In article <199810291325.HAA19001@einstein.ssz.com>, Jim Choate <ravage@einstein.ssz.com> wrote:
Forwarded message:
Date: Wed, 28 Oct 1998 22:10:08 -0800 From: Alex Alten <Alten@home.com> Subject: Re: Shuffling
From what I understand when one shuffles a deck of 52 cards 7 or more times
The concept of swapping to get a random string of bits is very interesting. 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"