[btilly]

That is more involved than I thought. I was looking for a covert information channel. For instance the assistant could hold the cards in 2 different ways, 4 cards represents 16 bits of information, plus 2 more bits for which card is the high card.

Here is a simpler one that impresses many people. Deal out 3 cards across, return to the top, 3 more cards, and so on until you've dealt out 27 cards in 3 columns. Have the other person pick a card but don't indicate what it is. Ask them to indicate which column has the card. Stack the 3 columns with that in the middle. Now redeal go through the same procedure. Repeat one more time. Now count the cards out. Card #14 is the picked card.

Why does it work? Well the first time you deal it could have been anywhere, the second time it is down to the 3 middle rows, the third time it is in the middle row, then you stacked it in the middle of the deck.

[rimantas]

Actually you may let the one you are showing the trick to to choose the order, you need just to notice where did the column with the card go. 2 if it is on the bottom, 1 if in the middle, 0 if on the top. When you got your three digits, reverse them and convert from ternary to decimal—that will be the number of cards above yours. In the case you are putting column with a card to the middle you'd get 111, that is 13^2+13^1+1*3^0=9+3+1=13. Hence your card is #14.

I think this was in one of the books by M. Gardner.

[rimantas]

Corrections: bottom-2, middle-1, top-0. 1×3^2+1×3^1+1×3^0=9+3+1=13