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?

[FredPuli43]

His claim is that his shuffled pack's sequence had never been replicated in the whole history of the world. That's patent nonsense as an absolute claim. It may have been done before. The mistake is to assume that you must shuffle the pack that large number of times before the same sequence occurs once more. What he has given is the only the chance of it happening again, not a prediction of when it will happen again.

[brionon]

However great the number it doesn't mean that the Hand will be the Last to appear-it could be the first. Innit.

[lankeela]

Of course it could happen - same as the lottery coming up 1, 2, 3, 4, 5, 6 - but extremely unlikely and as much as I like QI I agree with the original poster. Thing is we will never know....

[IanB]

Totally agree with Lankeela above. While I understand the enormity of the number and the resulting improbability, the tiny probability does not mean a particular card order will only occur every that many shuffles. That would only be true if you were deliberately arranging the cards in a succession of different orders, changing each time. In which case it would take you that long (an unimaginably long time as others here and Stephen Fry rightly state). But when shuffling you are arranging the cards in a random order, and therefore every possible order can be obtained on each shuffle. If you shuffle an infinite number of times, the average gap between identical card orders will be the huge number discussed, but there may be two consecutive identical configurations, or within a few hundred or thousand shuffles of each other within the overall sequence. Thus you cannot say for sure that a given configuration has never been obtained before, it just depends where in that infinite number of shuffles you happen to be.

[Old_Geezer]

In absolute terms Howard is correct. One can not know for sure.

In practical terms you could stake an infinite amount on Fry's claim being correct as feel confident of winning, as the odds against it are astronomical plus a bit.

[Mattk]

SF's exact claim was that as far as its mathematically possible to say, that exact sequence had never happened before.

[chelle7272]

The words 'mathematically possible' make all the difference

[squarebear]

The odds are zero. The chances of picking the lottery numbers are 1 in 14,000,000 (roughly), which is an every day event compared to this number. I really don't think people who think it could happen understand the scale of this number.

[jake-the-peg]

There are two points here

the first is the sheer number of combinations - no issue with that.

The second is that whether shuffling a deck 2 or 3 times is enough to ensure a random combination.

I have issues with that.

I can't find it right now but I recall that you need to do this 6 or 7 times and suddenly you get into a chaotic system and truely random combinations appear.

I'll see if I can find the reference if I get time

[joggerjayne]

It's no wonder I keep losing money at Blackjack!

[squarebear]

Exactly and no wonder there are so many bookies all doing extremely well when people believe that its possible to beat these kinds of odds.

[Ellipsis]

When you open a new deck of cards, then the cards are all in the same order.

If you shuffle them poorly, then there's a good chance that they'll end up in an order that has been seen before.

QI assumed that the deck was extremely well shuffled from a random starting position. If it was extremely poorly shuffled from a fixed starting position, a repeat is much more likely to occur. Still not very likely, but much more likely ...

[Svejk]

I think we all understand, SB. Either you don't understand or you're being obfucatious.
There is a world renowned professor of chance at Cambridge University. If I can somehow get an e-mail from him would that make you desist in this obstinacy.

[jake-the-peg]

Here we go

http://www.math.hmc.e...files/20002.4-6.shtml

7 shuffles to get a random pack - bit suspicious as 7 is a bit of a "magic" number

[squarebear]

That would be useful thetaliesin, as such odds to me are the same as zero and I genuinely can't understand why people would think it possible.

[sidkid]

The issue here is the difference between finite and infinite. The number of deck shuffles as pointed out is very large. The number is however, finite. To state that a sequence will NEVER be repeated is wrong and a little foolish.

[joggerjayne]

The odds of being struck by lightning, and surviving, are better than the odds of winning the Lottery (about 7m:1 I seem to recall).

If you wanted to bet on yourself being struck by lightning, you'd get very long odds.

So, instead of spending a £1 on a Lottery ticket, you'd be better off placing a £1 bet on yourself being struck by lightning.

[joggerjayne]

Just thinking about probabilities. Sorry.

[Svejk]

As an aside. When the lottery first started someone I knew was using 123456 as his numbers. I queried this & he said if they ever came up he'd be the lone winner.
A year on a paper printed the most popular numbers selected. First Place; 123456
Average times selected p.w. 40,000 +.