Non-Transitive Dice Are Weird

Originally published at: https://brian.carnell.com/articles/2021/non-transitive-dice-are-weird/

Non-transitive dice are beyond weird. As seen in the image below of Bradley Efron’s four-dice nontransitive set, these dice are not like normal six-sided dice in that each has a unique pattern of numbers. Imagine setting up a game where each person picks a die and then rolls that die 50 times. Whichever die rolls higher, the most times wins. The purple die will roll a higher number than the yellow die 2/3rds of the time. The yellow die, in turn, will roll a higher number than the red die 2/3rds of the time. Finally, the red die will roll a higher number than the green die 2/3rds of the time. Here’s where the weirdness of the non-transitive nature of the dice comes into play. The green die will roll a higher number than the purple die 2/3rds of the time. Wikipedia has a nice entry on non-transitive dice, including…