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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. Jan 21, 2021 at 19:58
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    A tricky task - optical similarity can be highly misleading, the slightest tactical nuance might make the difference. Jan 24, 2021 at 22:21
  • @2080 it would be best to define what you mean by similarity - optical similarity (i.e. humans at a glance with no understanding of chess rules would find the positions similar-looking) or gametree similarity (i.e. the positions are similar from the perspective of considerations pertaining to what should be played in each). Sep 11, 2021 at 0:54

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Ultimately, what is considered 'similar' depends on what one is trying to achieve by measuring similarity. I suspect, a common chess engine use-case would be to try predicting if the two positions are going to return same evaluation result.

Here are a few brainstorm-style ideas:

  • Compare lists of legal moves and measure the degree to which they overlap.
  • Base the measure on the number of pieces whose positions are mismatched
  • Base the measure on the minimum number of moves needed to get from position A to position B.

Some food for thought: https://en.wikipedia.org/wiki/Edit_distance

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