From: kaufman@ucunix.san.uc.edu (Stephen A. Kaufman)
Newsgroups: rec.gambling
Subject: Re: Blackjack tips for beginners/Casinos in Minneapolis
Keywords: shuffle, clumping
Date: 5 Nov 92 15:50:02 GMT
Organization: University of Cincinnati

In article <1992Nov5.043058.21009@kronos.arc.nasa.gov> hall@kronos.arc.nasa.gov (Michael Hall) writes:
>In article <Bx7zJL.8r9@ucunix.san.uc.edu> kaufman@ucunix.san.uc.edu (Dr.
K.) writes:
>>
>>The issue is not at all whether or not
>>over zillions of hands the sum of all possible decks played and shuffled
>>all possible ways using a set way of bringing in new cards and a set way
>>of shuffling produces virtually random results.  The issue is whether or
>>not, given a certain shuffle type and particular dealer,
>>the sequence of cards as they were placed in the discard tray
>>(and, thus, to some extent the results of the previous shoe)
>>can be correlated with the outcome of the next shoe, and, if so, whether
>>a human being (or a computer for that matter) can learn to take
>>advantage of that information!  My response is yes to both questions.
>
>What do you mean?
>
>I found no correlation of the win from one shoe to the next.  Thus I
>found no evidence for a chief tenant of TARGET.  (Of course, if the
>*cut* were not random, but say always in the middle, and the shuffle
>tended to put the top cards on bottom which then get cut back to the
>top, that would be another story.)
>
>I found an anti-correlation of one card to the next, after subtracting
>out the effects of removal.  Thus, I found identical-card anti-clumping
>on the local scale.  I also found like-card clumping when looking at
>the correlation from a whole group of cards to whole next group
>of cards, but the correlation was very small.  I take this as another
>strike against TARGET and NBJ, as Olson and Patterson claim like-card
>clumping is a huge effect that costs the player 5% of advantage (yeah,
>right) and can be exploited to yield 5% of advantage (yeah, right).  They
>do not mention identical-card anti-clumping (which occurs due to splitting,
>with aces and 8's being the most homophobic and 5's not minding each other's
>company at all).
>
>As I said, I found no harm of realistic shuffles to normal players and
>normal card counters.  There was some funny stuff with the 5 card 21 rule
>and the Resorts shuffle compared to a random shuffle, and the effect
>varied by seat position, but it was only .02% of advantage or so.
>
>Would you please just state exactly what you mean?
>

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.  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.  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).  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?  Since you say that you did find out that things
start to get strange when people split things and/or hit a lot of
cards to take advantage of a 5 card 21 or the like, I take that to
indicate that in fact your results show such correlations but that you
didn't really pursue it on the level I am talking about.  Please
elaborate.

Certainly experienced dealers know that that is true!  A story: playing
last year at Tropworld, I noticed at a table with three players
a hand in the middle of the shoe where everybody had pat twenty but for
one player with 19 or some such thing.  Needless to say, I did my
best to track that clump and sat down at the shuffle ready to pounce.
Sure enough, comes middle of the shoe and out pops a run of solid
tens, this time, thankfully, the dealer getting the 19 - at which she
says something like "the last time we had those cards I won!" clearly
meaning not "isn't that an interesting coincidence" but rather "you
fools, didn't you realize the rest of the deck was poor in tens and 
that the only hand you were going to have an edge at was the one
loaded with all the tens."  

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.

Dr. K.