Roll : A Language for Specifying Die-Rolls

Role-playing games (RPG’s) use a variety of methods for rolling dice to add randomness to the game. In the simplest form, a small number of identical dice are rolled and added, but more advanced forms involve cumulative re-rolling of 6’s, doubling the value of doubles, removing the lowest or highest result or counting the number of dice that are below a threshold, and many other weird and wonderful modifications. While die-roll programs and net-based die-roll servers exist, they can usually only handle the simplest form of die-rolls. This paper describes Roll, a simple functional language for defining how dice are rolled. Such definitions are then used to emulate die-rolls or make probability calculations. We describe two different semantics for Roll: One that corresponds to randomly rolling the dice and one for calculating the probability distribution. We discuss implementation issues regarding the latter.