Make Your Own Non-Transitive Dice at Home

I recently discovered a YouTube channel called “Numberphile” where a documentary filmmaker Brady Haran does a series of short interviews and clips with different mathematicians and physicists about numbers.  Since my short description simply does not do this series justice – please take a few minutes and watch this recent video of theirs about how Richard Feyman defeated every government safe in Los Alamos. Many of the videos in this series feature James Grime, a mathematician who recently invented a new kind of non-transitive dice as well as several games you can play with them.  That is, several games you can play with them and always win.  Non-transitive dice are designed in such a way that the first die will always tend to beat the second, the second will always tend to beat the third, and the third will always tend to beat the first.  Efron dice designed by American statistician Brad Efron and feature the same “circular pattern of victory” – but with four dice.  Grime dice by Numberphile star Professor James Grime feature five dice which have a similar “circular pattern of victory” with additional interesting properties. Encouraged by Professor Grime’s infectious enthusiasm, I designed three sets of printable non-transitive dice (three non-transitive dice, four Efron dice, and five Grime dice) which you can print on your MakerBot at home – either as dice where you color in the pips or which you can print with dualstrusion. By the way, my favorite part from any of these videos is where Professor Grime talks about how he thought up these dice in his mind, and now they occupy a real physical place in the world since he had them created.  This video includes a refrain any Thingiverse citizen is familiar with…  “I made a thing!” (Also, please don’t use these dice for evil.  Remember that with great power, comes great responsibility.)