I thought about this for a very long time. For any given deck of cards, there is a coefficient of the average magnitude of displacement from their current order after a shuffle. This can be positive or negative, but we take the absolute value. Then, divide the total number of cards in a deck by this number to get the number of times you need to shuffle. A total of 7 shuffles implies an average displacement of about 7 cards. I think it's reasonable if you alternate the cuts in between shuffles.

Sloppy shuffles have a much lower average displacement and thus need more shuffles to get to a random state.