From: Jim Choate <ravage@EINSTEIN.ssz.com>
Date: Fri, 30 Oct 1998 01:45:59 +0800
To: cypherpunks@EINSTEIN.ssz.com (Cypherpunks Distributed Remailer)
Subject: Re: Shuffling (fwd)
Message-ID: <199810291716.LAA19879@einstein.ssz.com>
MIME-Version: 1.0
Content-Type: text



Forwarded message:

> From: iang@cs.berkeley.edu (Ian Goldberg)
> Subject: Re: Shuffling (fwd)
> Date: 29 Oct 1998 16:16:41 GMT

> 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.

The only problem I see with this model, re real card decks, is that the
probability for a given card to fall to the top of the shuffled pile isn't
related in any way to the number of cards in either stack in a real-world
shuffle.

It also doesn't address the problem of 'clumping' where a group of cards (ie
royal flush) stay together through the shuffling. This is the reason that
real dealers try for a 1-for-1 shuffle each time.


    ____________________________________________________________________
 
       To know what is right and not to do it is the worst cowardice.

                                                     Confucius

       The Armadillo Group       ,::////;::-.          James Choate
       Austin, Tx               /:'///// ``::>/|/      ravage@ssz.com
       www.ssz.com            .',  ||||    `/( e\      512-451-7087
                           -====~~mm-'`-```-mm --'-
    --------------------------------------------------------------------