Icepool: Efficient Computation of Dice Pool Probabilities

Abstract

Mechanics involving the roll of multiple dice---a "dice pool"---commonly appear in tabletop board games and role-playing games. Existing general-purpose dice pool probability calculators resort to exhaustive enumeration of all possible sorted sequences of rolls, which can quickly become computationally intractable. We propose a dynamic programming algorithm that can efficiently compute probabilities for a wide variety of dice pool mechanics while limiting the need for bespoke optimization. We also present Icepool, a pure Python implementation of the algorithm combined with a library of common dice operations.