Mind-Blowing Stats / Facts

[MickyD]

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.

Of course it does. It's called probability theory. And of course odds are only impossible if they actually are impossible. Nobody is arguing that.

Do you have a link for that double jackpot event? I'm genuinely curious.

 

[GreenThing]

Of course it does. It's called probability theory. And of course odds are only impossible if they actually are impossible. Nobody is arguing that.

Do you have a link for that double jackpot event? I'm genuinely curious.

No, randomness is different. Maths tells you that you have to play 10 times to win at odds of 1 in 10, randomness tells you that you can win ten times or non at all.

Double lottery winners

 

[MickyD]

I'm sorry, but you're completely wrong about what maths says.

And that link?

 

[GreenThing]

I’ve added a link about someone in the uk, but there was a discussion about it on the radio a few weeks back.

 

[Quinny]

I recall listening to a very interesting In Our Time episode about randomness in mathematics a little while ago.

In Our Time - Random and Pseudorandom - BBC Sounds

Melvyn Bragg and his guests discuss mathematical randomness and pseudorandomness.

www.bbc.co.uk

 

[MickyD]

I’ve added a link about someone in the uk, but there was a discussion about it on the radio a few weeks back.

Somebody won £1M twice. In terms of odds, that's a very long way short of winning the 14M-1 jackpot twice.

And just to be clear: maths, in the form of probability theory, does say explicitly that you can win ten times or none at all. That's what so many betting types fail to get their head around, falling as they do for the gambler's fallacy. For instance, the odds of tossing ten heads in a row with a fair coin are 1 in 2^10 (1024), but the odds of tossing a head after nine consecutive heads are still just 1 in 2.

 

[smudja]

What I want to know is what's happening to the jokers in all these pack of cards and will all decks have hearts clubs diamonds and spades in them..

 

[MickyD]

OK, speaking of odds, who's heard of the Monty Hall Problem?

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

No Googling (or even googoling), now!

 

[GreenThing]

OK, speaking of odds, who's heard of the Monty Hall Problem?

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

No Googling (or even googoling), now!

Doesn’t matter if you change your mind or not. When the host opens the door and shows you one of the goats, the game is reset and the odds drop from 3/1 to 2/1.

 

[MickyD]

Doesn’t matter if you change your mind or not. When the host opens the door and shows you one of the goats, the game is reset and the odds drop from 3/1 to 2/1.

That does seem logical, doesn't it?

 

[MickyD]

Ave IT? This was also on QI once!

 

[Quinny]

OK, speaking of odds, who's heard of the Monty Hall Problem?

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

No Googling (or even googoling), now!

I think that was talked about on that In Our Time episode I mentioned... so I know of it

Edit: or it might have been this one about Probability! I've listened to a lot over the last year, especially the maths podcasts

BBC Radio 4 - In Our Time, Probability

Melvyn Bragg and guests discuss the strange mathematics of probability.

www.bbc.co.uk

 

[MickyD]

I think that was talked about on that In Our Time episode I mentioned... so I know of it

Yes, the correct answer is counter-intuitive on the surface. There's one external factor, though: the host knows where the car is, so his actions can change the odds after a door is chosen.

 

[Ave IT]

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.

Ah yes..... Therein lies a subtlety. The chances of any one pack of cards (Stephen Fry's) ever being reproduced or any one person you care to point at winning a lottery twice is infinitesimaly small..... BUT - there are many, many more combinations if you don't specify that dramatically cut the odds.

It's like my second favourite stat - the chances of any two players on a football pitch (including the ref) of having the same birthday is more than 50%..... even though (obviously) there are 365days and only 23 players. Combinations!

Anyway..... better get to the match!

 

[GreenThing]

It’s all about human perception. We’re told that you made the choice at 3/1 while the other door is 2/1, but in reality the game has been reset.

The human element also comes into the lottery. Should you choose the numbers 1, 2, 3, 4, 5, 6? The answer is no. But they have the same chance as any other sequences you might say, and that is the reason why not. Human perception tells us not to choose this numbers as they won’t come out, so the clever people who know that it makes no difference do choose them. And that is why you should not, they are the most popular numbers and if you win £1 million, you’ll be sharing the jackpot with 10,000 other winners.