From: hall@kronos.arc.nasa.gov (Michael Hall)
Subject: Re: Peanuts! Kelly Criterion Strategy Adjustments! Popcorn!
Organization: NASA/ARC Information Sciences Division
Date: Thu, 30 Jul 1992 23:02:08 GMT

Here is the promised repost of Hi-Opt I Kelly criterion strategy
adjustments, with the correct numbers this time for the 10 and Ace
columns.  The first line is for 1/50 of the bankroll, the second
line is for 1/300 of the bankroll, and the last line is for 1/oo
of the bankroll.

For example, if you were playing single deck blackjack with a 300
unit bankroll and put a 6 unit bet out and got a 10 vs dealer 10 showing,
you should not double until a true count of >=+11(!) If the bet were just
one unit, you should double on a true count >=+6. If the bet were
totally negligible, you should just maximize expected value, which
is done by doubling on >=+5 (the standard published index.)

                     Blackjack Count Strategy Adjustments

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

               1 deck, no double on splits, dealer hits soft 17


                              Hit/Stand Strategy

                                Dealer's Upcard

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

   Hard 18        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   
   Hard 18        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   
   Hard 18        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   

   Hard 17        ...   ...   ...   ...   ...   ...   -16   -17   -19    -4   
   Hard 17        ...   ...   ...   ...   ...   ...   -16   -17   -19    -4   
   Hard 17        ...   ...   ...   ...   ...   ...   -16   -17   -19    -4   

   Hard 16         -9    -9   -10   -12   -11     9     8     4     0     3   
   Hard 16         -9    -9   -10   -12   -11     9     8     4     0     3   
   Hard 16         -9    -9   -10   -12   -11     9     8     4     0     3   

   Hard 15         -6    -5    -7    -8   -10    10     9     7     3     5   
   Hard 15         -6    -5    -7    -8   -10    10     9     7     3     5   
   Hard 15         -6    -5    -7    -8   -10    10     9     7     3     5   

   Hard 14         -4    -4    -5    -7    -8    12    19   Hit    14     8   
   Hard 14         -4    -4    -5    -7    -8    12    19   Hit    13     8   
   Hard 14         -4    -4    -5    -7    -8    12    19   Hit    13     8   

   Hard 13         -1    -1    -3    -4    -6   Hit   Hit   Hit   Hit    13   
   Hard 13         -1    -1    -3    -4    -6   Hit   Hit   Hit   Hit    13   
   Hard 13         -1    -1    -3    -4    -6   Hit   Hit   Hit   Hit    13   

   Hard 12          2     2     0    -1    -2   Hit   Hit   Hit   Hit   Hit
   Hard 12          2     2     0    -1    -2   Hit   Hit   Hit   Hit   Hit
   Hard 12          2     2     0    -1    -2   Hit   Hit   Hit   Hit   Hit   

   Soft 20        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   
   Soft 20        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   
   Soft 20        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   

   Soft 19        ...   ...   ...   ...   ...   ...   ...   ...    18*  ...   
   Soft 19        ...   ...   ...   ...   ...   ...   ...   ...    18*  ...   
   Soft 19        ...   ...   ...   ...   ...   ...   ...   ...    18*  ...   

   Soft 18        -13   -13   -11   -12   -12   -20   -10   Hit   Hit   Hit
   Soft 18        -13   -13   -11   -12   -12   -20   -10   Hit   Hit   Hit
   Soft 18        -13   -13   -11   -12   -12   -20   -10   Hit   Hit   Hit   

   Soft 17        Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   
   Soft 17        Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   
   Soft 17        Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   Hit   

                             Double Down Strategy

                                Dealer's Upcard

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

   Hard 11         -9    -9   -10   -11   -12    -6    -4    -2    -2     0
   Hard 11        -10   -10   -11   -12   -12    -7    -5    -3    -3     0
   Hard 11        -10   -10   -11   -12   -13    -7    -5    -3    -4    -1   

   Hard 10         -8    -7    -9   -10   -11    -5    -2     0    11     5
   Hard 10         -8    -8    -9   -11   -12    -6    -4    -1     6     4
   Hard 10         -9    -8    -9   -11   -12    -6    -4    -1     5     4   

   Hard  9          2     1    -1    -3    -4     5    10   ...   ...   ...   
   Hard  9          0     0    -2    -4    -5     3     9   ...   ...   ...   
   Hard  9          0     0    -2    -4    -5     3     8   ...   ...   ...   

   Hard  8         14    10     7     4     4    17   ...   ...   ...   ...   
   Hard  8         12     9     6     3     3    16   ...   ...   ...   ...   
   Hard  8         12     8     5     3     2    15   ...   ...   ...   ...   

   Hard  7        ...    16    11    10    10   ...   ...   ...   ...   ...   
   Hard  7         20    15    10     9     9   ...   ...   ...   ...   ...   
   Hard  7         20    15    10     8     9   ...   ...   ...   ...   ...   

   Hard  6        ...    18    14    12    14   ...   ...   ...   ...   ...   
   Hard  6        ...    17    13    11    13   ...   ...   ...   ...   ...   
   Hard  6        ...    17    13    11    12   ...   ...   ...   ...   ...   

   Hard  5        ...    19    14    13    14   ...   ...   ...   ...   ...   
   Hard  5        ...    18    14    12    13   ...   ...   ...   ...   ...   
   Hard  5        ...    18    13    12    13   ...   ...   ...   ...   ...   

   Hard  4        ...    19    15    14    15   ...   ...   ...   ...   ...   
   Hard  4        ...    19    14    13    14   ...   ...   ...   ...   ...   
   Hard  4        ...    18    14    13    14   ...   ...   ...   ...   ...   

   Soft 20         11    10     8     6     6    17   ...   ...   ...   ...   
   Soft 20         10    10     7     6     5    16   ...   ...   ...   ...   
   Soft 20         10     9     7     6     5    16   ...   ...   ...   ...   

   Soft 19          8     5     4     2     1    14   ...   ...   ...   ...   
   Soft 19          7     4     3     2     0    13    20   ...   ...   ...   
   Soft 19          7     4     3     1     0    13    20   ...   ...   ...   

   Soft 18          3     2    -5    -6    -8    16   ...   ...   ...   ...   
   Soft 18          1     0    -6    -8   -10    15   ...   ...   ...   ...   
   Soft 18          0     0    -7    -8   -11    14   ...   ...   ...   ...   

   Soft 17          4     1    -3    -8    -9   ...   ...   ...   ...   ...   
   Soft 17          0    -2    -5   -10   -11    11   ...   ...   ...   ...   
   Soft 17          0    -2    -5   -10   -11     9   ...   ...   ...   ...   

   Soft 16         15     7     2    -2    -8   ...   ...   ...   ...   ...   
   Soft 16         11     5    -1    -4   -10   ...   ...   ...   ...   ...   
   Soft 16         10     4    -1    -5   -11   ...   ...   ...   ...   ...   

   Soft 15         18     8     2    -2    -5   ...   ...   ...   ...   ...   
   Soft 15         14     5    -1    -4    -7   ...   ...   ...   ...   ...   
   Soft 15         13     4    -2    -5    -8   ...   ...   ...   ...   ...   

   Soft 14         13     8     2    -1    -3   ...   ...   ...   ...   ...   
   Soft 14         10     6     0    -2    -4   ...   ...   ...   ...   ...   
   Soft 14          9     5     0    -3    -5   ...   ...   ...   ...   ...   

   Soft 13         11     7     3     0    -2   ...   ...   ...   ...   ...   
   Soft 13          8     5     1    -2    -3   ...   ...   ...   ...   ...   
   Soft 13          8     5     1    -2    -3   ...   ...   ...   ...   ...   

       * indicates adjustment in the opposite of normal direction
-- 
Michael Hall            \ Happiness is... making a big cover bet off the top of
NASA Ames Research Center\ a freshly shuffled deck and getting a blackjack,
hall@ptolemy.arc.nasa.gov \ while the pit boss is watching.