7

"komi" represents a number of points added to White's score at the end of a game of Go to compensate White for the fact that Black moves first. It is usually X.5 points (e.g. 7.5) to prevent a tie (points on the board are always integer values).

When i started learning the game forty years ago, komi had been "recently" raised from 4.5 to 5.5 points. The latter was probably too little, based on the fact that White won less than 50% of the games, and 4.5 was clearly too few.

Today, komi is set at 7.5 points, at least in games monitored by artificial intelligence, and all the computers reckon Black's chances at about 43%, at the start of the game, given an adjustment of that size.

The intermediate number which probably gives the most balanced game, appears to be 6.5, but that is a number that hasn't seen much use. Why is that, and how does the governing body (e.g. in Japan) set komi?

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    Have you read the article (senseis.xmp.net/?Komi) in Sensei’s Library? It gives quite a lot of information, but includes the statement “Today the standard komi in Japan is 6.5 points, introduced September 2002” (with a footnote “The Nihon Ki-in looked at about 15,000 tournament games from 1996 to 2001 and found that Black won 51.86 % of all games, a margin of nearly 4 percent over White. The directors voted to change to 6.5 komi and negotiate with the Kansai Ki-in and tournament sponsors”), which seems to disagree with your post. – PJTraill Jun 9 at 17:05
  • @PJTraill: Years ago, I did a (curve-fitting) model that suggested that the value of each handicap stone, x, was (2/3)x**2+12x-6. That suggests that komi should be 6 2/3. that is, (2/3)+12-6., It's closer to 7 than 6, but closer to 6.5 than 7.5. I think part of the confusion arises from the fact that we first identify the integer number, 7, then decide which way to go on the "halves," rather estimating x.5 directly. – Tom Au Jun 9 at 17:21
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    Interesting. At first sight there is no difference between 6⅔ and 6½, but one could use a random event to give White either 6 or 7, though that makes jigo possible again, which some may not like. There is also the question whether fair jigo depends on the level of the players. – PJTraill Jun 10 at 12:05
  • Afaik 7.5 is used for Chinese-style rules only. Japanese rules use 6.5. Area vs stone counting means that these two numbers are more similar than they seem. – mafu Jun 10 at 12:26
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Achieving the statistically perfect komi is interesting, but generally the difference between winning by 1/2 a point or winning by 1/3 a point does not change a game result. We play in units of one stone (i.e., one point in area scoring), not 1/3 stone.

I don't have my copy of Go Players Almanac so I can't readily check dates -- I'll try to update later -- but my memory is that before komi was introduced, jigo (a draw) was possible; but in the Japanese pro tournaments at least, a jigo counted in White's favor (though not as strongly as a win), since it was known that Black had a significant advantage.

The Japanese introduced komi in the early 1900s, at a value of 2. (Komi wasn't standardized for a time, so there are arguments for "introduced" at earlier dates -- see John Fairbairn's discussion at https://senseis.xmp.net/?HistoryOfKomi for examples -- but I think "early 1900s" is good enough for our purpose here.) 2 was pretty quickly seen as insufficient, and by 1934, komi had been raised to 4.5, where it stayed until the late 1950s / mid 1960s, when it was raised to 5.5.

When I began playing in the late 1980s, players indeed talked about how komi had "recently" been increased to 5.5. (Well, when the game is 2000 years old, I guess 20 or 25 years seems "recent".) When I began playing in amateur tournaments in the late 1990s, the komi could vary, depending on the rules in use. AGA tournaments tended to follow the lead of the Nihon Ki-in, and used komi of 5.5; but there was strong material support from the Ing Foundation for tournaments, with the caveat that the tournament had to be played using Ing's idiosyncratic rules (intended to make the game more accessible to children and beginners) -- one of which was komi set at effectively 7.5.

Sometime in the early 2000s, Chinese rules switched komi from 5.5 to 7.5. About the same time, the Nihon Ki-in switched from 5.5 to 6.5. The AGA switched from 5.5 to 7.5 effective 2005.

There was discussion about whether the AGA should make it 6.5 instead, but changing from 5.5 to 6.5 would affect only the margin of victory in the vast majority of AGA games, not the game result. (It's theoretically possible to have a game with weird seki formations where that may not be true, but it's very rare in actual play.) So for example, if Black with 5.5 komi wins by 1.5 points, then with 6.5 komi Black still wins, but by 0.5 points. If the reason for komi is to give both players an even chance, and 5.5 isn't enough, then 6.5 also isn't enough. So the AGA changed to 7.5 not 6.5.

You may be thinking, "what about the games that Black with 5.5 komi would win by 0.5 points? Doesn't shifting to 6.5 komi mean that instead White would win by 0.5?" The answer is that, with 5.5 komi, Black would not win by 0.5 (except in the unusual seki situations that rarely happen). This AGA article describes why: https://www.usgo.org/news/2013/09/only-a-passing-matter/ (I read a better explanation, but I'm not finding it now. Will update if I find it.)

A reasonable question is, why did the Japanese go with 6.5? I don't have a definite answer, but I believe it's mostly because they have a slightly different ruleset. In AGA rules, White must play last, which would penalize White under the Japanese rules. In Chinese rules, you get a point for each intersection you surround, and you get a point for each stone you have alive at the end of the game -- there is no penalty for filling in a point of your own territory, as there is with Japanese "territory" scoring. (There are also differences in how prisoners are handled -- they matter in Japanese "territory" scoring, but not so much in Chinese "area" scoring.)

The mathematician Elwyn Berlekamp proposed a system of bidding for komi. For example, on the first move, Black could play and pay 20 points komi, or pass. Next, White could play and pay 19 points, or pass. Eventually, one of the players moves, and pays the komi to the other player. Berlekamp arranged a short series of games between two pros living in America. IIRC, the komi paid tended be surprisingly high -- 9 or 10 points. (Thanks for reminding me of this -- I'll have to dig up the details.)

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  • In Chinese rules (thus also AGA rules), every intersection is either a point for Black or a point for White, unless there remain unfilled dame. Thus the difference in score between two games without unfilled dame must be even. The only situation where Black can win by 0.5 if if there is an odd number of unfilled dame; either a dame was forgotten by both players, or there is a seki where each player has an eye and there is exactly one common liberty. In Japanese rules it is false that "every intersection is worth a point to White or Black"; dame are not played out; every score is possible. – Stef Sep 4 at 10:57

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