Question

recursion: how to setup base cases for analyzing blackjack

Asked by: sapbucket

Hello,

  This one is tough. I've been programming games for a long time but haven't considered how to calculate EXPECTED VALUE for blackjack. The problem (for me) stems from the fact that I don't know how to setup a simulation because, literally, I don't know how many hits or splits or going to occur. By doing a little research it turns out we need to use a recursion algorithm with combinatrics to determine the expected value.

see http://www.tqsports.com/blackjack/blackjack.htm
or http://www.wizardofodds.com/blackjack/bjapx5.html

  The program needs to return the expected value for each of four "limbs" of a decision tree:
  1. Hit
  2. Stay
  3. Double Down
  4. Split

  If we sum all of the expected values for a single "limb", we get the expected value for that branch of the decision tree. The "limb" with the highest expected value is the correct decision for that situation.

  There are a certain number of outcomes that end a branch of a decision tree,  using a base unit of '1' we get:
  win = 1.0
  lose = -1.0
  push = 0
  natural = 1.5

  X = the set of known cards (a list)
  Y = the set of unknown card (a list)

  Pwin(X,Y) = the probability that given X known set of cards and Y unknown set of cards that we will WIN the hand
  Plose(X,Y) = the probability that given X known set of cards and Y unknown set of cards that we will LOSE the hand
  Ppush(X,Y) = the probability that given X known set of cards and Y unknown set of cards that we will PUSH the hand
  Pnatural(X,Y) = the probability that given X known set of cards and Y unknown set of cards that we will NATURAL the hand


  expected value for a "limb" of the decision tree may therefore become:
  E.V. = Pwin(X,Y)*(1.0) + Plose(X,Y)*(-1.0) + Ppush(X,Y)*(0) + Pnatural(X,Y)*(1.5)

 
  Well, that is as far as I know how to get. I don't know how to calculate the probabilities beyond that.

  Is there anyone here that knows how to point me in the right direction? I just can't fathom how to tackle this problem.

  Thanks for any advice. I know that I can't expect a solution here, but if you could help me with the SETUP of this problem I would really be happy.


sapbucket







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Asked On
2005-03-21 at 21:50:35ID21359606
Tags

blackjack

,

ppush

Topic

Perl Programming Language

Participating Experts
1
Points
500
Comments
111

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