From: hall@kronos.arc.nasa.gov (Michael Hall)
Subject: Re: Blackjack tips for beginners/Casinos in Minneapolis
Keywords: shuffle, clumping
Organization: NASA/ARC Information Sciences Division
Date: Thu, 5 Nov 1992 18:57:36 GMT

In article <Bx92nE.69z@ucunix.san.uc.edu> kaufman@ucunix.san.uc.edu (Stephen A. Kaufman) writes:

>Thank you for your clarifications.  But it is still not clear exactly
>what you did in order to measure these correlations.  I would be the 
>first to agree that over millions of hands there is no meaningful
>correlation between the RESULTS of the previous shoe in terms of won
>or lost hands and the results of the next.

Okay, good, though Olson and Patterson would of course say there is a
correlation.

>I would also assume
>that comparing the sum of millions of hands of real shuffle to the
>sum of millions of hands of "random" shuffle should show little 
>difference in the correlation of one card to the next within
>a deck.

It depends what you mean by "little", but the probabilities of the
next card do depend on the previous card (after subtracting out the
effects of removal) in a realistic shuffle as opposed to a random
shuffle.  I wouldn't necessarily call this effect "little".  It's
probably enough to change (some small part of) the proper strategy
if you are permitted to take into account the previous card.

>I would not even rule out your conclusion that there is
>a certain negative correlation. (By which I assume you mean something
>like: summing millions of simulated hands in the
>real world simulation produced a distribution in which tens followed
>tens a tiny fraction less often then they do in random cards (which, for
>6 deck shoes should obviously come out to be 95/312).

Right, though again it is the split cards that had this property: aces, 2's,
3's, 6's, 7's, 8's, and 9's.

>Now -- what
>NBJ proponents assume (I am not an NBJ proponent - it is a crock, but I
>also assume) -- is the following:  Let us describe a shoe of cards
>in the discard tray by means of an array of paramaters
>that tell us what percent of the time in that pile of cards tens follow
>tens, high cards follow high cards, low cards follow low cards and/or
>any similar kind of calculations. (I refer to these as coefficients of
>clumpiness. Obviously one could alos look at the inverse probabilities
>too).  Now, is there or is there not a correlation between the value
>of any one of those coefficients and its value after the standard
>shuffle is applied?

Yes, there should be.  (I feel like a prosecution expert witness being
tricked into helping the defense make its case.  Dr. K and I are not
particularly arguing, but I don't like to sound like I think NBJ has
any merit.)  In fact I have seen this experimentally: the like-card
clumping and anti-identical-card clumping effects are more noticeable after
a shoe has been in play through many shuffles than, say, after the
cards have been washed and played through once before the shuffle.
In other words, a random shoe tends to beget a random shoe, and a
clumped shoe tends to beget a clumped shoe.  

One thing I had intended to compute was the average distance by which
adjacent cards become separated in a realistic shuffle compared to a
random shuffle. I predict this distance would be shockingly low with
a realistic shuffle compared to a random shuffle.  Again, I did find
that the shuffle was too weak to even overcome a few cards in between
a split pair.

>[munch]
>Be that as it may - if you understand now what I am getting it I would
>welcome any simulation results that speak directly to that issue.

Should I run the average distance experiment, or do you have a different
experiment in mind?
-- 
Michael Hall            \ YOU HAVE THE ROCK.   VEGAS HAS THE ROLL.
NASA Ames Research Center\ - billboard near San Francisco
hall@ptolemy.arc.nasa.gov \
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