exampleDie

exampleDie is a hypothetical die used in documentation, teaching, and software simulations to illustrate dice behavior and random outcomes. It can refer to a physical die or a virtual object in a program, and it is commonly employed as a simple example in probability and game logic.

Physical characteristics often mirror a standard six-sided die, with faces numbered from 1 to 6. In fair variants, each face has an equal probability of 1/6. While standard dice typically have opposite faces summing to seven, exampleDie may be nonstandard in some examples to demonstrate biased or nonuniform outcomes, which helps in exploring how alterations to design affect results.

Mathematics and probability: For a fair six-sided exampleDie, the outcomes follow a discrete uniform distribution on {1, 2, 3, 4, 5, 6}. The expected value is 3.5. The second moment is 91/6 ≈ 15.1667, yielding a variance of about 2.9167 and a standard deviation of approximately 1.708.

Computing and simulations: In software, exampleDie is often implemented as an object or function that returns a random integer from 1 to 6, with optional methods to roll, set a seed, or configure bias. It serves as a testing stub for gameplay mechanics, probability calculations, or user interface behavior.

Variants and uses: Variants include dice with more or fewer sides, biased or loaded dice, or dice with alternative face arrangements. In education and development, exampleDie helps illustrate randomness, fairness, and the impact of design choices on expected outcomes.