A program can search a tree. Each node in the tree has a configuration stored with it. It has a child for each legal move of the player whose move it is.

If a given branch reaches a configuration where black has won, then that node is a leaf and is labeled true. No further moves are possible.

If a given branch reaches a configuration where white has won, then that node is a leaf and is labeled false.

If a branch reaches a configuration that has occurred previously in the same branch, that node is a leaf and is labeled false (since black has not won). Notice that the tree is finitely large because there are a finite number of configurations.

Finally, store a boolean value at each node of the tree. Work from leaves upward toward the root. At a node N that is white's move, store the logical 'and' of the values that label the children of N. At a node N that is black's move, store the logical 'or' of the values that label the children of N.

Finally, answer yes if the root of the tree is labeled true, and answer no if it is labeled false.