From: hall@kronos.arc.nasa.gov (Michael Hall)
Subject: BJ: Multiparameter 7&8 Hi-Opt I strategy adjustments
Organization: NASA/ARC Information Sciences Division
Date: Thu, 23 Jul 1992 20:48:49 GMT

A while ago, I generated the multiparameter strategy adjustments for
Hi-Opt I with a *combined* side count of 7's and 8's, and in this article
I'll reveal them (probably they have never been published anywhere before,
not even in Humble's expensive multiparameter Hi-Opt I tables.) To use
this data, you would adjust the running count by the number of excess
remaining 7&8's times the side adjustment. The adjustment procedure
is more fully explained in the file hi-opt1.txt in the rec.gambling
archive at soda.berkeley.edu.

Essentially, you are counting high (10) and low (3,4,5,6) cards, balancing
them against each other, and also counting medium (7,8) cards, which are
a bit fickle and act as either high or low or medium cards, depending on
the situation.  Only a multiparameter system can capture this fickleness.

Multiparameter 7&8's Hi-Opt I kicks butt on single deck.  It's better than
Zen. It's better than Hi-Opt II.  It's better than Wong Halves.  It's better
than Uston APC.   I consider it pretty much the best humanly possible system.
(Aces need to be side counted too, but just for betting.)

Alas, I'm giving up on it.  I find it much less confusing to figure out
excess remaining cards and the adjustment when I only have 4 cards to
worry about rather than 8.  So, I'm going back to just counting the 7's
for strategy (and aces for betting.)  This 7's only system is probably
slightly better than any other system like Uston APC.  (The 7's only
numbers are given in the hi-opt1.txt file.)  I'm also thinking of switching
to Wong Halves (doubled) for a couple of reasons - as my bankroll
exponentiates I'll be forced to play more double deck in the future (and
Hi-Opt I sucks for that), and also presumably the low risk indicies that
we dream of will be easier to generate for Wong Halves than for a
multiparameter system.

The tables for multiparameter 7&8's Hi-Opt I follow.  For each decision
there are two numbers.  The number before the slash is the main count
critical strategy adjustment index.  This number was generated via a
close-to-exact combinatorial analysis program that maximized expected
value (unfortunately.)  The number after the slash is the side count
(7&8's) adjustment number.  This number was generated using tables
of data from Griffin's "Theory of Blackjack" and a simple program I wrote.

For example, for hard 14 vs 10, the tables shows "+8/+5".  Suppose you
have seen half the deck, your Hi-Opt I main count is zero, and you
counted five 7&8's.  With half the deck out you would have expected
to see only four 7&8's, so you have seen one excess 7 or 8, which means
you should add +5*1 to your main count of zero for this strategy decision.
The adjusted running count is +5, and the true count is then 5/(1/2)=10.
You compare this to +8, and 10>8, so you should diverge from basic
strategy and stand.

Another place where you can get pretty wacky even with a neutral count is
on hard 17 vs 8, which is "-16/-8".  With half the deck gone, a running
count of -1, and just one excess used 7 or 8, you'd have an adjusted
true count of -18, which is less than -16, so you'd hit.  The pit
critters won't know what hit them ;-)


                 Hi-Opt I Blackjack Count Strategy Adjustments (main/78's)

                Cards:    2   3   4   5   6   7   8   9  10 Ace
                Values:   0   1   1   1   1   0   0   0  -1   0

                     1 deck, dealer hits soft 17


                            Hard Hit/Stand Strategy  (-24 to +32)

                                Dealer's Upcard

Player's     2      3      4      5      6      7      8      9     10     Ace 

Hard 18+    sta    sta    sta    sta    sta    sta    sta    sta    sta    sta
Hard 17   -20/0  -20/0  -24/0  -20/-2 -24/-2 -20/-2 -16/-8 -16/-6 -20/-2  -4/+1
Hard 16    -8/0   -8/0  -10/0  -10/-2 -10/-2 +10/-3  +8/-3  +4/-2   0/+1  +2/0
Hard 15    -4/0   -4/0   -6/0   -8/-2  -8/-2 +10/-3 +10/-3  +6/-2  +4/0   +4/0
Hard 14    -2/+2  -2/+1  -4/0   -6/0   -6/0  +12/+1 +20/+1 +20/+2  +8/+5  +8/+2
Hard 13     0/+2   0/+2  -2/+2  -4/+2  -4/+2 +24/+3   ...    ...    ...  +12/+3
Hard 12    +4/+2  +4/+2  -2/+2   0/+2  -2/+2   ...    ...    ...    ...  +20/+3


                            Soft Hit/Stand Strategy (-20 to +20)

                                Dealer's Upcard

Player's     2      3      4      5      6      7      8      9     10     Ace 

Soft 19+    sta    sta    sta    sta    sta    sta    sta    sta    sta    sta
Soft 18     sta    sta    sta    sta    sta    sta    sta    ...    ...    ...
Soft 17-    ...    ...    ...    ...    ...    ...    ...    ...    ...    ...


                           Hard Double Down Strategy (-12 to +16)

                                Dealer's Upcard

Player's     2      3      4      5      6      7      8      9     10     Ace 

Hard 11    -8/+1  -8/+2  -8/+1 -12/0  -12/0   -8/0   -4/0   -2/0   -4/+2   0/+1
Hard 10    -8/+2  -8/+2  -8/+1  -8/0  -12/0   -4/0   -4/0    0/0   +8/+2  +4/+1
Hard  9    +2/+2   0/+2  -2/+1  -4/0   -4/0   +4/0  +12/0    ...    ...    ...
Hard  8   +16/+2 +12/+2  +8/+1  +4/0   +4/0  +16/0    ...    ...    ...    ...
Hard  7     ...  +16/+2 +12/+1 +12/0  +12/0    ...    ...    ...    ...    ...
Hard  6     ...    ...  +16    +16    +16      ...    ...    ...    ...    ...
Hard  5     ...    ...  +16    +16    +16      ...    ...    ...    ...    ...
Hard  4     ...    ...  +16    +16    +16      ...    ...    ...    ...    ...


                           Soft Double Down Strategy (-8 to +20)

                                Dealer's Upcard

Player's     2      3      4      5      6      7      8      9     10     Ace 

  A9      +12/+1 +12/+1  +8/+1  +8/0   +8/0  +16/0    ...    ...    ...    ...
  A8       +8/+2  +4/+2  +4/+1  +2/0    0/0  +16/0    ...    ...    ...    ...
  A7       +2/+3   0/+3  -4/+2  -4/+2  -8/+1 +16/+1   ...    ...    ...    ...
  A6       +2/+4  -2/+3  -4/+2  -8/0   -8/0   +8/+1   ...    ...    ...    ...
  A5      +16/+4  +8/+4  +2/+2  -2/0   -8/0    ...    ...    ...    ...    ...
  A4      +20/+4  +8/+4  +2/+2  -2/0   -4/0    ...    ...    ...    ...    ...
  A3      +16/0   +8/0   +2/0   -2/-2  -4/-2   ...    ...    ...    ...    ...
  A2      +12/0   +8/0   +2/-1  -2/-2  -4/-2   ...    ...    ...    ...    ... 


                           Pair Split Strategy (non-DAS) (-6 to +6 except 10's)

                                Dealer's Upcard

Player's     2      3      4      5      6      7      8      9     10     Ace 

Ace,Ace     spl   spl   spl   spl   spl   spl   spl   spl   spl    -4
 10,10      +12   +12    +6    +6    +6   +12   +20   ...   ...   ...   
  9,9         0     0     0    -4    -4    +6   spl   spl   ...    +6
  8,8       spl   spl   spl   spl   spl   spl   spl   spl    +4*  spl   
  7,7       spl   spl   spl   spl   spl   spl   ...   ...   ...   ...   
  6,6         0     0    -4    -4    -4     0*  ...   ...   ...   ...   
  5,5       ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   
  4,4       ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   
  3,3        +6    +6     0   spl   spl   spl     0*  ...   ...   ...   
  2,2        +6    +2    -4   spl   spl   spl   ...   ...   ...   ...   

-- 
Michael Hall            \ I'm sorry sir, but you can no longer play coupons
NASA Ames Research Center\ in our casino.  Feel free to play slots, craps,
hall@ptolemy.arc.nasa.gov \ blackjack, or any other game.  But no coupons.