Fair Dice

A die (plural "dice") is any solid object with markings on each face that can be used to create a random number. Very useful when playing games of chance!

Fair Dice

In mathematics we say "fair dice" when we mean that there's an equally likely chance of landing on any face.

Two white six-sided dice showing the numbers three and five

Most people think of these little cubes
when we say "dice" ...

... but all of the Platonic Solids can make fair dice!
Five black dice in the shapes of the Platonic Solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron

Because of their perfect symmetry, every face is equally likely to land face-up.

So, using the Platonic Solids we can have dice with 4, 6, 8, 12 or 20 faces!

But with some imagination we can actually make fair dice with any number of faces we want.

Long cylindrical die with many flat rectangular faces along its length

How about these interesting dice?

Blue ten-sided die known as a pentagonal trapezohedron

Or this 10-sided one.

Weathered green glass twenty-sided die from the Roman Empire era

Or this 20-sided Roman die that's 1,800 years old.

So long as there's an equally likely chance of landing on any face then they are fair dice.

Professional Dice

Two translucent red casino dice with sharp edges and white pips

For very fair dice there are casino-grade dice with special qualities:

partly transparent so you can see any bubbles or weights inside
as close as possible to exact cubes
sharp edges and corners
dots filled with flush epoxy, so every face has the exact same weight and density

Try The Spinner !

The "d" Notation

Gamers and mathematicians use a short way to name these dice: the letter d followed by the number of faces.

d4
= 4 faces

d6
= 6 faces

d8
= 8 faces

d10
= 10 faces

d12
= 12 faces

d20
= 20 faces

So, a standard cube is a d6, and that 1,800-year-old Roman die is a d20.