Polyhedral Dice
Stochastic number generation

Most RPGs use dice to generate a random number that is used, modified by various bonuses and penalties, to resolve combat, spell-casting, lock-picking, or some other non-trivial action.

Many games use only traditional dice: one die will generate a number between one and six with a uniform distribution; two dice, a number between two and twelve with a peaked distribution (you’re most likely to roll seven), and so on: the more dice that are used, the more bell-shaped the distribution.

For example, with three dice (3d6) —

However, these number ranges and distributions don’t always meet the needs of the game: what if I want a number between one and twelve with equal probability of any number being rolled? To meet such needs, RPGs use polyhedral dice, mostly based on regular ployhedra (the Platonic solids).

Die	Polyhedron (number of faces)	Shape of faces	Image	Numbering
d4	tetrahedron (4)	equilateral triangle		1-4 (sort of… see below)
d6	cube (6)	square		1-6 or spots (pips)
d8	octahedron (8)	equilateral triangle		1-8 or spots (pips)
d10 (old style)	dodecahedron (20)	equilateral triangle		0-9 twice
d10 (new style)	decahedron (10) (an irregular polyhedron)	kite		0-9 or 1-10
d12	icosahedron (12)	pentagon		1-12
d20	dodecahedron (20)	equilateral triangle		1-20
d100 (old style)	two dodecahedra (20), usually of different colours	equilateral triangle		0-9, twice
d100 (new style)	two decahedra (10)	kite		0-9 & 00-90 (in steps of 10)

Most of these dice are read in a natural way: the number is read off the uppermost face of the die. If a d10 is numbered 0-9, a “0” can be read as zero or 10, depending on the circumstances.

An old-style d10 can be used as a d20, with each 0-9 sequence inked in a different colour. (This was commonplace when I started gaming in the 1980s, as “full” d20s weren’t available!) Any d10 can also be used as a d20 by using a second die (e.g., if an even number is rolled on the second die, add 10 to the number shown on the d10).

Reading a d4 is not so straight forward, as there is no uppermost face: at rest, a vertex is uppermost. Each face displays three numerals, so that the number can be read off each of the three visible faces when the die is resting on the table (or floor, or whatever) – the same numeral is upright on each face, sitting either on the bottom edge or in the top vertex.

For the d100, percentile dice, one die represents tens, the other units. This is much clearer with new-style dice where one is numbered in 10s: “30” & “7” is 37; “00” & “6” is 6; “60” & “0” is 60. With old-style dice there’s some ambiguity: is “3” & “7” 37 or 73? is “0” & “6” 6 or 60?

So old-style dice are usually distinguished by being of different colours, or by being rolled in order. Like “0” on a d10, “00” & “0” or (“0” & “0”) can be read as zero or 100, depending on the circumstances. This often indicates some catastrophic failure or phenomenal success!