Playing dice is a popular source of randomness especially for table games.

The playing dice has usually the shape of a six sided cube with numbers from 1 to 6 drawled on each side, and the sum of the numbers on the opposite sides must be seven. The playing dice can be considered as a generator of random numbers in a complete interval [1..N] with the same probability of appearance for all the numbers. Such generators are marked as 1dN. Therefore, the common cube is 1d6, tossing a coin for instance is the work of the generator 1d2 and etc.

Mdn means the sum M times used 1dn. It must be said that Mdn gives whole numbers inside the interval [M..M*N]. The probability of appearance of one number from this interval increases as the number gets closer to its center.

So, for example, if using playing dices d4 and throwing them twice, we’ll get the generator 2d4 that gives away the following variants:

Quantity of points Probable ending %
2 1/16 6.25
3 1/8 12.5
4 3/16 18.75
5 1/4 25
6 3/16 18.75
7 1/8 12.5
8 1/16 6.25

Example of generator, that doesn’t enter under the definition MdN: a cards deck, where the taken cards aren’t putted back in. It will be 1dN only for the first try, the distribution of the next attempts will depend on anterior results.

In role games such as based on Dungeons and Dragons rules playing dices with 4 (tetrahedral), 6 (cube), 8 (octahedral), 12 (dodecahedral) and other number of facets are used. Lou Zocchi invented a zocchihedrus playing dice with 100 faces. Usually to obtain numbers from 1 to 100 two 10 faced dices are used.

History
The firm date of playing dices invention is unknown. But some kind of forerunner random numbers generator, used in such plays as backgammon, must be older than 5 thousand years.