🚀 go-pugleaf

In article <LAINS.93Jan8190731@world.std.com>, lains@world.std.com (Layne L Ainsworth) writes:
|> 
|> On the BlackJack problem:
|> 
|> aIt might be knd of interesting to give as input the history of all
|> cards turned up in the game (current shoe). Emergent card counting!

   Yes, that should give a better playing strategy, but at a huge cost.
To make a hit/stay decision, you need to know the value of your hand and
some reasonable number of the cards that have appeared up to this point.  
This should always include the dealer's upcard and your two cards.  (Note that
I am not assuming any other players in the game.  I am also not allowing the
computer enough info to allow for splitting or doubling down, two things
you really need to use well to cut the bank's advantage.  I am ALSO assuming
that ONE deck is reshuffled after every play.  A three-deck shoe would make
these numbers worse.)  
This doesn't seem much more complicated than the original problem statement, 
but let's see:

   Item             Number of possiblilities
   Hand's value       9  (assume always stay on 19 and always hit on 10)
   3 cards seen        22,100       All of these numbers assume that
   4 cards seen        270,725       you have some nice way of storing the cards
   5 cards seen        2,598,960      compactly and non-redundantly.

  The algorithm has to be able to make a decision under any case:  3 cards known,
4 or 5.   If six cards are known, you might want to just assume that only 5 are,
and go with that.  Now....  each string must give a 1 or a 0 (hit/stay) for
each possibility.  That gives a total string length of
                                                             .
       9*(22,100 + 270,725 +  2,598,960) =  26,026,065 bits = 3.2 megs.

  You do NOT want to use strings this large.  you would need gigabytes
of quickly accessible memory during a run if you expect to sample a significant 
region of the problem space.

    Let me compare that with the string size for the original problem.

     Item             Number of possibilities
     Hand's value        9
     dealers upcard      52
     Is hand splitable?  2
      
    This gives only 9*2*52 = 936 bits per string, or 117 bytes.  That would
mean you could deal with a significant population size in about 500k total.
Even PC's can deal with this.

Rod