There is no nonlinearity or defiance of probabilities. It’s just simply the fact that comparing the face values between the dice outcomes has dice each winning over the next, because that operation is not transitive in general.

The “trick” here is only that people assume that dice A winning over dice B and dice B winning over dice C should mean that dice A should also beat C, which it doesn’t simply because dice outcome comparisons aren’t transitive.

So there’s no tricks or secrets, it’s just peoples intuition being wrong.

I personally prefer the intransitive set of D3s to explain this. Assume you have three dice R,B,G. They all have 1,2,3. But on ties we have tie breaker R>B>G on 1s, B>G>R on 2s and G>R>B on 3s. So it’s easy to see that for each dice there is 1/3 of times when it wins the ties, 1/3 where if losses, and the last 1/3 it either wins or loses based on which dice it’s facing. That might at face value seem like cheating because “I put the non transitive property into the tie breakers” but that’s just to make it easier to grok, you can change the dice to have faces (1,6,8),(2,4,9),(3,5,8) and you get the same without needing to handle ties. And since 1,2,3 are all equivalent in comparison to anything above 3, it’s practically the same as the first scenario.