Futility Closet

Nontransitive Dice

Posted in Science & Math by Greg Ross on June 18th, 2008

Mark the faces of three dice as follows:

  • Die A: 2, 2, 4, 4, 9, 9
  • Die B: 1, 1, 6, 6, 8, 8
  • Die C: 3, 3, 5, 5, 7, 7

Remarkably, you'll find that Die A tends to beat Die B, Die B beats Die C, … and Die C beats Die A.