The NN outputs a probability distribution over all the possible moves (illegal moves are set to 0 and the probabilities sum to 1). The MTCS call for this distribution, combine it with an exploration coefficient and Dirichlet noise, to form a score, and choses a move to expand until a certain number (in chess is 6000) of nodes have been visited. Nodes are expanded until leaf nodes are explored. This link explains it better than I:
The NN outputs a probability distribution over all the possible moves (illegal moves are set to 0 and the probabilities sum to 1). The MTCS call for this distribution, combine it with an exploration coefficient and Dirichlet noise, to form a score, and choses a move to expand until a certain number (in chess is 6000) of nodes have been visited. Nodes are expanded until leaf nodes are explored. This link explains it better than I:
https://joshvarty.github.io/AlphaZero/