I think it makes sense to use a Conv2D net for evaluating each position where you have different input channels for each figure type on the board. For example one channel for pawns:
an 8x8 matrix with 1's where there are white pawns, and -1's where there are black pawns. the rest should be 0.
Also input channels for bishops, knights etc... and then ...
In a MCTS (Monte Carlo tree search) the resulting tree is expanded by two policies:
tree-policy (selects next and unknown child nodes by a exploration-exploitation tradeoff)
default policy (selects known child nodes till terminal state e.g. with random uniform moves).
The term terminal state is often considered to be the end a tree. If you consider ...