Bayesian Poker: How to find distributions that you can't find using combinatorics
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This is my first question on stackoverflow and also my first time implementing a Baysian network so I will apologize ahead of time for any novice mistakes I make. 

The goal of my project is to implement a Poker player that does Baysian inference. There has been some work done on this by a group at Monash University in Australia led by Kevin Korb which I am using to reference off of. You can find their work here:

http://www.scribd.com/doc/55485155/Bayesian-Artificial-Intelligence

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&sqi=2&ved=0CG0QFjAC&url=http%3A%2F%2Fwww.csse.monash.edu.au%2F~annn%2Fpoker%2FUAI99.pdf&ei=_0ATUOCAJoikrQHMu4GIBg&usg=AFQjCNGrK-K2JJxabMq4RAL2p5MbMX_tkg&sig2=-d9Y9b8PORi6V_rA4B5uYA

The first reference, being a book, is more helpful and detailed (see Ch.5.5 & 11 for Poker). I am using the simplified version of Texas Holdem called Leduc Hold'em to start.

Leduc Holdem:
Leduc Hold’em is a two player poker game. The deck used in Leduc Hold’em contains six cards,
two jacks, two queens and two kings, and is shuffled prior to playing a hand. At the beginning of a
hand, each player pays a one chip ante to the pot and receives one private card. A round of betting
then takes place starting with player one. After the round of betting, a single public card is revealed
from the deck, which both players use to construct their hand. This card is called the flop. Another
round of betting occurs after the flop, again starting with player one, and then a showdown takes
place. At a showdown, if either player has paired their private card with the public card they win all
the chips in the pot. In the event neither player pairs, the player with the higher card is declared the
winner. The players split the money in the pot if they have the same private card.
Each betting round follows the same format. The first player to act has the option to check or bet.
When betting the player adds chips into the pot and action moves to the other player. When a player
faces a bet, they have the option to fold, call or raise. When folding, a player forfeits the hand and
all the money in the pot is awarded to the opposing player. When calling, a player places enough
chips into the pot to match the bet faced and the betting round is concluded. When raising, the player
must put more chips into the pot than the current bet faced and action moves to the opposing player.
If the first player checks initially, the second player may check to conclude the betting round or bet.
In Leduc Hold’em there is a limit of one bet and one raise per round. The bets and raises are of a
fixed size. This size is two chips in the first betting round and four chips in the second.

If you look at pg.185, Section 5.5.2.1 in Figure 5.14 there is a diagram for a Bayes Net for Poker. This is essentially the same one I am using for my project, but granted that there are no up-cards in Leduc Hold'em the two corresponding nodes for up-cards are not applicable for it. I was able to compute the joint porbability tables between the node pairs
(BPP_Win, BPP_Fin), (BPP_Win, OPP_Fin), (OPP_Fin, BPP_Fin), (OPP_Fin, OPP_Curr), and (BPP_Fin,BPP_Curr) **but I am not sure how to compute the joint probability of (OPP_Curr, OPP_Action)**. As I understand it some sort of sampling technique is necessary. 

As a follow up question, if I am able to compute this joint probability, then I should be able to compute the Marginal Probability of BPP_win given my current card by using BP and treating the joint probabilities as factors, correct?