Randomization with an imperfect shuffle

[Bozeman]

A few random questions:

Is there are good measure of how random a reordering of the deck is?

I typically make 5-10 "mistakes" vs. a perfect riffle shuffle, that is, instead of being 2121212121, my deck would be something like 2121221211 = 2 "mistakes". How many of these somewhat imperfect riffle shuffles is necessary to well randomize the deck?

How does this number depend on # of mistakes made?

What assumptions were used in the standard 7 shuffle result?

Does smooshing the cards help? How much?

Is there a better way to shuffle?

How do autoshufflers do it?

Craig