It just might be solvable, but something bothers me:
Even if the entire tree could be traversed, there is still no way to predict the opponent's next move. We must always base our next move on the state of the opponent, and make the "best" move available. Then, based on the next state we do it again.
So, our optimal move might be optimal iff the opponent moves in a certain way. For some moves of the opponent our last move might have been sub-optimal.
I just fail to see how there could be a "perfect" move in every step.
For that to be the case, there must for every state [in the current game] be a path in the tree which leads to victory, regardless of the opponent's next move (as in tic-tac-toe), and I have a hard time figuring that.
