Adversarial Monte Carlo Tree Search Asymmetry Monte Carlo Tree Search with UCT is praised for it's asymmetric tree growth, 
growing promising subtrees more than non-promising ones.

But in a 2-player adversarial game, when a win at one node is a loss at the node below it, wouldn't the tree growth be extremely favourable for the current player at each node, and result in a not so asymmetric tree growth?
The most explored path will be the Nash Equilibrium, because at each step we choose the best move for each player.
The asymmetry happens at each level towards the best move for the current player, thus overall the tree will not grow asymmetrically.