Last night at Ithaca Generator Game Night I mentioned to Marty and company that I had recently seen a video which claimed that while riffle shuffling will thoroughly mix a deck of cards in 7 shuffles, overhand shuffling takes over 10,000 shuffles to do the same. I've attached the video.
It links to two papers, one from 1998, http://projecteuclid.org/download/pdf_1/euclid.aoap/1177005705
which discusses the riffle shuffles, and one from 2006 http://arxiv.org/pdf/math/0501401.pdf
which discusses overhand shuffles.
I wonder how popular I'd be at a MtG competition if I sat across from a player with a deck of 60 prinstine, unbent cards in sleeves, overhand shuffling them to protect them, and then I called over the TD, showed them the papers, and said I'm gonna need to riffle-shuffle his deck at least 8 times to ensure they were properly randomized. I can't wait for even 10000 overhand shuffles.