Mind-Blowing Stats / Facts

[Ave IT]

As the title says …… (NERD ALERT!! 🤓)

I drive my family mad with this stuff - My all time favourite was one I picked up from QI when Stephen Fry casually shuffled some playing cards then said: “I’m about to do something that nobody in History has ever done before and nobody will ever be able to repeat again”. Then he put the pack of cards on the table and said ….. “that pack of cards is utterly unique and has never been produced in that precise order before”……

To bang the point home – “the Milky Way galaxy may have 200 billion stars – and if every star had a planet, and every planet had 10 billion people and if every person on every planet shuffled a pack of cards once a second for a thousand years the chances of anybody re-creating my pack of cards is so infinitesimally small as to be virtually zero!”.

Boom! ……. Beat that!!

(To explain the maths – the number of permutations of a standard pack of playing cards is 52-factorial (written 52!) which is short hand for 52 x 51 x 50 x 49 x 48 x etc. etc. all the way down to x3 x2 x 1. That may not sound that big but if you work it out actually comes to over 8x 10^67 (8 with 67 zeros after it – so big there is no name for it). So the Milky way thing is….. 200billion x 10billion x (seconds in a thousand years) = 6.3 x 10^31 (6.3 with 31 zeros) so still vastly, vastly too small to have any real chance of reproducing the exact pack of cards..... Isn't that great? )

 

[GreenThing]

“that pack of cards is utterly unique and has never been produced in that precise order before”

That’s not entirely true though. It is entirely possible that someone can shuffle the cards twice and get the same outcome. It might be right that every outcome has never been achieved as the number is so high, but chances are that a repeat shuffle has been achieved at lease once in history.

 

[Ave IT]

That’s not entirely true though. It is entirely possible that someone can shuffle the cards twice and get the same outcome. It might be right that every outcome has never been achieved as the number is so high, but chances are that a repeat shuffle has been achieved at lease once in history.

Pedant alert!!

The point is that the chances are sooo minute as to effectively be zero that any exact outcome will occur twice as there are over 8x 10^67 different possibilities - and as the 'milky way' example neatly illustrates it would take gazillions (there is no name) of years and attempts ... so whilst theoretically possible it is utterly, utterly improbable any randomly shuffled pack of cards has ever been reproduced before or will ever be again.

 

[MickyD]

That’s not entirely true though. It is entirely possible that someone can shuffle the cards twice and get the same outcome. It might be right that every outcome has never been achieved as the number is so high, but chances are that a repeat shuffle has been achieved at lease once in history.

I don't think you're grasping the true scale of absolutely gigantic numbers. Chances are very much not that a shuffle has ever been repeated. The probability is infinitessimally small so to all intents and purposes it definitely hasn't ever happened, to a certainty of colossal orders of magnitude.

Ave IT, if you're a fan of mind-bogglingly large numbers, beside which a googol (10^100) is an insignificant speck of dust, try looking up things like Graham's Number and tree numbers - both discussed here. Numberphile is a great channel all round, if you're into maths in general. Indeed, here's a whole playlist they've put togther on big numbers.

 

[MickyD]

Pedant alert!!

The point is that the chances are sooo minute as to effectively be zero that any exact outcome will occur twice as there are over 8x 10^67 different possibilities - and as the 'milky way' example neatly illustrates it would take gazillions (there is no name) of years and attempts ... so whilst theoretically possible it is utterly, utterly improbable any randomly shuffled pack of cards has ever been reproduced before or will ever be again.

Oh, crossed in the post, so to speak. What were the chances?

 

[pilgrimage]

I've got a headache 😊

 

[Quinny]

Ave IT, if you're a fan of mind-bogglingly large numbers, beside which a googol (10^100) is an insignificant speck of dust...

Ah, now you've taken me back to the time I was first introduced to a Googol by Carl Sagan when I were a nipper watching Cosmos:

Googol and Googolplex by Carl Sagan

Think about it! where GOOGLE got there name?

www.youtube.com

 

[mervyn]

Here’s a stat from my 8 year old grandson Sam which, once heard, you’ll never forget. His book of 365 stats informs us that the Atlantic Ocean increases in width each year by exactly the amount that the average toe-nail grows.

 

[GreenThing]

I don't think you're grasping the true scale of absolutely gigantic numbers. Chances are very much not that a shuffle has ever been repeated. The probability is infinitessimally small so to all intents and purposes it definitely hasn't ever happened, to a certainty of colossal orders of magnitude.

Ave IT, if you're a fan of mind-bogglingly large numbers, beside which a googol (10^100) is an insignificant speck of dust, try looking up things like Graham's Number and tree numbers - both discussed here. Numberphile is a great channel all round, if you're into maths in general. Indeed, here's a whole playlist they've put togther on big numbers.

The chances of winning the lottery (American one) one in 14 million. The chances of winning it twice is four in 10 billion. However, the same person has won it twice within a few years and winning the UK lottery twice has happened quite a few times. So back to the pack of cards, while the numbers are incredibly big, every shuffle is new and what has come out before doesn’t come into the equation so it is more than possible that the same shuffle has been repeated and other shuffles will never occur, ever.

 

[MickyD]

Ah, now you've taken me back to the time I was first introduced to a Googol by Carl Sagan when I were a nipper watching Cosmos:

Googol and Googolplex by Carl Sagan

Think about it! where GOOGLE got there name?

www.youtube.com

That series blew my mind at the time, along with Connections by James Burke. I still have the books that went with them.

 

[Quinny]

That series blew my mind at the time, along with Connections by James Burke. I still have the books that went with them.

I haven't got the James Burke book, but I most definitely have the original hardback copy of Cosmos ... and the (mainly Vangelis) original soundtrack album on vinyl (and the series on DVD).

Talking of Connections, this must go down amongst the best bits of timing in television history:

The BEST TIMED Shot in TV HISTORY?

James Burke hits his mark with perfect timing, in this astounding clip from the science documentary series, Connections.#short #shorts

www.youtube.com

 

[MickyD]

The chances of winning the lottery (American one) one in 14 million. The chances of winning it twice is four in 10 billion. However, the same person has won it twice within a few years and winning the UK lottery twice has happened quite a few times. So back to the pack of cards, while the numbers are incredibly big, every shuffle is new and what has come out before doesn’t come into the equation so it is more than possible that the same shuffle has been repeated and other shuffles will never occur, ever.

But that's what I mean by not grasping truly enormous numbers. Those lottery odds are insignificant compared with 52! And the odds of winning the lottery are not 1 in 14 million if you buy two differently numbered tickets - they're immediately halved, and so on. Buy 100 and they're down to a 'mere' 1 in 140,000. 52!, on the other hand, stays at 52!.

I'm really not sure where that four in 10 billion (1 in 2.5 billion) figure comes from. Whatever the true figure (which would depend on many factors) it's still pifflingly tiny compared to 52!. And anyway, has anyone actually won a 14 million to 1-odds lottery twice? Maybe big prizes, but the jackpot twice? That's the only one with those odds.

 

[MickyD]

I haven't got the James Burke book, but I most definitely have the original hardback copy of Cosmos ... and the (mainly Vangelis) original soundtrack album on vinyl (and the series on DVD).

Talking of Connections, this must go down amongst the best bits of timing in television history:

The BEST TIMED Shot in TV HISTORY?

James Burke hits his mark with perfect timing, in this astounding clip from the science documentary series, Connections.#short #shorts

www.youtube.com

Yes, that was James Burke for you! I spotted him in a pub in London once, and felt compelled to go over and shake his hand and tell him what an influence he'd been - not the sort of thing I'd ever normally do. I first knew him from Tomorrow's World and the Apollo Moon landings with Patrick Moore.

And he's still going, heading for his 87th birthday.

 

[GreenThing]

But that's what I mean by not grasping truly enormous numbers. Those lottery odds are insignificant compared with 52! And the odds of winning the lottery are not 1 in 14 million if you buy two differently numbered tickets - they're immediately halved, and so on. Buy 100 and they're down to a 'mere' 1 in 140,000. 52!, on the other hand, stays at 52!.

I'm really not sure where that four in 10 billion (1 in 2.5 billion) figure comes from. Whatever the true figure (which would depend on many factors) it's still pifflingly tiny compared to 52!. And anyway, has anyone actually won a 14 million to 1-odds lottery twice? Maybe big prizes, but the jackpot twice? That's the only one with those odds.

Yes, someone has won the jackpot twice.

I understand that the numbers are mind boggling, but the number is how many times you have to shuffle to guarantee a duplicate. Randomness doesn’t follow the rules of mathematics and what looks to be impossible generally isn’t, which is why I mentioned the lottery scenario. Smaller odds by a long shot, but it shows that impossible odds aren’t impossible.

 

[MickyD]

Here’s a stat from my 8 year old grandson Sam which, once heard, you’ll never forget. His book of 365 stats informs us that the Atlantic Ocean increases in width each year by exactly the amount that the average toe-nail grows.

I thought it was a fair bit more than that, what with the Mid-Atantic Ridge pushing everything apart, but I'm not going to argue with an eight-year-old with a book in his hand!