 on each of its six faces, which are rolled to demonstrate a randomly defined integer number from one to six, each of which is equivalent due to its regular geometric shape.

There are a huge number of varieties of dice:

by shape – dice can be polyhedral or irregular in shape,
In terms of content, symbols instead of numbers can be applied to their faces.
Such differences make it possible to use dice to produce results that differ from the classic "1-2-3-4-5-6" pattern. There are also dice, weighted on one side or with other changes invisible to the eye, designed to rig the results. The purpose of such dice is to deceive other players for money winnings or just for fun, such as magic tricks.

The dice is usually made in the form of a dice with numbers from 1 to 6 on its sides (they are usually arranged so that the sum of the numbers on diametrically opposite sides is 7). The dice can be thought of as a random number generator in the integer interval [1..N] with almost the same probability of all numbers in the interval being drawn. Such generators are denoted by 1dN.

So, for example, a regular die is 1d6; Coin tossing is the work of the 1D2 generator, etc.

The abbreviation MdN stands for the sum of M applications of 1dN.

It should be noted that MdN gives integers in the interval [M.. M*N]. The probability of a number falling out of this interval increases as it approaches the middle of the interval

History

The exact date of the appearance of the dice is unknown. The oldest dice, about 5,200 years old, were found in Iran along with a backgammon set during the excavations of the city of Shahr-i-Sukhta; The markings on the faces of the bones are almost identical to those of modern bones.

Other excavations of ancient burials of the Indus Valley civilization point to the South Asian origin of dice. Dice is mentioned as an Indian game in the Rig Veda, the Atharva Veda, and in the Buddha's list of games that he would not play. In the Indian epic Mahabharata, Yudhisthira and the Kauravas play dice in the northern principality of Hastinapur, over which a war begins.

According to Greek tradition, dice were invented by Palamedes to entertain bored Greek soldiers waiting for the Battle of Troy.

Modern dice owe their origin to an ancient skill game called "babki", which was played mainly by women and children. The gameplay consisted of throwing small bones of ungulates, butterflies, which is where the name of the game came from. The tetrahedral shape of the headstock was the first form of dice in history, and the material used to make it gave the name we still use today: "dice". Modern Mongolians still use these four-sided "shagai" dice for games and divination. In addition to classic pet dice, materials such as ivory, wood and various plastics are used to make modern dice. In historical chronicles, the game of dice and the game of money are often confused, but each of them has passed an independent path from ancient times and is still popular.

Gambling with two or three dice was a very popular form of entertainment in Greece, especially in the upper classes. They were constantly played during feasts.

The Romans were avid gamblers, especially during the heyday of the Roman Empire. Therefore, the game of dice was also widespread, although it was forbidden to be played; the ban was lifted only for the duration of the Saturnalia. Horace ridiculed the typical young men of the time who spent their time playing dice instead of riding. Throwing dice for money gave rise to many special laws in Rome: one of them stated that a person who allowed gambling in his home could not file a lawsuit, even if he was cheated or beaten. Already in those days, professional cheaters appeared among the players: in order to win, they deliberately weighted the dice they used on one side. Now some of these bones are kept in museums.

Dice players were frequenters of drinking establishments: the surviving frescoes depict quarreling players who are kicked out of the tavern by the owner.

The twenty-sided dice date back to the 2nd century A.D.

Tacitus noted that the Germans were passionate fans of the game of dice and could bet on their own freedom in the absence of money.

In the 11th century, Byzantium developed astragalomancy, the art of predicting the future using dice.

In the Middle Ages, the game of dice was a favorite pastime of knights, there were schools of the game and guilds of players. After the fall of feudalism, the Landsknechts gained a reputation as the most scandalous dice players of the time; The cubes were decorated with elaborate carvings depicting people and animals. In France, dice was played by both knights and ladies, despite new laws, including the prohibitions of St. Louis in 1254 and 1256.

The marking on the Chinese domino came from the marking of the dice.

Device 

Standard dice are small dice, most often 1.6 cm across, whose faces are numbered from one to six, usually by round dots called points. Traditionally, the opposite sides of the cube add up to seven, with faces 1, 2, and 3 sharing a common vertex, which can be clockwise or counterclockwise to the vertex. If faces 1, 2, and 3 are counterclockwise, the cube is called the right cube and vice versa. Western dice are usually right-handed, while Chinese dice are left-handed.

The glasses on the dice are arranged in a special order, as shown in the picture. On Asian dice, the order of the glasses is similar to the European one, but the glasses are placed closer to the center of the face; One point is bigger than the others, and four points are colored red. In some of the old sets, one point was indicated by an indentation without coloring. The black face of "one" and the combination of black and white on the face of "four" were considered unlucky, so red, the color of good luck in Chinese culture, was supposed to neutralize this sign. The word for four (四 [si]) is similar to the word for "death" (死 [si]) in Chinese and is considered unlucky. It is likely that the Red Fours are of Indian origin.

The result of a roll of the dice is considered random, as there are uncertain factors such as the movement of the thrower's hand and the position of the dice before the roll. Thus, the dice can be considered a prototype of a random number generator. Some people believe that glasses on the faces of cubes made in a certain style cause a slight displacement, but there has been no research to support this idea (by the way, this may be true for Asian dice with an enlarged image of one point). Casino dice are issued with flooded markings, which serves as a confirmation of the even distribution of random numbers.

The corners of some dice are rounded for a reason: the dice gets a slightly spherical shape, the sliding on the table surface increases, it rolls almost like a ball, and the distribution of the probabilities of certain numbers becomes uniform: the influence of the initial position of the dice and the nature of the movement during the throw becomes negligible.

The dice are thrown one at a time or in groups, from the hand or from a device designed for this purpose, on a flat surface. On the edge of the dice, which will be at the top after it stops, you can see the value of the roll. A typical dice game today is craps, in which two dice are rolled at the same time and bets are placed on the sum of the points of the two dice. Dice are often used to determine the number of moves on the board: for example, a similar method of determining the distance traveled by a player's piece on the playing field is used in the popular board games "Ludo" and "Monopoly".

For board games, you can use the results of the roll of the dice generated on the computer. The values are usually determined using a pseudo-random number generator and then displayed on the screen as some face of the dice. It is also possible to do the opposite, when dice rolls provide the generation of random numbers for computers.