The Value of Chess Squares

What you'd expect, but with precision. (But...real precision, or faux?)

In a general way, the findings of this academic paper are just what you’d expect: central squares are more valuable than those closer to one’s home files, and squares near the enemy king are even more valuable. (Water is wet, dog bites man, news at 11.) But you might find some of the specifics interesting, and might find it interesting to compare the generic results taken from grandmaster games to those specifically from Magnus Carlsen’s practice.

A question, though. Just skimming the paper, I’m not sure there’s any value in comparing the Carlsen data to the all grandmasters set, because I expect that piece values will vary with openings. (This seems pretty obvious after a moment’s reflection.) Thus if Carlsen’s repertoire doesn’t exemplify the average opening distribution of grandmasters in general, it’s unlikely that the differences in square values represent some sort of Rosetta Stone for figuring out the differences between his understanding and those of his weaker colleagues. The researchers should therefore take a subset of GM games that proportionally matches Carlsen’s games, and then do the comparison. (If they in fact did that, and I missed it in my skimming, my apologies - and please point this out in the comments.)

There are some causation vs. correlation issues here as well, but I think the end user of the study can get around this with a bit of thoughtfulness. For instance, at the bottom of page 13 we read this “insightful” comment: “Therefore, having a white knight positioned on f5 often confers an advantage.” Huh, you don’t say. No kidding, Sherlock.

This is rather well-known, and blindingly obvious to even slightly experienced club players. But is the White position better because a knight is on f5, or is a knight on f5 because White’s position is better - and the nature of the advantage is such that a knight can outpost itself on that square? A naive reading of the study would suggest that one should strive to put knights on f5. That’s too simplistic, only slightly more sophisticated than going for the four-move checkmate. If one has internalized the value of a knight on f5 - when it’s possible and sensible - then one will be attuned to the possibility of creating and occupying such an outpost when the right preconditions are in place. The better the player, the greater the sensitivity to a large range of possible preconditions. But we all know about the value of the f5 square, even if we won’t be as successful as Carlsen in getting a knight there. As Rudolf Spielmann once said of Alexander Alekhine’s reputation as a great tactician: “I can see the combinations as well as Alekhine, but I cannot get to the same positions.”

Anyway, even if my criticisms are relevant, the sort of data examined in the paper can be useful, particularly if we can do our own tests. For instance, I might not be sure which plan is best at the end of a given opening line. So I might have Stockfish play a bunch of super-fast games against itself, and then see what squares get more heavily weighted. If Plan A is primarily aimed at getting pieces to the squares that got the heavier weight and Plan B’s squares proved less effective, then I may have discovered something. Further, deeper exploration of Plan A may reveal the relevance of other squares whose importance wasn’t immediately obvious, which could expand my general understanding of how that variation and plan will work itself out a few moves further along. This more fine-grained approach seems likelier to be of value.

Other ideas, readers?