QI

[HowardKennitby]

The QI repeat broadcast tonight.

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

[Old_Geezer]

On average more than one person in the UK wins the lottery jackpot each draw, whilst the number each week struck by lightning is ?

Wow the top card has an equal chance of ending up on the bottom as any other card after 7 shuffles ? Blows my mind.

[squarebear]

This is a popular misconception about probabilty. The chances of 1,2,3,4,5,6 coming up in the lottery are as equal to any other combination and again, this is nothing compared to the odds as shown of the card shuffling.

sidkid - It is more than "very large". It is so astronomically huge (1% of the known universe to cover every pattern remember), that you will never recreate the same pattern.

[ChuckFickens]

I like that the number of possibilities is....

"80 unvigintillion, 658 vigintillion, 175 novemdecillion, 170 octodecillion, 943 septendecillion, 878 sexdecillion, 571 quindecillion, 660 quattuordecillion, 636 tredecillion, 856 duodecillion, 403 undecillion, 766 decillion, 975 nonillion, 289 octillion, 505 septillion, 440 sextillion, 883 quintillion, 277 quadrillion, 824 trillion"

There are numbers in there I've never even heard of!

[joggerjayne]

//the number each week struck by lightning is?//

One and a bit.

Of whom, 98.5% survive.

[Mick-Talbot]

monkeys, typewriters, Shakespeare....given enough time blah blah ...blah

It has possibly happened but who can prove it has ?

[sidkid]

Squarebear....I fear you have made your mind up! but just to repeat, this is a finite number. To state that a sequence can never be repeated requires that you are dealing with an infinite number. Agreed, the number of deck shuffles is very, very, very large, but there is a finite number of them. Not infinite. Surely this is obvious?

[Mick-Talbot]

What do we regard as a shuffle?
Imagine a fresh pack un-shuffled, I would normally do 3 cuts ...is that a shuffle?

If so it is not that unlikely that the same shuffle has happened before ....is it?

[Ellipsis]

The QI way of thinking about this is to use permutations and combinations to come up with the odds.

But if instead you think of what happens in practice ...

If you start with an ordered deck and make one cut, the chance that somebody else would repeat the same cut is about 1/50.

If you make two cuts, (placing the top of the deck at the bottom after each cut) it's about 1 in 2500.

Three cuts, it's about 1 in 125,000.

Six cuts would be about 1 in 125,000 squared, or about 1 in 16 billion.

Each cut is the equivalent of a single overhand shuffle. I know 16 billion is a big number, but it's a lot less than 80 unvigintillion and a lot more likely to have been repeated in all of history. It comes down to the definition of "shuffling" ...

[squarebear]

Let's try to imagine the number 80,658,175,170,943,878,571,660,636,856,403,76
6,975,289,505,440,883,277,824,000,000,000,000
another way

Area of the Sahara Desert: 9 000 000 (km^2) = 9.0 × 10^12 m^2.
Depth of the sand in the Sahara: approx 100m
Volume of sand in the Sahara: (9.0*10^12)*(100m) = 9.0*10^14 m^3.
Volume of a grain of sand: 1.13 x 10^-13 m^3

Therefore the number of grains of sand in the Sahara is: (9.0*10^14 m^3)/(1.13 x 10^-13 m^3) = approx 8.0x10^27 grains of sand or
8,000,000,000,000,000,000,000,000,000 grains of sand or 8 octillion grains of sand. This number is so minutely small compared to the original number that for each grain of sand in the Sahara you would need billions and billions (about 80,000,000,000,000) of Sahara deserts for each of our original grains to make a figure even approaching this.

Now if I were to pick one single grain of sand out of just one this astronomically large amount of Sahara Deserts, you genuinely believe given as much time as you like, that you could tell me which one?

[sidkid]

Squarebear, I admire your persistence with your large figures and various examples. But you are still confusing never with unlikely.

[squarebear]

You think it is just "unlikely" to find the grain of sand?! It is impossible.

[sidkid]

Yes - I think it is unlikely. Very unlikely. But still possible. The possibility exists. There is no denying that simple fact.

[squarebear]

"But still possible". How would you even attempt to start such a task?

I think we will have to agree to disgree then unless the mathematics professor can chip in.

[sidkid]

There really is no need for a mathematics professor to point out the fact that your particular grain of sand exists, therefore it is possible to find it. Difficult and very unlikely but possible. Not impossible as you suggest.

[squarebear]

Sorry but I say that the chances of finding it are so infinitesimally small that it is impossible and so we appear to have come up to a stalemate.

[sidkid]

<<the chances of finding it are so infinitesimally small that it is impossible>> This statement simply does not make sense. Good Grief!!

[ChuckFickens]

It could be claimed to be a statistical impossibility though, as in it's probability is so low it can be counted as 0.

Or the other way round is, even if something has a probability of 0 that doesn't mean it won't happen, which is what happens when there are a infinite amount of possibilities the probability of each one is 0 but each of the infinite amount of possibilities could happen.

[mccfluff]

ow

[squarebear]

"It could be claimed to be a statistical impossibility though, as in it's probability is so low it can be counted as 0. "

Finally someone else sees it. How anyone can think it is perfectly possible to pick out a random pre selected grain of sand in billions of billions of Sahara Deserts is beyond me.

[Khandro]

I think God could do it, but I'm not sure that he plays cards.