From: kaufman@ucunix.san.uc.edu (Stephen A. Kaufman)
Subject: Re: Blackjack tips for beginners/Casinos in Minneapolis
Keywords: shuffle, clumping
Organization: University of Cincinnati
Date: Fri, 6 Nov 1992 02:34:33 GMT

In article <1992Nov5.185736.5814@kronos.arc.nasa.gov> hall@kronos.arc.nasa.gov (Michael Hall) writes:
>
>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.
>
But this is precisely what Ellis Davis' NBJ proposes to do!
Why would you not be permitted to change your strategy based
on the previous card?

>
>again it is the split cards that had this property: aces, 2's,
>3's, 6's, 7's, 8's, and 9's.
>
Again - NBJ - Hall is coming down your path!

>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.  
    (capitals mine - Dr. K.)

QED!!! Michael Hall has now officially acknowledged that the
fundamental principle of all card clumping systems (like NBJ - no
matter that the advantage claims for that particular system are ludicrous and
the strategy specifics are nothing short of mathematically imbecilic) --
his own words are as fine a description of the principle as I have
ever seen.  (By the way - a fundamental teaching of NBJ is that
sometimes the cards clump identical, sometimes "anti-identical"!)

 The only questions remaining are: 1) Can a real world player
take advantage of this relationship to produce a result superior to
that of simple counting? 2) Does the counter who ignores this
information do so at his/her peril? (for example the last shoe just
went to a sky high count and never came down.  Next shoe: do you
raise your bet as soon as the low card clump has started
and the "true" count suggests a positive e.v.
or do you wait for the direction and rate-of-change of
the count to indicate that you have left that unpleasant clump behind?)
(another corollary: you've just played through a highly clumped shoe.
Count is zero and all of a sudden high cards start covering the table.
Do you lower your bet like any reasonable counter or do you raise
it because more high cards should now come out?)  Of course
these are intended to be rather simple-minded alternatives - obviously
even if the clumping claims are true it is the "coefficient" of
clumpiness that will determine the proper play.  But how do we
determine such a coefficient and how do we take advantage of it?
>
>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.
That is the reason I asked people to do the experiment with ordered
cards and different backs in my first posting in this thread.  The
result -- for the stutter shuffle -- is not only do cards end up
SHOCKINGLY close to each other (in certain parts of the deck more
so than others) -- but that interleaved as they are, they usually stay
in the same sequence in which they started!!

>
>Should I run the average distance experiment, or do you have a different
>experiment in mind?

Do so indeed!  It would be most interesting.  An additional
test that would be useful would be is the degree of correlation between
the average lengths of like card clumps in subsequent shoes.

Michael - I think that the only difference between us is that you
have found some correlations but assumed they were too minimal to
be taken advantage of or to adversely impact a good counter's game;
whereas I think those responses are premature.  Moreover, these
clumping tendencies impact
a counter's results more so than the average basic strategy player,
because the counter ends up raising his bet too soon (in the long run).
I just haven't been able to figure out a way to demonstrate how to
take advantage of it through simulation! Fortunately, though, I
know how to do it over the table!

Dr. K.
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