I'm looking for metrics that quantify how similar/different two positions are.

I have found a paper that used pawn structures to search for similar games in a database. This one tries to use reachable squares, as well as attack and defense structures do achieve this.

Metrics can be arbitrary, but I wonder if other approaches exist.

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    Similar positions will have similar game trees from that position, with similar branches in fact explored by chess engines. If a somewhat crude similarity measure can be found, perhaps it could be refined by using that similarity measure on a large number of positions reachable from the given position, in much the same way that chess engines can take a static evaluation function and apply it to a tree of reachable positions. I have no idea how to flesh this out, but there are various metrics which have been used in discrete math to measure tree similarity. – John Coleman Jan 21 at 19:58
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    A tricky task - optical similarity can be highly misleading, the slightest tactical nuance might make the difference. – Hauke Reddmann Jan 24 at 22:21

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