## March 29, 2008

### Polyhedral Dice

Stupid Question ™
Nov. 3, 2003
By John Ruch

Q: What was the first recorded use of a non-six-sided die in gaming?
—Channingway Blvd. Grifter, Chicago, Illinois

A: “Gaming” generally means role-playing games (RPGs), a genre in which strange dice are standard equipment.

And by “non-six-sided,” you must mean the polyhedral dice used in such games—a set that includes not only a six-sided die, but also a four-sider, eight-sider, 12-sider and 20-sider. (And usually a 10-sider, too, though technically it’s not a polyhedron.)

The first RPG use of such dice was in the first RPG—the famous Dungeons & Dragons (D&D) game.

However, D&D did not invent the dice. D&D co-creator E. Gary Gygax, who was the first gamer to use polyhedral dice, told me he originally found them in a school supply catalog from California, where they were sold as tools to teach math and probability.

The dice were (and still are) used in math classes by making up little games with them. So to be technical about it, we can go farther back to find the first “gaming” use.

Perhaps very far back, indeed. Strange rounded stones etched with facets numbering from 3 to more than 100 and dating to around 2000 BC have been found around Europe. Their purpose is unknown, but they could be a sort of multi-sided dice, perhaps used in divination. In any case, dice games certainly originated in divination.

The five shapes that make up the polyhedral dice are also known as the Platonic solids. They were known to the ancient Greeks and codified by Plato’s Academy, where they were used to teach geometry. Euclid (c. 300 BC) proved them to be the only possible regular polyhedra, meaning the only three-dimensional solids that could have congruent facets tha all met at equal angles.

Occultists have sometime ascribed mystical properties to the Platonic solids, which may have led to a dice divination “game” using them. Polyhedral objects—almost certainly dice—with zodiacal markings are known from the late Roman/early Christian era in Europe.

The six-sided (cubical) die became the gaming standard not because it’s a Platonic solid but because it’s easy to make, and probably because it stems directly from the “knucklebones” (paw or hoof bones) of animals used earlier.

Probability studies actually began with six-sided dice in the 1650s, when the great mathematicians Blaise Pascal and Pierre de Fermat puzzled out the problems of dice-rolling. Cubical dice have been used to teach probability ever since.

However, even when polyhedral dice didn’t exist (or at least not en masse), there were certainly thought experiments done about them in probability classes, in terms of wondering what would happen if there were more than six sides.

I polled a variety of math educators and none could say who introduced the polyhedral dice to math teaching when. The best guess was that it was sometime in the 1960s, when probability first became a standard part of high-school math. Still, use of dice, especially polyhedral dice, remains pretty rare in math classes.

Gygax found his dice in 1972 and used the new statistical spreads they made possible to create the rules of D&D from the wargame Chainmail. However, the supply of dice was too low to sell them at first. So from 1974 to 1980, D&D came only with marked cardboard chips that were pulled randomly out of a bag. Eventually, the game’s publishing company began selling dice separately, and in 1981 they became a standard part of the game package. In the interim, the 10-sided die had also been created.

There is a story going around that D&D co-founder Dave Arneson may have found some 20-sided dice in England before Gygax found his; but the two men have a long-standing feud over who invented what in D&D. There’s no evidence for an Arneson claim; he did not respond to my questions, and Gygax discounted the story.