In reply to Martin Sirera.

Thanks for writing. I understand what you are saying: a good shuffle should mix up the cards, including the top card. This analysis is for an idealized mathematical shuffle. As you state, you would not want to do this in a real card game because after 8 perfect shuffles (when using an "out shuffle," which is defined in the article), the cards are back to their original order! For a real shuffle there is random variation about how many cards fall from the Top and Bottom portions when you shuffle. A real shuffle can be studied by using the Gilbert-Shannon-Reeds (GSR) model, see the link in the third paragraph. Instead of a deterministic result such as TBTBTBTB..., a real shuffle involves random sequences that look like (for example) TBBTBBTTTBTBTT...