When transpositions are possible in a game, usually the number of them will grow exponentially with the search depth, making deep search much more costly than needed. Ideally, we would like to these branches of the search to share their computation. - Monte-Carlo Graph Search from First Principles / HN

In game-tree search or other applications of tree search, often we can find multiple possible sequences of moves or actions transpose to the same state. For example, in chess, 1. d4 d5 2. Nf3 leads to the same position as 1. Nf3 d5 2. d4.

However, standard implementations of Monte-Carlo Tree Search (MCTS) usually do not do this. They treat the game as a branching tree and inefficiently re-search every instance of each duplicated position within the tree.