# QI

HowardKennitby | 22:31 Sat 03rd Nov 2012 | TV

Re the deck of cards shuffling; am I the only one who thought that SF's claim was nonsense?

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I missed it. What was his claim?
Watch it here, or fast forward to the shuffling bit.

He claimed that if you shuffle a pack of cards, they will end up being arranged in a unique order and quoted an enornous number. In that, he was right, the number is written 52! and equates to (52 x 51 x 50,,,,,x2 x 1).

Where I found myself disagreeing is that he claimed that the order in which his cards ended up had NEVER been done before. In that, he cannot 100% be right. It's most unlikely, but never is the wrong word.
Sounds pefectly plausible to me. What is it you disbelieve?

Imagine 2 cards. There are 2 possible options
3 cards= 6 options ABC, ACB, BAC, BCA, CAB, CBA
4 cards = 24 options
5 cards = 125 and so on.

The number increases factorially until it reaches the crazy number that was displayed on the show for 52 cards.
5 cards is in fact 120 options but the chances of it being repeated are so infintely small as to say it is hasn't been done before.
Question Author
I am not questioning the calculation of the number of possibilities.
That has nothing to do with claiming that a certain event has NEVER occurred before.
I don't think you understand the size of the number. Listen again to his explanation about trillions of planets to get the sheer scale of this number.

Compared to this, me picking out a grain of sand on the Sahara desert and asking you to guess which one is like choosing heads or tails on a coin.
Question Author
The size of the number is irrelevant.
Of course it is. If I think of a number between 1 and 10, you will get it right 10% of the time on average. Now if I guess between 1 and 100, it will take you 100 guesses and take ten times longer.

As the number increases to the astronomical number displayed, there won't have been enough card shuffles in all the word since cards were invented to touch even a fraction of a millionth percent of reproducing it.
As with all probabilities it is possible to get the same result shuffling the pack twice in a row it's just that it is incredibly unlikely, on the other hand it is true that he could not, with total certainty, say that his deck was in an order never before seen but it is pretty darn likely with a probability factor approaching one
Imagine you could shuffle the deck 1000 times per second. Everyone on Earth has their own deck of cards, and they're all shuffling them too, 1000 times each second. Now imagine everyone continues to do this for the next 10 billion years.

In all those shuffles you wouldn't have rearranged the cards even a fraction of the total number of possible ways.

The size of the universe is estimated to be something like 15 billion light years in radius. A light year is the distance light travels in a year, or about 140,000,000,000,000,000,000,000 kilometres. The volume of the universe is then (assuming it's spherical) about 1.1 x 1070 cubic kilometres.

It would take a whole 1% of the entire universe to lay out all the different arrangements of the deck, if you put each one in its own cubic kilometre.

The chances of duplicating an existing shuffle, while at first might not seem impossible, but is never going to happen.
True, but it COULD happen on the next shuffle, just because an event is unlikely doesn't make it impossible. Don't get me wrong, I wouldn't bet on it happening (I don't do the the lottery because I can see the odds) but the term 'never' indicates a finality which doesn't exist in this case, for all practical purposes yes, but scientifically no.
"The size of the number is irrelevant."

LOL!.... errr, no it's the most relevant thing in the claim!
I think we will have to agree to disagree then. If I pick a square kilometre over 1% of the Universe and you believe you can pick the same one then you should be on TV.

It will not happen on the next shuffle or indeed any other shuffle.
Squarebear, its only a suggestion, but is it possible there's a flaw in the way your working it out.
Using your method you'd assume that 365 people in a room would all have a different birthday, if you see what I mean. Just because there are many combinations it doesn't follow that chance seeks out the maximum number.
Have as many goes as you like, you will never guess which number I am thinking between of 1 and 80,658,175,170,943,878,571,660,636,856,403,76
6,975,289,505,440,883,277,824,000,000,000,000
whether you believe you will or not.
17.?
Damn! you got it!

Well that's my theory shot to pieces :-)

I got lost at "imagine a pack of cards......" :P

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