General Information

Dice are small cubes of ivory, bone, wood or metal, used in gaming. The six sides of a die are each marked with a different number of incised dots in such a manner that the sum of the dots on any two opposite sides shall be 7. Dice seem always to have been employed, as is the case to-day, for gambling purposes, and they are also used in such games as backgammon. There are many methods of playing, from one to five dice being used, although two or three are the ordinary numbers employed in Great Britain and America. The dice are thrown upon a table or other smooth surface either from the hand or from a receptacle called a dice-box, the latter method having been in common use in Greece, Rome and the Orient in ancient times.

Dice-boxes have been made in many shapes and of various materials, such as wood, leather, agate, crystal, metal or paper. Many contain bars within to ensue a proper agitation of the dice, and thus defeat trickery. Some, formerly used in England, were employed with unmarked dice, and allowed the cubes to fall through a kind of funnel upon a board marked off into six equal parts numbered from I to 6.

It is a remarkable fact, that, wherever dice have been found, they differ in no material respect from those in use today, the elongated ones with rounded ends found in Roman graves having been, not dice but tali, or knucklebones. Eight sided dice may be used in aid of children in learning the multiplication table. The teetotum, or spinning die, used in many modern games, was known in ancient times in China and Japan.

Probability

Dice are the most ancient of all 'probabilty generators'. Modern day dice have 6 sides, with the numbers 1 to 6 on them. Each opposite pair of faces sums to 7.

When a dice is thrown, there is an equal probabilty of 1/6 = 0.1667 that any number will appear.

When 2 dice are thrown, the following table determines the outcome:

 123456
1234567
2345678
3456789
45678910
567891011
6789101112

The probabilities are:

(2,12) : 1/36 = 0.02778
(3,11) : 2/36 = 0.05556
(4,10) : 3/36 = 0.08333
(5,9) : 4/36 = 0.11111
(6,8) : 5/36 = 0.13889
(7) : 6/36 = 0.16666

so the probability of throwing a 7 with 2 dice is the same as throwing say a 6 with 1 dice.