Nontransitive Dice

Nontransitive Dice are pretty amazing things. Basically, in these dice, when they are set up pairwise, one die will beat another 2/3 of the time. However, there’s no “best” die. Even though A beats B and B beats C, A DOES NOT BEAT C. I bought a wonderful pair of Efron’s Dice from the Museum of Math.  For the math nerd, you really have to get a set. They’re amazingly interesting and they really teach kids about probability in a wonderful way!

Without going into all the details, normally, when you play dice you assume transitivity:

  • If B beats A
  • And if C beats B
  • Then C beats A

Which sounds obvious; however, it’s not. take, for example, the game rock, paper, scissors.

Rock-Paper-Scissors from Wikipedia

In this case:

  • Rock beats scissors
  • Scissors beats paper
  • But rock DOES NOT BEAT paper.