Non-transitive Dice

nontransitive dice

This is a non-transitive dice set, i.e. every dice in it is weaker than some other dice. Can you design a non-transitive set with only 3 dice?


Remark: "Weaker" means that it loses more often than it wins.


The simplest solution is given by:

2, 2, 4, 4, 9, 9;

1, 1, 6, 6, 8, 8;

3, 3, 5, 5, 7, 7.

Another solution is given by the so-called "Miwin's dice". They are as follows:

1, 1, 3, 5, 5, 6;

2, 3, 3, 4, 4, 5;

1, 2, 2, 4, 6, 6.