Supervisor: Karsten Riisager

Dungeons and Dragons is a popular fantasy tabletop roleplaying game. During the game players must roll dice of various shapes and sides to determine the outcome of different tasks, quests or fights.

In this Colloquium I will outline a derivation of the probability distribution functions for the different rules involving dice in the newest rendition of the game, 5th edition, and present special cases of the found solutions together with simulated results for comparison.

The types of rules in question are the ones of the form “roll 4, 6-sided dice and sum the highest 3” and “roll 2, 20-sided dice and throw away the highest/lowest”, but also cases of the form “roll 8, 6-sided dice and sum”.

The found solutions are made to facilitate physical dice, that is, loaded dice where the position of the center of mass skews the probabilities of the die sides. A discussion of the statics and dynamics of 2D dice will therefore also be made.