Re: Shuffling (fwd)
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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 --'- --------------------------------------------------------------------
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
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