At its simplest, a fair die means that each of the faces has the same probability of landing facing up. A standard six-sided die, for example, can be considered “fair” if each of the faces has a probability of 1/6.

Can there be a die that has an odd number of sides to it? If you are limited to polyhedral dice, then no. They do sell “D3” dice, but they are six-sided, with two sides showing each number between 1 and 3. Similarly, you could make a D5 using a ten-sided polyhedron.

And there is six possible outcomes, the numbers one to six. The probability when rolling a regular six-sided dice that the score is an odd number is three-sixths or three out of six. Both three and six are divisible by three. Therefore, this fraction could be simplified to one-half.

six faces

100 sided isohedra are shapes such as a dipyramid, unwieldy and not very graceful. The 100 sided “zocchihedron” isn’t an isohedron and hence isn’t a fair die (the sides don’t appear with equal frequencey).

An unfair die looks like an ordinary 4-sided die but the probability of a face landing on 2 is three times the probability of landing on 1. Similarly, the probability of landing on 3 is two times that of landing on 1 and the probability of landing on 4 is four times that of landing on 1.

Though 10-sided dice are not Platonic solids, all of their faces are the same shape and size. This means that they are as fair as Platonic solids in any reasonable situation. An example of an exception to this is if you drop a d10 through a very thick fluid.

Unfair dice are dice with nonuniform density distribution and unequal proba- bility for each outcome of a die toss. Mathematical models made by Wolfram Mathematica are programmed to simulate dice toss with given distributions of initial variables.