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Jumble Bumble...never done before...not so fast

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948855.  Sat Nov 03, 2012 10:44 am Reply with quote

So, dear QI Elves, you had Stephen at the end of the latest episode "do something no human being has every done before" only, you're not quite right.

The statement revolves around the 52 factoral total for the number of cards in a card deck (I believe you guys said 54~52 + 2xjokers) however this number doesn't equate to the total number of possible shuffled positions of a deck of cards, but rather every position a card can ever have. This include non-total deck positions in a shuffle.

Further, we have to consider type of shuffle in the case of determining probability and likelihood that the same shuffle has been performed before. Consider that Stephen did three types of shuffles, two of which were are called "perfect" or "true" shuffles. That is, a card shuffle in which each half is cut as Stephen said "ABAB". Such shuffles are statistically negligible since any person can replicate it exactly. While Stephen did this type of shuffle twice two different ways none the less it is the same. So much is this type of shuffle negligible that it comes down to a factorial of 2! or just 2.

When it comes to the initial shuffle, the only uneven random shuffle, Stephen did it 4 times pulling roughly each time 1/4th of the deck to shuffle back in top to bottom. He broke that shuffle up 8 times the first shuffle, 6 times the second, 3 the third, and none the last. This becomes a new probability range.

4!+8!+6!+3!+0!+2!=41073 this is no where near the several quadzillion possibilities that 54! gives us.

To discover just how many times this shuffle has actually been replicated we can do some other basic math.

The common playing deck has been around for nearly 1500 years (originating in China in around the 6th century). If we assume a few things; 1) that at least one person has been playing with a deck of cards each day of the year since it's inception~which I suspect isn't far off from the truth by looking at how the deck has dissiminated~ 2) that most people play one of two games (the two most popular games is solitaire in some form or Quibbitch, both of which are games that actually pull the cards of the deck into their suits and order) and 3) the average number of times a person shuffles a deck per sitting is 12~ six times initially using perfect shuffles and then 6 times over the course of game play with quick non-true shuffles) we can argue that over the 1500 year history there have been 6570000 shuffles world wide from an initial deck (a deck that has all cards in order and in suit). This tells us that there is about 160 instances in which the exact same shuffle that Stephen did on show has occurred in the past.

Just because you can factor 54 ordinals for the card deck doesn't equate to unique shuffles.

948908.  Sat Nov 03, 2012 6:49 pm Reply with quote

This is an old party trick which is truly an 'impossible to duplicate', unlike the limited shuffle that Stephen Fry did.
Say "I am going to show you something that has never been seen before in the whole history of this universe, and will never be seen again in the possible future of this universe."
Produce one apple and a knife, cut the apple in half, and show the cut face, "which is, of course, absolutely unique", in the strict meaning of those much abused words.
Now, slice off the front of the half apple, and eat it.
"No one will ever see that again."

Prof Wind Up Merchant
949519.  Mon Nov 05, 2012 7:27 am Reply with quote

I have been discussing this on another thread.


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