Why does it matter that only the cut is imperfect? Isn’t an imperfect interleaving also expressible as a modification to the unevenness of that left/right pile split? It seems the “0110” system doesn’t track relative order of cards but only the landing of each card, which allows each left/right landing to be treated as an independent event. If there’s no dependency on card order, modifying the cut split is a simple way to express both an uneven cut and imperfect interleaving with one variable.

But that assumes the model is only tracking cards’ arrivals in the left and right piles, not their ordering relative to one another. I only got that from the article.

Am I missing something? Is it that the left/right split is actually only informative about the amount of mixing that has occurred under the assumption that the interleaving was perfect, and therefore if imperfect interleaving is possible then one must weaken that guarantee - which then requires a more complex tracking system?