That is such an interesting idea! I wonder if someone has systematically studied hand shuffling biases and what consequences it has (or should have) for brick and mortar casinos
Suppose you're at a full table and 12 of the last 20 cards are aces or tens (rare but possible). These get shuffled and cut into the first three decks, giving you a true count of four (12/3) for the first half of the shoe, which is significant.
We never really put it into practice, though, since: 1) you have to track the count for the last 20 cards in addition to the regular count, 2) shuffles change, 3) dealers are inconsistent, 3) casinos use different shuffles, 4) the typical advantage is likely to be much smaller.
My knowledge on this is at least 20 years out of date, though, so who knows?
Let's call the two splits L for left and R for right and consider the resulting deck to be defined as a sequence of these letters indicating whether that card was taken from the left or right pile so in theory you can specify a shuffle uniquely like "LRRLLLLLLRRR...". This method of labeling shuffles has the advantage of being extremely easy to record and also makes the bias I found apparent where there are way too many pairs of "LR" and "RL" compared to "LL" and "RR" like the "7 shuffles is enough" model suggests there should be.
For some reason, when I did all this analysis last year, I was mostly thinking about how to ensure my MTG decks are sufficiently shuffled. I didn't really think about the implications for card counting. However, normal riffle shuffling seems to have less bias (but still present) than the mash shuffling I looked at and I think most casinos use machines for shuffling these days.