From: jamesr@Autodesk.COM (James Rowell)
Newsgroups: rec.gambling
Subject: Re: Rank of Hold`em Pocket Cards
Date: 18 Nov 92 18:14:47 GMT
Organization: Autodesk Inc., Sausalito CA, USA

mzimmers@netcom.com (Michael Zimmers) writes:
>
> Considering that Sklansky was a professional actuary and that Malmuth
> is a professional mathematician, what makes you think that wasn't how
> they created the tables in the first place??

They *may* have used such tables, but if so it seems to me that they
have adjusted them in the book according to how strong they feel
certain pockets are IN PRACTICE.

    For example
    Group 1 has AA, KK, QQ, JJ,
    Group 2 has TT
    Group 3 has 99
    Group 4 has 88 (third in the list)
    etc.

There are other examples of how unevenly distributed certain
classifications of cards are, and it just doesn't *seem* to me
that they have been arranged according to a purely mathematical
evaluation.  Also since the ordering of the hands in the tables
was changed from the earlier volume (Sklansky's) that gives us
a clue as well.  I was thinking that every few years, as people
get used to the latest and greatest tables, and adjust their play
accordingly, new tables will have to be released to compensate!

> If you've got a better idea for ranking pockets, we're all ears...

Well, I thought what I posted was the basis of a better idea.
But I'll elaborate.

I dug up an old article that Steve R Jacobs sent out.  I'll quote it.

> Last week I posted a question that involved playing head-up Texas
> hold'em against a player who holds AD AH.  With these two cards
> and the two cards held by the opponent removed from the deck,
> there are 1,712,304 possible 5 card boards that can be formed
> from the remaining 48 cards, and each of these boards have equal
> probability of occuring.  The number of boards that result in
> wins, ties, and losses for the AA hand are listed below for
> several opposing hands.
>  
>             1712304 possible boards
>             -----------------------
>    other       AA      AA      AA       AA    AA     AA     AA 
>     hand      wins    ties    loses   %win   %tie   %lose  %gain
>  
>    AC  AS     37210 1637884   37210    2.17 95.654   2.17   0.00
>  
>    6S  5S   1314307    6415  391582   76.76  0.375  22.87  53.88
>    7S  6S   1315168    5499  391637   76.81  0.321  22.87  53.93
>    8S  7S   1315602    5030  391672   76.83  0.294  22.87  53.96
>    9S  8S   1322321    5215  384768   77.22  0.305  22.47  55.78
>    5S  4S   1338060    7101  367143   78.14  0.415  21.44  56.70
>  
>    KS  KC   1388072    6538  317694   81.06  0.382  18.55  62.51
>    2S  2C   1392072    8560  311672   81.30  0.500  18.20  63.10
>    KD  KH   1410336    9308  292660   82.36  0.544  17.09  65.27
>    2D  2H   1414342    9814  288148   82.60  0.573  16.83  65.77
>    7S  2S   1423187    6488  282629   83.12  0.379  16.51  66.61
>  
>    7S  2C   1493820    6236  212248   87.24  0.364  12.40  74.84
>    AS  KS   1493670   21503  197131   87.23  1.256  11.51  75.72
>    7C  2D   1506721    6846  198737   87.99  0.400  11.61  76.39
>    7D  2C   1506544    7607  198153   87.98  0.444  11.57  76.41
>    7D  2H   1519445    8217  184642   88.74  0.480  10.78  77.95
>  
>    AC  KS   1574439   21449  116416   91.95  1.253   6.80  85.15
>    AC  6S   1584291   15246  112767   92.52  0.890   6.59  85.94
>    AC  KD   1588961   23072  100271   92.80  1.347   5.86  86.94
>    AC  6D   1598778   16718   96808   93.37  0.976   5.65  87.72

Pretty cool eh?

Here Steve is doing, for just a few examples of hands, what I was
talking about.  If you carried the idea far enough and ranked each
of the `52 choose 2' possible pocket starters against each of the others
and then averaged the results for each hand you might get an overall
idea of how the hand can stand up in general.

Simple no?  I'd like to know how Steve generated this table, computer?

I'm not saying that what Malmuth and Sklansky wrote was no good
(that would be just a little too presumptuous even for me!) but
that I'd like to see the unadjusted tables so that I can make
my own decisions about ranking the hands.  I'm not talking about
anything else like position, or how you play the hands at all.
Also, wouldn't it be interesting to see how M&S's rankings compare
to a rigorously derived table?  I think it'd be enlightening.