Help with Treeview and minimax algorithm thinking

I am new to vb.net 2005, I need somebody to guide me about treeview control. I have to create a project backgammon game, doors game about the computer player, which means artificial intelligence. Well I tried to google search to read somehow about minimax algorithm and treeview control, but I am complicated. I have in my mind, that I have to create a treeview control at runtime, but I am not sure about what do I have to store in it properly. My thinking is the following: First of all we have the Pc's and User's current situation of distributed checkers on the board. User's checkers are separate from Pc's Checkers. Every time the dices roll for Pc player, we have many options of playing even if they are the worst, even if they are better or best. A new situation is formed after playing. Depending on every new formed situation the players will play.
So may anyone tell me if I am thinking in the right way with my attached diagram? Do I have to include in my diagram the current formed situation of distributed checkers each time and for any supposing playing for each player so that to choose with minimax algorithm the best able to do for Pc? What is your opinion? If yes, do I have any problem with memory consumption? I need somebody to guide me with that, because I want to begin creating code in the right way for the right purpose. Question 2: When the game is at beginning how do I predict the best move for Pc??? Do I have to predict every possible moving for the opponent for each possible couple of dice??? How big that tree could be? Should I have to use separate trees? Is that right??? Any suggestions please? Any help will be much appreciated. Thank you so much in advanced.