Definition:Die
Definition
A die (plural: dice) is a device for generating random numbers, traditionally between $1$ and $6$.
A die usually consists of a cube on which each face denotes a different number, usually (again) from $1$ to $6$.
Traditionally, opposite faces add to $7$, so:
- $1$ is opposite $6$
- $2$ is opposite $5$
- $3$ is opposite $4$.
The idea is that when you roll it, or throw it, or otherwise cause it to land upon a flattish surface, one of the sides will be face-up, and (with a good design of die) which side that is can not be precisely predicted.
Hence it serves as a generator of a discrete uniform distribution.
By using dice with different shapes (usually either platonic solids or prisms), a different probability space can be generated.
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Also see
Historical Note
Dice have been around for thousands of years, and have formed the basis of humanity's love-affair with gambling throughout history.
Even the clothing of Jesus Christ was reportedly gambled for at his crucifixion in a dice game.
An early reference to the design of a die can be found in W.R. Paton's $1918$ translation of The Greek Anthology Book XIV:
- The numbers on a die run so: six one, five two, three four.
Linguistic Note
Note that the plural of die is dice.
Beware the tendency to use the word dice as a singular noun:
- I threw a dice and it came up six
as this (while colloquial) is technically incorrect.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): die