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.
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)
- 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".)
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