From: kaufman@ucunix.san.uc.edu (Stephen A. Kaufman)
Subject: Re: Card Clumping (was: Deuces Wild Video Poker in Vegas)
Keywords: Clumping
Organization: University of Cincinnati
Date: Tue, 17 Nov 1992 01:35:07 GMT

In article <1992Nov16.211519.5795@kronos.arc.nasa.gov> hall@kronos.arc.nasa.gov (Michael Hall) writes:
>
>Geez, I was away on "business" Thursday night through Sunday.  But in any
>case I don't think I'll get to it soon, as it has a low priority on my
>list of things to do.
>

Figured you were on such a "business" trip.  Hope you had
a valuable one!

Seriously, though, if you could ever do some simulations along
the lines of my suggestions it might prove most interesting.  Let
me give a specific example.  Supposing, just supposing, that
what you (and I) say about non-random
shoe shuffles is correct --- that clumped shoes
tend to produce clumped shoes --- and that using that information
an astute player determines that over long stretches of such shuffles
certain cards (tens, perhaps) will occur after certain sequences
more or less frequently than the "count" indicates.  Say that
3 or 4 times a shoe a player is regularly able to predict that the
next (hit) card or the dealers hole card is a ten with a relative
increase in probability of say 10% (i.e. if 30% of the unseen cards
are 10's, when such a prediction is made it actually turns out to
be correct 40% of the time).  The following questions present
themselves:
1) How many shoes and how many guesses must be made at the +10%
rate for the results to be statistically convincing at say a 99%
confidence level?
2) If we are convinced by the statistics, then aside
from knowing when to take insurance, what changes should be made in
 a) betting strategy when sitting at first base and predicting the
first card will be a ten?  (presumably we want to stick as close
as possible to Kelly)
 b) basic strategy and counting strategies when the hole card is
    predicted to be a ten?
 c) hitting/doubling/splitting strategy when the hit card is predicted
    to be a ten?
 d) both b) and c) is true?  (Actually this one is easy for a counter,
for it is usually just the strategy that is correct at that average count
level:  if you are counting tens and 40% of the remaining cards are
tens, then whatever strategy applies to such a count would apply
if you can accurately predict that the same probability holds for
both cards in question in spite of the count.  Note that this does
not apply to all plays, though; only those where only one more card
will or won't be taken.  Strictly speaking, though, I guess it really
isn't even that simple, for there is always a very good chance that the dealer
will have to take more than one more card.  But it should be close
enough for empirical purposes.)
 Of course, Michael, you seem to think that it is non-ten cards that
can be predicted with greater confidence.  So just ask the same
questions for them.
  Any takers?


>-- 
>\When you're down on your luck counting cards, just
>\repeat this (CMU football) chant: "That's all right.
>\That's okay. They're going to work for us some day!"

CMU!!? Who wants to work in Pittsburgh?!  I've heard the same
said of other football noteworthies like Northwestern, Yale, and Harvard!

Dr. K.
Newsgroups: rec.gambling