The long history of dice
Posted 9 October 2006 at 10:45
Dice are among the oldest manufactured objects that survive in any quantity, and the reason is mundane: they are small, they are hard, and they were made in enormous numbers over a very long period. What makes them interesting here is that their history is a sustained practical argument about how to make an object behave unpredictably on purpose.
The earliest gaming pieces of this kind were not cubes at all. Astragali, the small ankle bones of hoofed animals, land on four distinguishable faces and were used across the ancient world. They are not symmetric, so the four faces do not appear with equal frequency, and the traditional scoring conventions applied to them reflect that: the rarer landings were worth more. The frequency structure of the object was priced into the game long before anyone described it as a probability.
The move to a cube is the move to symmetry, and it is a considerable manufacturing achievement. A fair cube requires uniform density, square edges, and pips that do not shift the centre of mass. Surviving examples show a long slow improvement in all three, and also show that the improvement was not universal: loaded and shaved examples turn up in the same archaeological contexts as fair ones.
Numbering conventions took a long time to settle. The now familiar arrangement in which opposite faces sum to seven is common but was never the only one, and the two mirror image versions of that arrangement both persisted. There is no arithmetic reason to prefer either; the sum to seven rule is a convention that makes an unfair die slightly easier to detect by inspection.
The modern precision die, with sharp edges and pips filled to the same density as the body, is a late object. What it represents is the end point of that long argument: an object engineered so that its six outcomes are as close to indistinguishable in frequency as manufacture allows. It is a curious thing to have spent several thousand years perfecting, and a good reminder that the arithmetic in these games came a long way after the objects did.
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