**UPDATE**: I have made a website of the simulator (dnd.matteoferla.com).

**SEEN ALSO:**Description of battle simulator and some analysis, the GitHub code for the encounter simulator, analysis of dice equivalence

As explored previously, dice with the same mean can safely be replaced with each, a principle nicknamed dice equivalence in a previous post.

**Utility:**Changing a boring 1d8 for a crazier dice combination spices things up.

**Sidedness:**The number of sides of a die. Not sure if there is a word to describe the number of sides of a polyhedron. Hence this made up word.

**Mean**: This is half its sidedness plus 0.5. The 0.5 is because a die starts from 1, otherwise one would make a fencepost error. As a result a 2d4 is actually equivalent of a 1d9, not a 1d8. A bonus of +1 is equivalent to increasing the sidedness by 2.

**Variance:**

- The variance greatly increases with sidedness.
- The variance of multiple dice is the sum of each variance (Bienaymé formula).
- Bonuses do not affect variance and a fixed damage has therefore zero variance —damage dealt as when visiting the plane of Mechanus.
- Variance decreases the more dice are used and the distribution becomes closer to a bell curve —flipping coins would give a bell curve.