How are odds affected by a die’s number of faces?
If you toss a coin, both sides have an equal chance of landing face up. There are only two possible outcomes: heads or tails. Rolling a cubed die gives six possible outcomes: six faces each as likely to land face up. 12-sided dice have 12 possible outcomes, and therefore twice the uncertainty that a given number will be rolled than with a to correctly predict a rolled number. A die must have faces of the same shape and size, with angles that exhibit symmetry, for an equal chance that each will land face up. Shapes following this rule are called isohedra, and the most common isohedra for dice are the five platonic solids; the tetrahedron (four faces), cube (six), octahedron (eight), dodecahedron (12) and the icosahedron (20).
Answered by Rik Sargent