Non-transitive dice

Idea from the blog “Notiziole di .mau.” of Maurizio Codogno (mathematician, Italy)

Imagine saying to your friend "choose any die, and then I'll choose another one. Then we roll our die 10 times, and whoever gets the lowest score the most times will lose.”

If the friend chose A, you choose C.

If the friend chose B, you choose A.

If the friend chose C, you choose B.

Dice of this type are called non-transitive , because it is not possible to create a transitive order of value between the dice (see Wikipedia).