Topic: Shuffled
 Message: Posted by: Steve Martin (Apr 1, 2006 08:07AM)

Aside from passing the same deck of cards between us whenever we have been together, do you think it is likely that you have held a randomly-shuffled deck that has shared exactly the same order as a randomly-shuffled deck that I have held?

Bear in mind that each one of us has shuffled decks of cards many hundreds (if not thousands) of times in our lives.
 Message: Posted by: Andrei (Apr 1, 2006 09:09AM)
I won't give out the answer, because I've just read something based on this, in an Economics textbook. It had to do with distributing resources.

Andrei
 Message: Posted by: Josh the Superfluous (Apr 1, 2006 09:15AM)
In an idle state? or during a shuffle? e.g. during an overhand before completing the last few packets. If you riffle twice do both count?

My guts tell me yes. How many shuffled combos does a close-up worker come up with over a career?
 Message: Posted by: Steve Martin (Apr 1, 2006 09:23AM)
Josh - let's say a final shuffled deck. When you've finished shuffling.

I would agree with you that a close-up worker must generate many, many shuffled decks over the course of a career... the number is huge - probably hundreds of thousands...
 Message: Posted by: Daegs (Apr 1, 2006 02:13PM)
Well... its 52!... I'm not going through the trouble of figuring what that is, but its large enough to never actually come up with the same order as anyone else, or if you did its probably 1 other random person in the last hundred years, definatly not two specific people, at least not likely.
 Message: Posted by: Steve Martin (Apr 1, 2006 02:22PM)
The number of possible arrangements of a 52-card deck is indeed 52 factorial (52!).

How many is that, and what is the implication of that in considering the answer to the question?
 Message: Posted by: Josh the Superfluous (Apr 1, 2006 03:15PM)
Well I don't know the math, but I'd ballpark it as a really big number if not more. So let's say one guy is getting hundreds of thousands of career shuffles, within this big amount. Would a like guy hit upon 1 of the same mixes? My guts still tell me yes. I've seen flipped coins land on their edges. Intellectually, I'm guessing Daegs is probably closer to the statistical facts.
 Message: Posted by: Josh the Superfluous (Apr 1, 2006 04:59PM)
Of course this huge number, which I'm dying to find out, probably doesn't take into account the number of people who open packs arranged in new pack order and riffle them twice.
 Message: Posted by: magicjohn2278 (Apr 1, 2006 05:25PM)
We know that the number of different ways of mixing a deck is that big number Tomas posted a couple of weeks ago, starting with 8 and with 66 digits after it...

.. the chances of us matching are going to be one in a pretty big number!

... so the answer to your question is "Probably no (but it could happen!)".
 Message: Posted by: LobowolfXXX (Apr 1, 2006 06:58PM)
52! is a huge number, but that considers only "pure" randomness. It depends what you consider our startings points to be. Each of us has taken a newly-opened deck and given it, say, six riffle shuffles...betcha dollars to donuts that some of THOSE match.
 Message: Posted by: Josh the Superfluous (Apr 1, 2006 07:53PM)
And solitaire players arrange the deck before each shuffle.
 Message: Posted by: Andrei (Apr 2, 2006 12:37AM)
The question is assuming the deck was thoroughly shuffled, with 7+riffles, box cuts and a few washes in between.

Andrei