BQM 67: Fair komi adjustment to board size?
How should fair (e.g. 6.5 points) komi for 19x19 games be adjusted to non-19x19 games?
http://www.dragongoserver.net/phorum/read.php?f=4&i=1034&t=1034 states, that komi is independent of board size (if board size does not drop below 9x9). Is that correct? Proved by statistics? Or how should komi be adjusted to non-default board sizes? -- Frs, Feb 2003
Bill: Komi depends on board size.
I believe that we have discussed that somewhere here on SL. :-)
Nico: I have not found anything satisfactory regarding this issue on SL. Please can someone come up with a more definite answer to this question, especially for 9x9 and 13x13 boards ?
Charles Komi obviously does depend on the size of the board, for very small boards. I don't feel that it can differ much between 13x13 and 19x19 (some discussion at handicap for smaller board sizes which explains why I think that); but if someone told me that there are 13x13 go hustlers who can take Black and give 10 komi then I wouldn't be really surprised. My idea of the graph of komi against board size N is that it decreases rapidly when N is small, is effectively flat from 13x13 to 19x19, and is probably a little less for N very large. But who knows?
Anthony? I did a quick calculation and komi of 5.5 is 2% of the board area if the board is 19x19. However, it is 7% of the board for a 9x9. That's a lot to give for going first.
Alex Weldon: Yes, but the advantage of going first is inversely proportional to board size. So Black in 9x9 has a HUGE advantage (if there's no komi, it's virtually impossible for W to win if both players are sufficiently strong and of equal rank), so White's komi should be equally huge. For a very large board, 6.5 komi would be almost negligible, but a large board would make for a very long game, and Black's first move advantage would be accordingly diluted. It makes sense to me that, except at the very low end of the scale, komi wouldn't change much. If we want to be more precise, you could probably fit something like Alog(Bn) + C to it pretty closely.
Bill: Actually, I think that proper komi approaches a constant as board size increases. It should be about half the miai value of the first play, and I think that that is a constant on sufficiently large boards. If it were not, then the influence of a stone would increase appreciably with board size, and the best initial play would be at the center (as it is with small square boards). The history of opening on tengen on the 19x19 suggests that that is not the case.
Bob McGuigan: I remember seeing something that suggested that playing Black on a 9x9 board with no komi for White is equivalent to a four rank difference, similar to a four stone handicap on a 19x19 board.
Actually, I calculate fair komi to be the height of the "line of territory" for that board plus the height of the "line of influence" for that board (see platinumdragon). For example: on 9x9 board komi should be 5 (2nd line of territory + 3rd line of influence), on 19x19 komi should be 7 (3rd line of territory + 4th line of influence), etc. This does fail for boards that are too small (like 5x5) though, which are solved anyway. It also fails for infinite board, where komi seems like it should be infinity but is actually 0 (since white can play mirror go and black can't break it). Any objections? ~srn347
anonymous: I object. How do you determine the lines of territory and influence and what are they anyhow? If I understand these correctly there is virtually no line of influence on a 9x9 board, for example. The third line is still a territory line. Also, on almost any board the fourth line is not a territory line for the same reason it is not a territory line on a 19x19 board. platinumdragon's definition has nothing to do with territory and I have to say his weak playing strength doesn't inspire confidence in what he says. As for mirror go on an infinite board, Black can break it just the way it is broken on a 19x19 board. Other discussion of this topic has indicated that komi is essentially constant as board size approaches infinity, again contradicting the line of territory/line of influence idea.
Platinumdragon's definition doesn't apply well in practice (as far as playing on the "line of territory/influence" for actual territory/influence), but those lines are still significant in the evaluation of the first move advantage on such a board size. And yes, this DOES contradict that it approaches a constant, I am objecting to the idea that it does. Furthermore, mirror go cannot be broken on an infinite board (no center point, ladders go on forever, etc). ~srn347