Re: Shuffling (fwd)

Forwarded message:

> From: iang@cs.berkeley.edu (Ian Goldberg)
> Subject: Re: Shuffling (fwd)
> Date: 30 Oct 1998 18:46:44 GMT

> >> 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.

> >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. :-)

What I was refering to was that let's say we've just finished playing a hand
of cards and the next dealer collects them from each player and stacks them
up prior to shuffling. Since the selection of cards is related to the
thickness of the two half-decks (and not a strict 1-to-1) it is reasonable
to expect an above average number of such shuffles (ones with grossly uneven
card counts, exactly what that would be I don't know), now as a player I'm
going to know about this bias and can use it to my advantage. I admit it
probably won't change the odds much but sometimes a few hundreths over a
long time can make a difference.

It seems to me the next question that needs asking is:

Given the probability model we've discussed what does the difference in
odds relating to clumping show in relation to uneven deck splitting. If
the deck is split even (26:26) v 27:25 v 28:24 v etc.


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In article <199810301934.NAA26157@einstein.ssz.com>,
Jim Choate  <ravage@EINSTEIN.ssz.com> wrote:
>Forwarded message:
>
>> From: iang@cs.berkeley.edu (Ian Goldberg)
>> Subject: Re: Shuffling (fwd)
>> Date: 30 Oct 1998 18:46:44 GMT
>
>> >> 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.
>
>> >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. :-)
>
>What I was refering to was that let's say we've just finished playing a hand
>of cards and the next dealer collects them from each player and stacks them
>up prior to shuffling. Since the selection of cards is related to the
>thickness of the two half-decks (and not a strict 1-to-1) it is reasonable
>to expect an above average number of such shuffles (ones with grossly uneven
>card counts, exactly what that would be I don't know), now as a player I'm
>going to know about this bias and can use it to my advantage. I admit it
>probably won't change the odds much but sometimes a few hundreths over a
>long time can make a difference.

That's true.  That's why you need to do it seven times, in order to
properly randomize the deck.

It's for exactly this reason that players at computer-dealt bridge
tournaments complain about "flat" distributions.  When they play in
"real life", people usually don't shuffle seven times, and the resulting
suit distributions end up skewed ("ghoulies" is the extreme case of this).
The players are used to this, though, and when they get actual random
hands, the distributions are much flatter.

   - Ian