February 2008 statistics from GoBase for results of games played with a certain komi.
Table of contents |
Black wins | White wins -------+--------+--------+-------- B+R | 557 | W+R | 557 B+T | 2 | W+T | 2 -------+--------+--------+-------- B+0.5 | 70 | W+0.5 | 70 B+1.5 | 68 | W+1.5 | 63 B+2.5 | 65 | W+2.5 | 43 B+3.5 | 47 | W+3.5 | 58 B+4.5 | 37 | W+4.5 | 41 B+5.5 | 29 | W+5.5 | 26 B+6.5 | 21 | W+6.5 | 25 B+7.5 | 18 | W+7.5 | 19 B+8.5 | 21 | W+8.5 | 14 B+9.5 | 14 | W+9.5 | 8 B+10.5 | 5 | W+10.5 | 3 B+11.5 | 4 | W+11.5 | 5 | | W+12.5 | 1 B+13.5 | 2 | W+13.5 | 2 B+14.5 | 2 | W+14.5 | 2 B+15.5 | 1 | | B+16.5 | 1 | W+16.5 | 3 | | | | | W+17.5 | 2 | | W+19.5 | 1 B+20.5 | 1 | | B+24.5 | 1 | | B+29.5 | 1 | | -------+--------+--------+-------- Total | 967 | | 945 | 50.58% | | 49.42%
Margin of error is 2.3%
Black wins | White wins -------+--------+--------+-------- B+R | 124 | W+R | 140 B+T | 1 | W+T | 2 -------+--------+--------+-------- B+0.5 | 1 | W+0.5 | 13 B+1.0 | 13 | W+1.0 | 2 B+1.5 | 16 | W+1.5 | 2 B+2.5 | 1 | W+2.5 | 10 B+3.0 | 11 | W+3.0 | 9 B+3.5 | 6 | W+3.5 | 4 B+4.5 | 1 | W+4.5 | 4 B+5.0 | 6 | W+5.0 | 6 B+5.5 | 4 | W+6.0 | 1 | | W+6.5 | 1 B+7.0 | 6 | W+7.0 | 4 B+7.5 | 4 | | | | W+8.0 | 1 B+8.5 | 1 | W+8.5 | 1 B+9.0 | 3 | W+9.0 | 4 B+9.5 | 2 | W+9.5 | 2 | | W+10.5 | 1 B+11.5 | 1 | | B+15.5 | 2 | | -------+--------+--------+-------- Total | 203 | | 207 | 49.51% | | 50.49%
Margin of error is 4.9 %
Note that under area scoring, the net score before komi is almost always odd. An even net score only happens when certain seki positions are on the board that result in an odd number of neutral points. With komi 7.5, this meant that scores of the form B+X.5, where X is even (0.5, 2.5, 4.5, 6.5, etc) are very rare. Similarly, scores of the form W+X.5 are rare when X is odd (1.5, 3.5, 5.5, 7.5, etc).
Ing rules specify komi as 8, with black winning jigo, which makes it effectively 7.5. Again, given that the net score under area scoring is generally odd, this means that with Ing rules, wins by an even number of points are rare.
Andy: Combining the results of komi 6.5 and 7.5 given above gives black a winning percentage of 50.4% with a margin of error of 2.0%, suggesting that both values of komi may be equivalently correct.
Herman: Both values are incorrect by definition, because they include the .5 points. As the main page explains, the correct komi is necessarily a whole number. What these statistics do show is that both the values 6.5 and 7.5 are probably quite close to the correct komi.
Combining them is not particularly meaningful, especially since those games were mostly played under different scoring rules. The 6.5 is usual in territory scoring, the 7.5 in area scoring. Since area scoring counts dame points, the correct komi may not be the same under both rulesets (Although usually it gives either the same result, or area scoring is 1 point better for black. So the correct komi for both is probably either the same or one point higher under area scoring)
Bill: I also made the point that the apparently fair komi could be different under different conditions, when I acted as a sort of referee for an article in the American Go Journal in the 1970s. However, I got my hands on the raw data for the article, and observed that a komi of 7 points would have given the most equal division of results to Black and White than any other whole number komi, for Japanese pro games with either a 4.5 komi or a 5.5 komi. The fact that still seems to hold with different komi and different rules some 30 years later does suggest that 7 points is a fair komi under both area and territory scoring. Without a group tax, of course. ;)
Some computations made on DGS games can be found at http://www.altespace.org/go/no_handicap/
See also (dead link? archive seems to have been cut at 2010) http://computer-go.org/pipermail/computer-go/2006-August/006246.html
For the above dead link, I think I found a copy. Searching through the Internet Archive, I found this: https://web.archive.org/web/20080724184135/http://computer-go.org/pipermail/computer-go/2006-August/date.html#start
The thread for 006246 can be found through this, and is called "Odd experimental results" from Don Dailey. However, it seems to not have been archived there. Searching for this in Google, I found this: http://article.gmane.org/gmane.games.devel.go/6874/match=odd+experimental+results