The game is "jacks or better". Given a particular 5-cards hand (i.e.
10 Clubs, 10 Diamonds, 6 Diamonds, 6 Spades, 4 Spades), there are 32
strategies to proceed, from "replace none" to "replace all". There are
9 standard poker winning hands, from "royal flush" to "jacks or
better". This creates a 32 x 9 matrix, with S(i,j) being a
probability of using i-th strategy and getting j-th winning hand. In
the above example S(1,1)=0, since if we hold all cards, there is no
chance of getting "royal flush". S(1,8)=1, since if we hold all
cards, we already have "2 pairs" (8-th winning hand).
Is there a research or publication that provides an efficient
algorithm for calculating all these probabilities for any hand with
sufficient math justification that can be followed and verified? I am
not looking for a computer program that provides an answer (there are
quite a few of those), since there is no way to verify calculation.
Obviously, computer simulation may be set to go through all possible
permutations, but that will take quite some time. |
