How not shuffling the deck theoretically is more magical

Mark · 05-16-2011, 08:57 AM

This is something I thought of last night and I might as well be the first one who thought of this in relation to a full deck of playing cards. Magicians always tend to think that having the deck shuffled is fair but is it really?

The Monty Hall problem
You may or may not be familiar with the Monty Hall problem. If you are, you can skip this section. If not, let me elaborate:

Let's say there are 3 closed doors and behind 1 of the doors there is a prize. You now may pick one of the doors so you have a chance of 1 in 3 that you pick the correct one. Once you picked a door, you are asked if you would like to change your mind. Would you change your mind and choose for another door or would you still go for the door you chose at first?

You may not want to but you better change your mind because you only had a 1 in 3 chance of instantly picking the correct door so there is a 2 in 3 chance the prize is behind one of the other doors. It's not a guarantee but changing your mind and choosing for one of the other two doors now does increase your chances. That is, if your intuition isn't always spot on.

A deck of playing cards
Let's look at this in relation to a full deck of playing cards. If you ask a spectator in what position i.e. the 7 of Spades is and let's say they choose for the 23rd position. The chance that the 7 of Spades is actually at that position is way small (1 in 52). But if you shuffle the deck, the chance the 7 of Spades now is in the 23rd position still is way small, but slightly bigger than before you shuffled.

'ACAAN'
Now if you would ask a spectator to think of any card and any number. The chance that the card they think of is actually located at the number they think of again is way small. If anyone now shuffles the deck once the spectator selected their card and their number (even when they didn't say them out loud yet; just in their minds.. and they wouldn't have a reason to change their minds and think of another number or card) the chance that the card they think of is at the desired number after the shuffle is bigger than before.

'Ambitious Card Routine'
A little easier to follow along: you bury a selection in the middle of the deck and have the spectator shuffle the deck. The chance the card is either on top or the bottom of the deck after the shuffle is pretty big compared to when the card really was in the middle of the deck. This is actually the reason why I never shuffle the cards during an 'Ambitious Card Routine'. I may have the spectators shuffle because they think it's way fair while it actually isn't if you think about it.

Of course, the chance is still way too small to make an actual trick out of this but I thought it was just a neat thingy to share.

05-16-2011, 08:57 AM	#1
Mark Join Date: Feb 2010 Location: The Netherlands Posts: 935	How not shuffling the deck theoretically is more magical This is something I thought of last night and I might as well be the first one who thought of this in relation to a full deck of playing cards. Magicians always tend to think that having the deck shuffled is fair but is it really? The Monty Hall problem You may or may not be familiar with the Monty Hall problem. If you are, you can skip this section. If not, let me elaborate: Let's say there are 3 closed doors and behind 1 of the doors there is a prize. You now may pick one of the doors so you have a chance of 1 in 3 that you pick the correct one. Once you picked a door, you are asked if you would like to change your mind. Would you change your mind and choose for another door or would you still go for the door you chose at first? You may not want to but you better change your mind because you only had a 1 in 3 chance of instantly picking the correct door so there is a 2 in 3 chance the prize is behind one of the other doors. It's not a guarantee but changing your mind and choosing for one of the other two doors now does increase your chances. That is, if your intuition isn't always spot on. A deck of playing cards Let's look at this in relation to a full deck of playing cards. If you ask a spectator in what position i.e. the 7 of Spades is and let's say they choose for the 23rd position. The chance that the 7 of Spades is actually at that position is way small (1 in 52). But if you shuffle the deck, the chance the 7 of Spades now is in the 23rd position still is way small, but slightly bigger than before you shuffled. 'ACAAN' Now if you would ask a spectator to think of any card and any number. The chance that the card they think of is actually located at the number they think of again is way small. If anyone now shuffles the deck once the spectator selected their card and their number (even when they didn't say them out loud yet; just in their minds.. and they wouldn't have a reason to change their minds and think of another number or card) the chance that the card they think of is at the desired number after the shuffle is bigger than before. 'Ambitious Card Routine' A little easier to follow along: you bury a selection in the middle of the deck and have the spectator shuffle the deck. The chance the card is either on top or the bottom of the deck after the shuffle is pretty big compared to when the card really was in the middle of the deck. This is actually the reason why I never shuffle the cards during an 'Ambitious Card Routine'. I may have the spectators shuffle because they think it's way fair while it actually isn't if you think about it. Of course, the chance is still way too small to make an actual trick out of this but I thought it was just a neat thingy to share.