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Re: Shuffling (fwd)



In article <[email protected]>,
Jim Choate  <[email protected]> wrote:
>Forwarded message:
>
>> Date: Wed, 28 Oct 1998 22:10:08 -0800
>> From: Alex Alten <[email protected]>
>> Subject: Re: Shuffling
>
>> The concept of swapping to get a random string of bits is very interesting.
>> >From what I understand when one shuffles a deck of 52 cards 7 or more times
>> the card order becomes unpredictable e.g. random.
>
>Only if it is a 'fair' shuffle. There are poker players I've met who could
>put a given card anywhere in the deck after 4-5 shuffles.
>
>>  The shuffle must be
>> what is called a "near perfect" shuffle.
>
>Perfect for who? Idealy the 'perfect' shuffle (if I understand your meaning
>of perfect) would be for each card in each deck-half to interleave 1-to-1.
>This does not produce random anything, it does make it very hard for people
>to count cards, which is why you shuffle - not to create a necessarily
>random ordering of the cards, just so mis-ordered nobody can remember what
>the sequence was and predict reliably what the sequence will be. This is
>incredibly important in games like poker or rummie where the cards pile up
>and players can see the sequence (and if they can remember it use it).

The "7 times" theorem uses the following model of a shuffle:

o The deck is cut into two parts, with the number of cards in each piece
    binomially distributed (with mean 26, of course).
o The resulting deck is then achieved by having cards fall from one or the
    other of the two parts; a card will fall from one of the parts with
    probability proportional to the number of cards remaining in the part.

   - Ian "Who took a course in Randomized Algorithms last year"