Komi and perfect play

[yebellz]

This post is a bit old (May 2020), but it addresses KataGo “opinions” of fair values of komi:

@hexahedron

Actually if you’re going by KataGo, 6 isn’t right. 6.5 is actually estimated as slightly more fair than 6 right now as of the tip of the current run.

Obviously a non-integer value isn’t going to be fair under theoretical perfect play, but it could easily be more fair in practice. Or in other words on 6 komi, black presumably wins enough more of the non-drawn games than white does that counting the drawn games for white actually increases the fairness of the match.

This is not surprising at all, really. We know from parity considerations, unless something “weird” happens, Japanese rules will with 50% probability each cost black one or zero points compared to Chinese rules. So until the level of play becomes so fantastically strong that bots are predicting the final parity of the game better than chance even in the opening and early midgame (they are very far from this right now), we should expect that if an integer is found to be a highly fair komi in Chinese, then that integer minus 0.5 should be highly fair in Japanese, and the more fair the former, the more fair the latter. Since 7 is very close to fair in Chinese, we should expect 6.5 to be very close to fair in Japanese.

Actuallly KataGo prefers 7 Chinese just a bit for white, therefore it also prefers 6.5 Japanese just a bit for white. But less than it prefers 6 Japanese for black.

Japanese rules black winrates for empty board top move on a very very recent 40 block network (not even released yet, but soon), with a few thousand playouts:

5.0 komi - 58.7%
5.5 komi - 55.2%
6 komi - 51.9%
6.5 komi - 48.9%
7 komi - 45.7%
7.5 komi - 42.1%