Multidice

Multidice refers to the practice of rolling more than one die at a time to determine the outcome of a task in games or simulations. It is a common mechanism in tabletop role-playing games, board games, and probabilistic experiments. The most widely used notation is NdS, where N is the number of dice and S is the number of sides on each die (for example, 3d6 means three six-sided dice). Results are typically combined by summing the dice, though some systems use only the highest die, or apply thresholds for success.

In probability terms, rolling NdS produces a distribution that broadens as N increases. The mean of a single S-sided die is (S+1)/2, so the mean of NdS is N(S+1)/2. The variance of a single S-sided die is (S^2-1)/12, so the variance of the sum is N(S^2-1)/12; the standard deviation is the square root of that. These properties influence strategy and difficulty, as increasing N widens the distribution and raises expected outcomes.

Variants include exploding (open-ended) dice, where a maximal roll adds another die to the total; keeping the highest or a subset of dice; or rolling a pool of dice and counting successes rather than a simple sum. Some games use advantage/disadvantage-style mechanics by effectively rolling multiple dice and selecting results.

Multidice systems are used to model skill checks, combat resolution, and random events, with examples including ability score generation in Dungeons & Dragons (4d6, dropping the lowest) and various dice-pool mechanics in other RPGs and board games.