Polyhedral dice are dice with more or fewer than six sides. They were once almost exclusively used by fortune-tellers and in other occult practices, but they have become popular lately among players of wargames, trading card games, German-style board games, and role-playing games. Although polyhedral dice are a relative novelty during modern times, some ancient cultures appear to have used them in games (as evidenced by the presence of two icosahedral dice dating from the days of ancient Rome on display in the British Museum). 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).
Dice with various numbers of faces are often described by their numbers of sides, with a d6 (or “D6”) being a six-sided die, a d10 a ten-sided die, and so forth. When more than one die is used, the standard terminology is to have two numbers separated by the ‘d’ or ‘D’ – Number of Dice d Number of sides on each die. Hence 2d6 (or 2D6) is simply Two Six-Sided Dice, suitable for games of Monopoly or Craps.
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 5, 7, 10, 16, 24, 30, 34, 50, or 100 sides, but other than the 10 sided, they are rarely used.
|20-sided die||10-sided die||4-sided die|
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.
There is some controversy over whether manufacturing processes create genuinely “fair” dice (dice that roll with even distributions over their number span). Casino dice are legally required to be fair; those used by all others hold no such requirement.
Spherical dice also exist; these function like the plain cubic dice, but have an octahedral internal cavity in which a weight moves which causes them to settle in one of six orientations when rolled. However, these dice are somewhat awkward in use because they require a flat and level surface to roll properly — an uneven surface often causes them to stop partway between two numbers, while a sloped surface will obviously cause the dice to keep rolling.
Cowry shells or coins may be used as a kind of two-sided dice (“d2”). (Because of their shape, cowry shells probably do not yield a uniform distribution.)
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