Self Working Card Tricks

Originally posted on September 9, 2018 by Damien

The first card trick I ever learned was a pretty simple one that required no sleight of hand, and worked if you could follow the simple instructions. It used 21 cards, and allowed you to identify a chosen card. The trick is simple, get the volunteer to select a card, and place it back into the packet of 21 cards. You then deal the cards into 3 piles, asking the volunteer to note which pile their card is in. Place that pile in between the other piles and repeat two more times. After that their card will be in the middle of the middle pile, allowing you to reveal it in whichever way you feel works best.

I learned a nifty variation a few years later that only uses 15 cards, and has a nice reveal where the chosen card rises out of the deck. After the third round of dealing into piles, the chosen card will be in the middle pile. Square up one of the other piles face down, then deal the middle pile on top so that the cards protrude alternately above and below the first packet. Square up the last packet and place it on top, level with the first packet. You should have a packet of cards with 3 cards sticking out on one side, and two on the other. Pick all the cards up, and push the 3 cards back into the packet. Keeping some pressure on the other cards, pushing the two remaining cards back into the packet should cause the chosen card to rise up.

These tricks are nifty enough, but a couple of years ago I found a far more impressive version from mathematician Matt Parker, which allows you to place a chosen card anywhere among 27 cards. Rather than go through the explanation of how it works, I’ll simply show this video of the trick and how it is done:

Matt has an even nicer version of this trick, that uses nearly a full deck, needing 49 cards. He demonstrates the trick at the end of the 27 card trick video.

Unfortunately, he doesn’t explain how to do the 49 card trick, but with a bit of thought I was able to work out how to do it. In order to understand the 49 card trick, it really is easiest to watch the first video, get a good understanding of how the 27 card trick works, and practice until you can do it in your sleep.

Done that? Good, let’s get on with the 49 card trick. The whole basis for the 27 card trick was being able to count in base 3, and having a number of cards that was equal to the number of piles raised to the power of how many times you dealt them out (3 piles, 3 times dealing = 3³ = 27 cards). So, to start with, the 49 card trick uses 7 piles, dealt twice (7²=49 cards). Now, because there are 7 cards per pile, we need to count in base seven to determine which position to place the packet with the chosen card in it.

Don’t worry if you’re not sure about counting in base 7, it’s just like counting in decimal, if you’ve suffered a nasty industrial accident and have lost 3 fingers (sorry, bad joke…). For the purposes of the trick, we’re thinking of the piles as being numbered 0 through 6 (like the piles were 0 to 2 in the 27 card trick). So, when you get the volunteer’s number, you need to workout how many times it can be divided by 7, and what the remainder is.

Here’s an example: the volunteer says their number is 13. Firstly we need to think in terms of how many cards go above the chosen card, so that’s 12 cards. 7 goes into 12 once, and has a remainder of 5.  Now, when you deal out the cards, the pile with the chosen card goes into position 5 the first time, and into position 1 the second time.

Another example, let’s say our volunteer picks a big number, and says 42. That’s 41 cards to go above the chosen card. 41 divided by 7 is 5, with a remainder of 6. When we deal out our cards the pile with the chosen card goes into position 6 the first time, and position 5 the second. So, hopefully those instructions, combined with the videos, are enough to get this trick working for you. One idea I had regarding the set up for this trick, rather than having a special 49 card deck set up, or having to sneak 3 cards out, somehow, was to get the volunteer to remove three cards. I like to explain this as being so that if I’ve memorised the order of the cards, having three cards removed randomly will mess me up.