Started by Daniel Solis (1) (2)

*…Some of these definitions are in common usage now, some are even rather obvious, but others I've added in an effort to come up with new ways to use dice.*

# Anatomy of a Die

**Die** — A polyhedron with symbols or numbers on each side, rolled to give a randomly generated result. Traditional cubes marked with one to six pips per side are the most common and have been widely used for all manner of games for centuries. Hobby gaming popularized the use of dice based upon the use of other Platonic solids of 4, 8, 12, and 20 sides, and there have been many variations since. The commonest non-regular polyhedra is the 10-sided, a trigonal trapezohedron. For a rather fantastical array of fair dice that will likely never see manufacture, see fair dice.

**Side** — A flat facet of a die.

**Size** — A designation of die determined by however many sides it possesses. The common shorthand is "d" followed by the number of sides. A six-sided die is a "d6."

**Pip** — The small inked hollows on the sides of traditional dice used in place of numerals. Traditionally, the pips on a die are balanced, such that the total number of pips on two opposite sides of a die always total seven.

**Result** — The number or symbol on the die that is considered mechanically relevant.

**Target Number** — A number against which a result is measured to determine an outcome. Usage of target numbers varies, but mechanics commonly include either rolling over or rolling under the TN. Target numbers may represent the difficulty of an action, but may also represent individual competancy or be completely abstract.

**Head** — The number on top side on a stationary die. This is most often counted as the result.

**Foot** — The number on bottom side on which a stationary die is resting.

**Cocked** — A die that has been rolled and has an indeterminate result, usually because it has landed on an uneven surface.

**Modifier** — Any mechanic external to the die roll itself that would artificially change its result.

**Roll** — v. The act of throwing the die. n. Any dice that have been rolled together.

**High** — The highest possible result on a single die.

**Low** — The lowest possible result on a single die.

# Anatomy of Dice Rolls

*(Terms that apply to collections of dice, usually after rolling)*

**Pool** — Several dice rolled together. The amount of dice that can be rolled are often determined by external mechanics that may include character attributes and situational modifiers.

**Set** — Any dice in a single roll that match each other.

**Width** — The number of matching dice in a set.

**Height** — The result shared by all the matching dice in a set.

**Radicals** — Any results that do not match any other results, and are thus not part of a set. Also known as "waste dice."

**Peak** — Among several dice rolled, the peak is the highest actual die result.

**Valley** — Among several dice rolled, the valley is the lowest actual die result.

**Sum** — The results of several rolled dice, added together.

**Maximum** — The highest possible sum from a dice roll.

**Minimum** — The lowest possible sum from a dice roll.

**Suit** — An attribute of certain dice that distinguishes them from other dice in the same roll. Differently colored dice are often used in this manner.

**Exploding** — A die that may be re-rolled, usually because it has come up with the highest result for that die. Usually the new roll is added to the old result. For example, an "exploding" d6 that comes up 6 would then be re-rolled, with the new result added to 6. This produces gaps in the possible outcomes, for dice that are numbered starting with 1. Exploding dice often are allowed to "explode" on re-rolls as well, producing results with no theoretical limit.

# Mathematics of Dice

**Average:** The average result of rolling a die with x sides is (x + 1)/2. For example, the average result of rolling a d6 is 3.5 (although you will never actually roll this result, of course).

**Single Die:** The results of a single (fair) die are linear, that is, there is an equal chance of any number from 1 to the number of sides (assuming the sides are numbered sequentially from 1).

**Multiple Dice:** The results of rolling multiple dice range from a minimum equal to the number of dice to a maximum equal to the sum of the sides, but rather than being linear the results approximate a bell curve. That is, the results in the middle of the range are more likely than results at the extremes, because more combinations of the two dice give medium results than extreme results.

Using many dice skews the curve to the right, because each die gives a minimum result of 1, so the minimum result is always equal to the number of dice rolled.