#132: Fair die

Mathematics textbooks are full of references to fair dice. Fairness they define as yielding equal numbers of each of the 6 possible outcomes, when a die is tossed a very large number of times. A die that came up ‘5’ for the first 30,000 or so tossings, might. however, make one suspicious about exactly how fair it was, even if ‘5’ didn’t reoccur in the next 5,000…it all just shows that humans aren’t naturally attuned to the meaning of probability (anyone’s first 5 minutes in Las Vegas illustrate that).

Today’s invention is a truly fair die.


It consists of a cube with some electronics on board. Each side of the die has a seven-seg display. Whichever of the six sides lands uppermost is the one which displays the result in the usual way (whilst the other five sides show the other five numbers, if necessary).

At each toss, the number to appear on the uppermost face is read from a pregenerated list containing exactly equal numbers of each of the 6 possible outcomes (and distributed along the list using a simple numerical shuffling technique).

If you were concerned that the (predestined) list could be ‘hacked,’ security features, such as holograms, could be embedded in each of the faces. The batteries would require charging occasionally and after say six million throws (that’s 1M 1’s, 1M 2’s, 1M 3’s, etc), the system would shut down permanently.

One Comment:

  1. I’m not at all sure that this attempt to equalise the sum of mr^2 about each of the three main axes is valid http://coolmaterial.com/home/machined-dice/

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