A set of dice is nontransitive if the binary relation – X rolls a higher number than Y more than half the time – on its elements is not transitive. Different sets of such dice are known.
'Rolling higher' is a stochastic event and 'more than half of the time' an other one.
Most often probabilty is presented as a kind of measure and in trivial cases such as coins or usual dice it is obviously connected to physical/spatial objective properties. For this particular case however it appears to be a kind of (cyclic) ordering.
How would a Frequentist and a Bayesian explain away this fact?