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?

[Mick-Talbot]

I think the key is that you have to start with a randomised pack.

[Khandro]

CBX; // If the odds are 6 to 1 of getting a 6 when rolling a dice, and I permit you 1 roll, you have a 1 in 6 chance. If I allow you 2 rolls, you have a 1 in 3 chance.//
This rationale suggests that if you give me 6 rolls, I am certain to get a six! I see what you are saying, but with each individual roll the ODDS remain firmly at 6 to 1. Are you not confusing 'chances' and 'odds'?

[CBX2012]

You still don't understand squarebear. The combinations illustration you post only really applies on the first try and if we only get one shot. On the second try, because there are 2 matches available, the odds of a match have doubled (i.e. reduced by half how long in your illustration). Carry on reducing 10,000,000,000,000,000 times.

Each one of these 10,000,000,000,000,000 attempts has an ever increasing chance to match the ever increasing pool of previous decks. These probabilities stack unlike random dice. It scales in 2 different directions to become certain over time (and 0.99999999 waaay before that).

In fairness to you, QI is partly to blame to talking about the size of the combinations in physical terms. They made it seem as though you need to get through half of them to have a 0.5 probability of a match. It's many many many trillions of tries less than that and they misrepresented the problem.

FYI I agree with you about perception of odds by people. Personally I never play the lottery or gamble with the odds against me. I think I'll leave it here.

[CBX2012]

Oh one last thing

Khandro: no you're absolutely right i put that poorly. Certainly 6 goes at rolling a dice isn't certain to produce a 6. It's a combinations with repetition scenario. I was trying to point out to you that the cards scenario is completely different and the odds change each shuffle. Thanks for that!

[Mick-Talbot]

Is anyone agreeing that you need to start with a randomised pack?

Otherwise think of it as a big knockout 52 planets each of 416 billion people will take you over the 7 shuffles.

[Khandro]

CBX; :-) Your certainty sent me scurrying to look up the marvellous correspondence between Fermat and Pascal on probability, and I found, built on their findings; "The total of different sequences possible in a 52-card deck is a figure 68 numerals long: if all the people on earth counted a million arrangements a second 24 hours a day for 80 years, they could not count a millionth of a billionth of 1 percent of the possibilities."
[and before you gamble away the farm folks, just out of interest] The total number of 5-card poker hands possible is 2,598,960. Here are the odds on drawing a royal flush, - 649,739 to 1; a full house - 693 to 1 ; a straight 254 to 1 ; and one pair 1.37 to 1.

[Mick-Talbot]

Ah from jtp's link

By the way, the overhand shuffle is a really bad way to mix cards: it takes about 2500 overhand shuffles to randomize a deck of 52 cards!

[tommy-h]

Just finished reading this thread.Does anyone have an aspirin,my head hurts!

[Mick-Talbot]

WOW .............................

http://www.youtube.com/watch?v=Is8zSSe9Kt4

[Svejk]

You gotta love AB. The foremost expert in the world(probably)sends us the answer, and still the debate rages.
At the second coming they'll still be at it 'hammer & tongs' in R&S.

[Mick-Talbot]

All this has made me more confident about winning the lottery.

[sidkid]

Squarebear: I still maintain that unlikely (or extremely unlikely or very, very, very unlikely) is not the same as impossible. History is littered with clever people who said something or other could never happen. It doesn't matter how many Sahara deserts you bring to the table, your little grain of sand is out there......therefore it is possible to find it. Unlikely, agreed. But NOT impossible.

[ChuckFickens]

I think QI are at fault here... they should have used the phrase "statistical impossibility" instead of just "impossibility"... but it's an entertainment show and the average person wouldn't understand the difference.