Wednesday, January 23, 2008

Often missing from a discussion of Any Card At Any Number is mention of a trick by Bertram Adams called Adamathica. He marketed it in 1921 as a set of instructions in hardbound form. He said he had 100 copies for sale and I would imagine it is quite rare. I found a set of instructions at Ask Alexander.

The effect is described as follows:

Spectator is asked to make a free mental selection of any card in a deck of 52. This selection is made purely mentally without reference to any deck, hence it is not forced in any way. The same spectator, or another if there be more than one, is now asked to name any number from 1 to 48. The spectator is then told that the card that he has mentally selected will be made to assume a position in the pack at the number mentioned. Through the entire experiment the performer does not see the face of the cards as they are handled face down.

Free selection of card. Free selection of number. And yet the mentally selected card ends up at the chosen number. Sounds impossible. Adams claimed it took him ten years to develop it.

Unfortunately Adamathica is not the Holy Grail ACAAN that many are seeking. It was a version of the 27 Card Trick, a dealing routine using a full deck in which the mentally selected card to could be manoeuvred to a chosen number. In later advertisements, perhaps sensing some resistance to his mathematical creation, Adams said: ‘You may think it the poorest excuse for a trick you ever saw but send me your dollar. I will send it by return mail then if you don’t like it say so, I will send your money back quick.’

It was a clever idea and if you’re interested in the mathematics of the 27 Card Trick you can find more in Martin Gardner’s invaluable Mathematics, Magic and Mystery where chapter three is given over to what is known rather amusingly as Gergonne’s Pile Problem.

The routine that follows uses the work of Bertram Adams combined with another old idea to produce what I think is a reasonably interesting mathematical version of any card at any number. It’s never going to make it into your table hopping repertoire but you might want to give it a run at your local magic club.


‘As is well known, Charles Babbage was the scientist who invented the Difference Engine, a form of early computer designed to make calculations quickly. This was back in the 1820s when the idea of calculating machines was pure science fiction. He was inspired by in his work by an exhibition he saw of a mysterious automaton known as Von Kempelen’s Chess Player. It took the form of a mechanical man dressed in Turkish garb and would sit at a table and take on all comers at games of chess. It usually won. But it wasn’t the chess games that interested Babbage. It was a card trick that the automaton performed. Babbage couldn’t figure out how it could possibly work without some form of calculating machine being employed. And that’s the card trick I’m about to show you.’

All of the above is pure fiction but it helps set the rest of the effect in context. And the effect is this. One spectator chooses four cards from the deck and places them in his pocket. It’s a free choice of cards and you never see them until the finale of the trick. A second spectator has a free choice of any card in the deck. Using a little of Bertram Adams’ thinking from Adamathica you are now able to bring the thought-of card to the exact position in the deck indicated by the total value of the four pocketed cards. So if the four cards add up to 29, the chosen card will be at the 29th position in the deck. The trick is entirely self-working and you don’t need to see or know any of the chosen cards to bring about the effect.

The method has two main elements. The first is forcing the total value of the four pocketed cards. The second is manoeuvring the selected card into the right position in the deck.

The deck is stacked so that if any four adjacent cards are removed their combined values will total 28 or 29. This is the familiar 14/15 stack. The arrangement is described in Annemann’s 202 Methods of Forcing and is as follows:

7 - 8 - 6 – 9 – 5 - 10 – 4 – J – 3 – Q – 2 – K – A – K – 2 – Q – 3 – J – 4 – 10 – 5 – 9 - 6 – 8 – 7 – 7 - 8 etc.

You’ll have two aces left over. Place these on the face of the deck.

This stacked deck is usually used to force either the number 14 or 15 when a pair of adjacent cards is removed and the values totalled. Jacks equal 11, Queens 12, Kings 13.

If four adjacent cards are taken they will total 28 or 29 or 30 which is I think a more suitable total for this trick.

Incidentally some time ago Peter Duffie asked me who originated this stack. Generally it is credited to Annemann but I found an earlier reference to it in The Sphinx (May 1924) where it is used by T Page Wright in his A Prophetic Card Discovery. He says the arrangement was inspired by one devised by William Larsen Jr. The more I find out about Wright and Larsen the more I admire their work.

Step 1: Tell your Charles Babbage story as you spread the deck face-up. The stack won’t be noticed. Then spread the deck face-down across the table and ask the first spectator to remove any four cards together. Except for the two aces on the face of the deck, he has a free choice. Ask him to put the four cards in his pocket for now.

Step 2: Hand the deck to the second spectator and ask him to shuffle the cards, which effectively destroys your stack. Have him place the deck on the table and then cut the cards and look at the card he has cut to and remember it. You need him to cut a card in the central third of the deck. Most people will do this naturally when asked to cut the deck. It’s a good idea to turn away as soon as he has cut the deck. It guarantees you can’t see his selected card and makes the whole process look incredibly fair. When he has remembered his card tell him to replace the cut portion and square the deck.

Step 3: If for some reason the spectator cut shallow or deep you can now adjust the deck so that his selection is in the middle. Pick up the deck and just shuffle a few cards around so that the selected card is positioned correctly. If it’s already in the centre third of the deck, give the cards a false shuffle that keeps the selection in that centre portion. Either way you appear to shuffle the deck which further convinces the spectator that his card is lost.

Step 4: Deal the cards out, from the top of the deck, into four face-up heaps, asking the spectator to look for his card so that he knows where it is. ‘But not to give anything away that would reveal which card you are thinking of. Don’t smile or grin or stare or blush.’

At the end of the deal say, ‘The automaton asked only one question at the end of the deal. Which pile is your card in?’ Let the spectator answer and then gather up the piles so that his pile is second from the top of the deck. Obviously do this as casually as you can as you talk about Charles Babbage watching this trick.

Step 5: Deal the cards out for a second time. Again the cards are dealt from the top of the face-down deck into four face-up piles. Once again ask the spectator to watch out for his card. As you deal, say, ‘And this was the part of the trick that intrigued Babbage because later he realised what the automaton must be doing. You see every card in the deck has a value. There are the numbers Ace to 10. And there is the Jack which equals 11. The Queen is 12. And the King is 13. And it seemed both obvious and yet impossible to Babbage that if you could add up all the totals of these values, as the cards were being dealt, you would be able to calculate the total value of the cards that were missing from the deck. Let me show you what I mean.’

Then, seemingly as an afterthought, ask the spectator which pile his chosen cards lies in. Gather up the four packets except this time pick up the pile containing the selected card so that it lies third from the top of the deck. You can if you wish give the cards a quick full deck false shuffle to further confuse the spectators.

The thought-of card is now in position for the finale. It lies 29th from the top of the deck. I think that’s remarkable given that you’ve only dealt the cards out twice.

Step 6: Ask the first spectator to take out the four pocketed cards and total the values. You’ve already told him that Jacks equal 11, Queens 12, Kings 13. The addition is done openly which means you’re free to help him arrive at the total which will be 28 or 29 or 30.

Step 7: Remind everyone that only the second spectator knows the name of the card he is thinking of. Ask him to name it. Repeat the name of the card and say, ‘And this is the part that baffled Babbage. Because he couldn’t figure out how anyone or anything could possibly make your (to second spectator) thought-of card arrive at your (to first spectator) chosen number. But that’s exactly what happened. Let’s see if we’ve got this right.’

Count down to the number. You will either find the chosen card at the number called in the case of 29 or it will be the following card in the case of 28. Either way it is an easy finish to make. The slightly more difficult outcome happens when the cards total 30. But all you need to do is deal 30 cards face-down into a pile then pick the pile up and double lift to reveal the chosen card.

NOTES: You’ll never disguise the fact that this is a mathematical card trick but that doesn’t stop it being an interesting card trick, hence the Babbage themed patter that takes it into the realms of pseudo memory and calculation. Your story gives the spectators a reasonable sounding explanation to hang onto, that somehow you were able to count the values of the face-up cards, deduce the value of the missing cards and find a way to position the thought-of card. Good luck on making that work!