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still doesn't answer the question

Posted By: Timothy Chow
Date: Tuesday, 8 July 2014, at 10:11 p.m.

In Response To: still doesn't answer the question (Stuart Gardner)

I think people are conflating two distinct issues here. Dice can fail to be precision dice for two very different reasons: (1) someone has intentionally rigged the dice for the purposes of cheating, or (2) a lazy manufacturer is selling low-quality dice as "precision dice" to make a fast buck.

Detecting intentional rigging, assuming that you have complete control over the dice in question for a long enough time, is a well-studied problem. You can easily teach yourself some of the main techniques by Googling "detecting crooked dice."

Detecting low-quality dice is a different problem. Some of the same techniques may still apply, but the aforementioned lazy manufacturer isn't going to be inserting tiny bits of magnetic material into the dice, so testing with a magnet makes little sense. More importantly, intentionally rigged dice will usually have a large bias (under the right conditions), so as long as you know what the relevant conditions are and can create them at will, the bias should be relatively easy to detect with only a few trials. Poor-quality dice, on the other hand, may have only a small bias, in which case you may need to invest considerable time and effort to gather enough statistical information. However, if you have enough patience, the simplest and most obvious test should work well: Just roll the die over and over again and record the results. Then apply a χ2 test to see how evenly distributed the numbers are.

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