Komi is a Japanese go term adopted into English. In a game of Go, Black has the advantage of first move. In order to compensate for this, White can be given an agreed, set number of points before starting the game. These points are called komi. The English term "compensation points" or simply "compensation" is often used as a translation for komi.
Fujiwara no Sai hears about komi for the first time in Hikaru no Go
(Image by Takeshi Obata, slightly altered by Herman Hiddema)
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A typical value for komi is in the region of 5-8 points, but numerous different values have been used in practice - see below for details. To prevent a drawn game in the case of jigo, the komi is commonly set to a fractional value such as 6.5. 
Almost all tournaments nowadays, both amateur and professional, use komi. This has not always been so, however. In fact, komi was rarely used in professional tournaments before 1937, and its gradual introduction into professional play was not without controversy.
Today the standard komi in Japan is 6.5 points, introduced September 2002. Before that, it was commonly 5.5. Korea also switched from 5.5 to 6.5, as have most western countries that use territory scoring.
The usual komi in China was formerly equal to the 5.5 used in Japan, but was changed to 7.5. The jump is two points, because under area scoring the score is almost always odd. The Ing rules also have a komi of 7.5, specified as 8 points with Black winning jigo. The American Go Association have also changed komi from 5.5 to 7.5 in August 2004, effective 2005. The New Zealand rules specify a komi of 7.
Although there were some games played with compensation in the 19th century, more substantial experiments came in the first half of the 20th century. Several values were experimented with, until a value of 4.5 became the standard from the 1940's onward. Game results from the next two decades showed that 4.5 komi still favored black, so a change was made to 5.5 komi, which was mostly used for the rest of the century in both Japan and China. At the start of the 21st century, the komi was increased yet again, to 6.5 in Korea and Japan and to 7.5 in China.
- See also: History of Komi.
In theory, the perfect komi for a given ruleset is a well-defined concept: it is the number of points by which Black would win given optimal play by both sides. Unless the ruleset allows fractional winning margins (which none of the common ones do), this is necessarily a whole number. Due to the absence of perfect players this number cannot be determined with certainty, but it is possible to make a reasonable guess at it, at least for some rulesets.
When area scoring is used (as in Chinese, Ing, AGA and New Zealand rules), the winning margin without komi is always odd, unless there are an odd number of points in seki. Since seki is fairly rare, and since a komi of 5.5 points has proven insufficient in professional play, and since a komi of 9 is generally considered far too much, it seems likely that the perfect komi is 7.
When territory scoring is used (as in Japanese and Korean rules), the score is usually either the same as with area scoring, or one point better for White. This suggests that the perfect komi under territory scoring rules is either 6 or 7. Statistical evidence from professional games suggests 7 (see below).
Because it is as yet impossible to determine perfect play, statistical analysis has been used to judge whether a given value of komi is fair or not. For example, the following are statistics for professional games played on 19x19 with a komi of 5.5
- Total: 12607 decided games
- Black wins: 6701 games (53.15%)
- White wins: 5906 games (46.84%)
- Black wins: 6701 games (53.15%)
This shows that a komi of 5.5 slightly favors Black, and is therefore apparently not enough compensation for White to overcome the first move advantage of Black.
Looking at the data further, we can also take into account the margin of victory. Of the set above, this is:
- Black wins by 0.5: 369 games (2.92%)
Although it is tempting to use this as evidence that if komi were 1 point higher, these games would have been won by White, this is not completely fair. The problem is that pros play to win only, because winning by a little or winning by a lot is still winning - the same goes with losing. Thus, strategies change when a player loses or gains the advantage: the player who is behind will try to introduce complexities, perhaps losing points in the process - anything to pull ahead. The player who is ahead, on the other hand, may be willing to play sub-optimally in order to reduce complexities, so long as he gives up fewer points than his lead. See A Rich Man Should Not Pick Quarrels.
For this reason, the only reliable statistic is whether more games are won by W (or B) for a given komi. To get solid evidence of the perfect komi, good statistics for an upper bound are needed.
- See also: Komi Statistics
Of course there needs to be made a distinction between perfect komi as defined above and fair komi, which can be defined as that komi that gives a person against an evenly matched opponent a winning percentage that is as close to 50 percent as possible (treating a draw as half a win and half a loss). Perfect komi stays constant, but as insights change over time, fair komi can change with them, possibly even becoming fractional despite the used ruleset if the statistics can justify it. It is likely, though, that the historical 5.5 komi is an artifact of tradition and imperfect knowledge (and a desire to avoid jigo) rather than an insight different from today.
It is sometimes postulated that the correct komi is independent of board size for all but the smallest boards. For area scoring, this would give 9 for 7x7, 4 for 6x6, 25 for 5x5 (w cannot live), 2 for 4x4, 9 for 3x3, 0 for 2x2 (1 with a superko rule), and 0 for 1x1. (All of these are area scoring, territory scoring komi may be one point lower.)
See also Handicap for smaller board sizes.
Komi is not normally used in handicap games, except perhaps a komi of half a point given to White in order to avoid a drawn game.
Komi can also be used in handicap games to compensate for differences in strength that exceed the traditional maximum handicap of 9 stones. Such a komi, given to Black rather than to White, is called "reverse komi" (gyaku komi in Japanese).
Komi can also be used to 'fine tune' a handicap, like Dragon does. This is especially useful on small board Go, such as on a 9x9 board, where a single handicap stone compensates for a much greater difference in strength than it is the case on a 19x19 board.
Consider a game where black passes as first move. So white plays first move, and the game starts just as if white were black, with the difference that white still has the komi advantage. This can be interpreted as if white played a game with reversed komi; the advantage he has is 2*komi (the komi he has + the komi that black does not have)
We can assume that by passing, black lost an amount of points equal to the value of the first move, which is about 14 points according to professionals.
It is then normal that the value of komi be equal to half the value of a move in the opening.
See also: /discussion#toc4
see also: /value of first move
Because of the difficulty of determining a fair komi, a few amateur tournaments have adopted a system whereby players arrive at the komi through some form of bidding (Auction Komi).
This idea removes disputes over the value, by bidding for who is prepared to give the most points for being allowed to be black. If both agree on the same value then nigiri (or some other form of lottery) would be used otherwise the person offering the most gets black.
As an alternative, the rule "One player chooses the komi for white, the other one chooses what color to play." (Fair Komi) guarantees jigo for perfect play and provides fair komi for imperfect play.
Anonymous: It should be noted I think that for perfect play is a big qualifier here.
 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.
 The first significant professional tournament to adopt 6.5 komi seems to have been the 3rd LG Cup in 1998. This was an international tournament, but Korean-sponsored. Some Korean tournaments are still using 5.5 komi in 2002.
 Under Chinese rules there is very little practical difference between 5.5 and 6.5 komi, hence the jump directly to 7.5. Note also that in China it's usual to talk of 2.75 or 3.75 zi (子, meaning stone), rather than 5.5 or 7.5 komi.
 I was in Japan during the transition to 5.5 point komi. Then most pro games used a 4.5 point komi, but some used a 5 point komi with White winning jigo. I am unaware of any Japanese pro games with a 4 point komi with White winning jigo. -- Bill
 Bill: Which pros? The traditional value is 10 pts., and the first Environmental go game? revealed that Jiang Jujo and Rui Naiwei did not agree on the value of the first move. Rather, it seems that the value of the play is inferred by mathematically inclined amateurs to be two times komi.
- Komi Go
- Mathematical Bounds of Komi
- Why Chinese Komi should increase by 2 point steps (or another explanation on Chinese komi)
- Pie Rule
- Reverse komi
- About The Value of the First Move