"But a long term sum of results is a completely different game." That's exactly the point! A naive intuition about dice is that they have a single probabilisti

"But a long term sum of results is a completely different game." That's exactly the point! A naive intuition about dice is that they have a single probabilistic long-term score. E.g. 6-sided die is 3.5. So if one dice beats another, it should be transitive (the intuition goes). It's the summation (implied by averaging over time) that leads to the naive intuition.