## Saturday, May 26, 2012

### It's Math in a Card Trick!!!

I haven’t wrote about many mathematical card tricks in the last little while. The last one I remember was the guessing one where you must try to guess each card’s value incorrectly through the deck. Because of probability and the number e, you will find it difficult to get through 52 cards incorrectly.
The reasoning behind that trick is pretty hard to beat. However, that trick definitely isn’t the best trick out there. The one I want to talk about today is a tad more impressive; something that with a little practice, you will be showing to all of your friends.
Here is how the trick goes: take a seemingly mixed deck of cards and cut off a stack. Then, supposedly by feeling the weight of the cards, determine the number of cards in the cut. You can repeat the effect as many times as you like with your own variations (riffling the cards and saying you can hear each click, etcetera), and it should fool your spectators.
The method is extremely simple. It has a little mathematical reasoning behind it, and involves a small mental calculation.
First, you must arrange the deck in a specific order before the trick. You can fan the deck out and people won’t tell a pattern, but there is one. The stack goes like this:
3C
6H
9S
QD
2C
5H
8S
JD
AC
4H
7S
10D
KC
3H
6S
9D
QC
2H
5S
8D
JC
AH
4S
7D
10C
KH
3S
6D
9C
QH
2S
5D
8C
JH
AS
4D
7C
10H
KS
3D
6C
9H
QS
2D
5C
8H
JS
4C
7H
10S
KD
If you look closely at this pattern, it is going up by three for each card. For the suits, you could technically do it however you want for this trick. However, it is traditionally ordered at clubs, hearts, spades, diamonds in a repeating sequence. You can remember this with the acronym CHaSeD.
Once you’ve got that done, you can begin the trick. If you know some false shuffles (the performer seemingly shuffles the deck without changing the order), you can use them. I would not recommend trying a false cut however, since cutting the deck is okay for this trick.
When you are cutting the deck, occasionally glance at the bottom card (do this while making a hand gesture or some natural movement that will not make it apparent that you made that glance). Wait until it is a higher card, and once it is, memorize that card value. Say it is the Queen of Spades.
Now, you can cut the deck yourself, or have the spectator cut it. Once you have the stack, glance at the bottom card. Let’s say that is the Nine of Spades. Here is what you have to do.
First, make sure you understand the following:
A = 1
J = 11
Q = 12
K = 13
So, the Queen of Spades is equivalent to 12. Subtract the 9 (Nine of Spades) from the 12 (Queen of Spades).
12 - 9 = 3
Now, multiply this number by 4.
3 x 4 = 12
Now, ask yourself this question: is there any way I am holding 12 cards?
You will be able to tell if you are or aren’t holding 12 cards. In this case, you would be holding 12 cards.
Let’s say the bottom card is the Jack of Hearts and you cut to the Four of Spades. Same thing; do the following calculation:
(11 - 4) x 4
7 x 4
28
Now, ask yourself if you are holding 28 cards. If you actually try this, you will find it clear that you are holding more than 28 cards.
Here’s what you do. With our sequence, there is a four every thirteen cards. Because of this, we can add or subtract 13 to the number we have and it won’t make a difference. So, let’s try it.
28 + 13 = 41
In this scenario, 41 would be a reasonable estimate, and the correct answer.
Let’s try one more; say the bottom card is the Jack of Diamonds and you cut to the Queen of Hearts. So, you would do:
(11 - 12) x 4
-1 x 4
-4!!!!
You can’t have -4 cards. However, we can add 13 as we please.
-4 + 13 = 9
9 + 13 = 22
This stack would have 22 cards.
It will take practice to make the glance at the bottom of the cut and the bottom of the deck more slick, and the mental arithmetic quicker, but it is definitely a cool effect. If you know false shuffles, it will become even better. But most importantly, it is a fun way to bring math into your everyday life.