Suppose we have a two player game like Tic Tac Toe where the two players take turns to play their moves. It is my understanding that in the game tree that MCTS builds, consecutive levels in the tree correspond to different player's turns.
So, for instance, in the root node it is Player1's turn to play, in the children of the root node it is Player2's turn to play, in the children of those children it is Player1's turn again, etc.
Is that correct?
If so, is it really prudent to treat nodes where it's the enemy's turn to play the same as those where we choose the next action (i.e. by averaging rollout results in backpropagation). Since, it's not us choosing the next action but the enemy, shouldn't we "pick" the minimum "return" (like in minimax) in those cases instead of the average like we do for nodes where we get to pick the next action?
By picking I mean to only count the win ratio of that child node (i.e. the minimum win ratio).
I suspect I am missing something (e.g. that might mess up exploration vs exploitation with UCT) but I can't put my finger on it.
What do you guys think about this?
Edit: Maybe a solution to this is only considering good moves for the opponent? But then again.. how do we define good? Heuristics?