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Hello I am currently working on an implementation of MCTS and I ran into the problem that my tree traversal policy selects nodes with terminal game states. Furthermore how do I prevent selecting a Node that only has children Nodes with terminal game states ( and so on and so on )?

MCTS Tree

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What you can do is to add a counter $t$ to each node, initially 0, indicating how many of its children are terminal.

When $t = c$ where $c$ is the number of children of a node, the node itself becomes terminal and increments the $t$ counter of its parent. Note that with this definition leaf nodes are automatically terminal, as they have no children, giving $0 = 0$.

As one more optimization, if a node has a terminal child that is losing, you can immediately mark its parent as terminal and winning.

Then, during selection you can ignore any terminal child.

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