Many games have multiple paths to the same states. What is the appropriate way to deal with this in MCTS?
If the state appears once in the tree, but with multiple parents, then it seems to be difficult to define back propagation: do we only propagate back along the path that got us there "this" time? Or do we incorporate the information everywhere? Or maybe along the "first" path?
If the state appears once in the tree, but with only one parent, then we ignored one of the paths, but it doesn't matter because by definition this is the same state?
If the state appears twice in the tree, aren't we wasting a lot of resources thinking about it multiple times?