Baffling Prediction

Following is an simplified excerpt from
M.Gardner,Mathematics, Magic and Mystery

The Trick: You, as the magician, ask a spectator to shuffle a deck of cards and place it on the table. You then write the name of a card on a piece of paper and place it face down without letting anyone see what has been written.

Now deal twelve cards to the table, face down. You ask the spectator to touch any four. The touched cards are turned face up. The remaining cards are gathered and returned to the bottom of the pack.

We will assume the four face-up cards to be a three, six, ten, and king. You state that you will deal cards on top of each of the four, dealing enough cards to bring the total of each pile up to ten. For example, you deal seven cards on the three, counting "4, 5, 6, 7, 8, 9, 10." Four cards are dealt on the six. No cards are dealt on the ten. Each court card counts as ten, so no cards are placed on the king.

The values of the four cards are now added: 3, 6, 10, and 10 equals 29. The spectator is handed the pack and asked to count to the 29th card. This card is turned over. Your prediction is now read. It is, of course, the name of the chosen card.

Method: After the deck is shuffled you casually note the bottom card of the pack. It is the name of this card that you write as your prediction. The rest works automatically. Gathering the eight cards and placing them on the bottom of the pack places the glimpsed card at the 40th position. After the cards are properly dealt, and the four face-up cards totaled, the count will invariably fall on this card. The fact that the deck is shuffled at the outset makes the trick particularly baffling.

It is interesting to note that in this trick, as well as in others based on the same principle, you may permit the spectator to assign any value, from 1 to 10, to the jacks, kings, and queens. For example, he may decide to call each jack a 3, each queen a 7, and each king a 4. This has no effect whatever on the working of the trick, but it serves to make it more mysterious. Actually, the trick requires only that the deck consist of 52 cards - it matters not in the least what these cards are. If they were all deuces the trick would work just as well. This means that a spectator can arbitrarily assign a new value to any card he wishes without affecting the success of the trick!

Further mystification may be added by stealing two cards from the pack before showing the trick. In this case ten cards are dealt on the table instead of twelve. After the trick is over, the two cards are secretly returned to the pack. Now if a spectator tries to repeat the trick exactly as he saw it, it will not work.