From: iang@cs.berkeley.edu (Ian Goldberg)
Date: Sat, 31 Oct 1998 03:18:33 +0800
To: cypherpunks@cyberpass.net
Subject: Re: Shuffling (fwd)
In-Reply-To: <199810291716.LAA19879@einstein.ssz.com>
Message-ID: <71d1ik$b4o$1@abraham.cs.berkeley.edu>
MIME-Version: 1.0
Content-Type: text/plain



In article <199810291716.LAA19879@einstein.ssz.com>,
Jim Choate  <ravage@einstein.ssz.com> wrote:
>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.

Yup.

   "It's only a model."  -- Monty Python and the Holy Grail

>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.

It actually _does_ address the normal, statistical clumping that goes on.
It _doesn't_ address clumping that occurs because, say, you were playing
poker while eating a peanut butter sandwich. :-)

   - Ian