From the introduction: Most RPGs (role-playing games) use some sort of randomizer when resolving actions. Most often dice are used for this, but a few games use cards, rock-paper-scissors or other means of randomization. There are dozens of different ways dice have been used in RPGs, and we are likely to see many more in the future. This is not an evolution from bad methods to better methods - there is no such thing as a perfect dice-roll system suitable for all games (though there are methods that are suitable for none). But how will a designer be able to decide which of the existing dice-roll method is best suited for his game, or when to invent his own? There is no recipe for doing this - it is in many ways an art. But like any art, there is an element of craft involved. This paper will attempt to provide some tools and observations that, hopefully, will give the reader some tools for the craftsmanship involved in the art of choosing or designing dice-roll mechanisms for RPGs. User summary: A technical and comprehensive essay on the manufacture, use, and probabilities of dice of various types and sides.