I took these pictures of Roman and Babylonian dice at the Pergammon museum in January.
Although these are from very different time periods, they share a lot in common; the arrangement of the dots on each side, the circles around the dots – they’re basically the same die, thousands of years apart.
It struck me that these dice must have been much in demand, but that they are easier to test than they are to make true. To find out if a die is fair, you simply throw it as many times as you can and record the distribution of results.
To make it fair, you need to pick a geometry to match the number of face you need, carve it as accurately as you can and then keeping tweaking the weights and filling in the holes until it rolls evenly.
Once the die has been corrected, there should be a 1/6 chance of each side showing up. We’d use a chi squared test nowadays to check this;
? (observed – expected)^2/expected
Obviously, the more throws, the closer you get to an even distribution. This remains the most accurate way of testing dice, particularly hand-made dice which may contain eccentricities from uneven weight distribution or face geometry.
But then here’s a chinese die I bought in Burma – this is a different approach to solving the same problem – you spin it. It’s only made of wood, but it should give more random results than a slightly uneven bone die.
Only one way to find out really, I’d rather someone else did the throwing though.