Dicerolling

Dicerolling is the act of rolling one or more dice to generate random integers. It can be performed with physical dice or through digital simulations and random number generators. Dicerolling is a common mechanism in gaming, probability teaching, and statistical experiments, offering a simple way to model discrete randomness.

Most common dice are six-sided (d6) with faces numbered 1 through 6. Other dice used in tabletop RPGs include d4, d8, d10, d12, and d20. For a fair die with s sides, each face has probability 1/s. When multiple dice are rolled, the result is the sum (or the list of results) and the distribution is the convolution of the single-die distributions. The expected value of a single s-sided die is (s+1)/2; for k dice the expected sum is k*(s+1)/2. The variance of a single s-sided die is (s^2-1)/12; for k dice the variance is k*(s^2-1)/12. The sum of two six-sided dice has a well-known triangular distribution, peaking at 7.

Reliability and bias: physical dice may be biased due to manufacturing or wear; loaded dice are designed to favor certain faces. Digital dice rely on pseudo-random number generators; good RNGs and seeding reduce predictability. Some games use mechanics like advantage/disadvantage, rolling multiple dice and taking the highest or lowest result to alter distribution.

Applications: Dicerolling underpins many tabletop games, as well as simulations and probabilistic demonstrations. It provides a tangible example of random variables, probability distributions, and combinatorics, illustrating how simple rules produce complex outcomes.