Yesterday (November 1) on KUOW Presents, they presented a segment from Wisconsin Public Radio's "To the Best of Our Knowledge" that talked about Math and Magic Tricks and Binary numbers.
They interviewed Persi Diaconis, a magician and mathematician who is currently a professor of Statistics and Mathematics at Stanford University. In one part of the program, they talked about how card magicians (and poker cheats) can use knowledge of binary numbers and 'perfect' card shuffling to take a card at the top of the deck and move it to any desired position in the deck while apparently shuffling the cards into a random order.
The link to Jim Fleming's complete interview with Persi Diaconis is near the bottom of the "To the Best of Our Knowledge" page for this program under the "Special Web Extras" section. The uncut interview is ~34 minutes, roughly 12 of which made it into the KUOW Presents show. The part on using binary and perfect shuffles runs from around 4:54 - 6:40, but I found the entire interview interesting.
I need to turn this into classroom material because I'm sure that the students will find it fascinating.