Komi

    Keywords: Rules, Go term

Chinese: 贴目 (tiē mù)
Japanese: コミ , 込み (komi)
Korean: 덤 (dum)

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.

A scene from Hikaru no Go
Fujiwara no Sai hears about komi for the first time in Hikaru no Go
(Image by Takeshi Obata, slightly altered by Herman Hiddema)

Table of contents


Linguistics

In Japanese, komi basically means 'included', as in zei-komi (Tax included). In Go, komi means the number is included in the final calculation of points. Giving komi is komi-dashi and receiving it is komi-morai. The English term "compensation points" or simply "compensation" is often used as a translation for komi.

If you use kanji, 込み出し is correct. To give komi is 込みを出す。

Typical values for komi

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. [6]

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.

Territory scoring

Today the standard komi in Japan, where territory scoring is used, is 6.5 points, introduced September 2002.[1] The Honinbo tournament used a komi of 4.5 points in 1939, changing to 5.5 komi in 1973. The Meijin tournament used a komi of effectively 5.5 (5 points with White winning jigo). Korea also switched from 5.5 to 6.5,[2] as have most western countries that use territory scoring.

Area scoring

The usual komi in China, where area scoring is used, 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.[3] 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.

History of Komi

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.

The Correct 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). Note that, with integer komi, ties could still be broken by using the button, which awards wins evenly to Black and White in the event of a tied score.

Statistical Komi Analysis

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%)

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 gains or loses 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

What have we learned from AI

Since the advent of AlphaGo and other AI bots, we have explicit probabilistic evaluations. With standard komi of 7,5 the bots think White is ahead by 55%-45%. KataGo expresses the advantage in points too and scores White up by half a point. This seems to indicate that fair komi is 7 points. More experiments are needed though before making firm conclusions.

For territory scoring, the perfect komi is likely to be 6 points based on the following data:

KataGo 1.15.3 with NN [ext] kata1-b28c512nbt-s7709128960-d4462231357 (2024-10-12) gives the following black winrates for the empty board under Japanese rules and 1 million visits:

  • komi=5: 62.5% (distance from 50%: 12.5 pp)
  • komi=6: 52.8% (distance from 50%: 2.8 pp)
  • komi=7: 42.4% (distance from 50%: 7.6 pp)

Of these, komi=6 is the closest to 50% winrate, which is the theoretically correct winrate for perfect komi, and thus komi=6 is the current best estimate with the given KataGo/NN versions and settings.

The imperfect komis' distances from 50% are roughly 10 percentage points, which is quite large. As bot strength increases, the distance should grow, as bots get closer to claiming "I have never lost while playing with 1 point advantage!🔥"

Interestingly enough, KataGo still seems to find it difficult to utilize komi to its fullest: Black winrate is 2.8 pp higher than 50% at perfect komi. Furthermore, if you give white one point extra advantage (komi=7), the distance from 50% only grows to 7.6 pp, whereas if you give black the one point extra advantage (komi=5), the distance from 50% grows to the considerably larger 12.5 pp. All of these discrepancies disappear if you subtract about 2.5 pp from all three winrates, i.e. if KataGo just played 2.5pp better with white.

For comparisons with pro game statistics quoted on SL, it is useful to evaluate the same with the extra 0.5 points (again 1M evals with same KataGo):

  • komi=5.5: 57.9% (distance from 50%: 7.9 pp)
  • komi=6.5: 47.5% (distance from 50%: 2.5 pp)
  • komi=7.5: 37.7% (distance from 50%: 12.3 pp)

For comparison, here are collected pro statistics from SL:

  • komi=5.5: 53.15% (distance from 50%: 3.15 pp)
  • komi=6.5: 50.58% (distance from 50%: 0.58 pp)

There is also a value for komi=7.5, but since it is based on games played under area scoring, it cannot be used to determine perfect komi under territory scoring. As such, it was omitted from the above list.

To estimate correct komi from game statistics, ideally one would have two values, komi=n with black winrate over 50% and komi=n+1 with black winrate under 50%, and then pick the komi corresponding to the winrate closer to 50% as the best guess of perfect komi. Unfortunately, pros these days do not play games with even komi, or with larger than 6.5 komi under territory scoring, so there is no data for komi=6 or komi=7.

The statistics the komi=6.5 winrate was based on say that the final score was >-0.5 in 967 games, =-0.5 in 70 games, and <-0.5 in 945-70 = 875 games. If we assume that using komi=6 instead of komi=6.5 would not have substantially changed play (this assumption is as reasonable as it ever gets since we're only off by 0.5 points), then changing the 70 games where the score was -0.5 to draws gets us a sample for komi=6. This fictitious sample has 967 black wins, 70 draws, and 875 white wins. Counting half of the draws as black wins and half as white wins, we get black winrate of (967+70/2)/(967+70+875) = 52.41%. Incidentally, KataGo also counts draws as half-wins for both (see parameter drawEquivalentWinsForWhite which is 0.5 by default), so for comparability we should do this (instead of e.g. not counting draws at all, not that it makes much of a difference here).

Similarly, the score was >0.5 in 967-70 = 897 games, =0.5 in 70 games (sic), and <0.5 in 945 games. Again assuming that using komi=7 instead would not have changed play, we construct a fictitious sample for komi=7. We get 897 black wins, 70 draws, and 945 white wins. Counting half of the draws as black wins again, we get black winrate of (897+70/2)/(897+70+945) = 48.74%.

Collecting the results, we have the estimated pro black winrates:

  • komi=6: 52.41% (distance from 50%: 2.41 pp)
  • komi=7: 48.74% (distance from 50%: 1.26 pp)

Based on this, one would conclude that the best estimate for perfect komi based solely on this pro game data is komi=7. However, the distances from 50% are quite similar, so this isn't very conclusive. Crudely estimating the uncertainty in these percentage estimates, a 95% symmetric CI around the median for a Beta(1002, 910) distribution is [50.17%, 54.64%], and for Beta(932, 980) it is [46.51%, 50.99%]. The beta parameters were derived as Beta(k, n-k) where e.g. k = 967+70/2 and n = 967+70+875 in the komi=6 case. These CIs overlap, which suggests that the evidence from pro game data is inconclusive. So both komi=6 and komi=7 are consistent with the data. While this is closer to a back-of-the-envelope calculation than a serious analysis, it should be good enough for this conclusion.

Interestingly, the same roughly 2.5 pp advantage to black is found in the komi=6 pro statistics as well as the KataGo winrates. For pros, letting white count all the draws as her wins compensates for this, resulting in nearly 50% winrate with komi=6.5, but not so with KataGo, to whom such a gift is too big. It seems that fully countering black's first move advantage is difficult for both top humans and AI, and the 0.5 addition in komi masks that fact.

In summary: AI says that perfect komi for territory scoring is 6, and pro game statistics do not contradict it. Neither does theory, which suggests that perfect komi for territory scoring should be either equal to perfect komi for area scoring, or one less (i.e. komi=6 or komi=7, assuming that the perfect komi for area scoring is 7). From this perspective, the Japanese traditional komis of 5.5 and 6.5 are both correct, doing their best to be perfect while avoiding ties.

Fair komi

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.

The Dragon Go Server offers a "proper handicap feature" with fine-tuned komi intervals (..., 1.5, 2.0, 2.5, ...) to balance even minor rating differences to a 50:50 chance for both players.

It is sometimes hypothesised``""^"¿where?"`` that the correct komi only depends on board size for 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 in Handicap Games

Komi is not normally used in handicap games. Komi can be used to compensate for differences in strength that exceed the traditional maximum handicap of 9 stones. Also, in some events, half a point of komi may be given to White to avoid a drawn game.

Komi can also be used to 'fine tune' a handicap, like Dragon Go Server does. In some cases, komi is given to Black rather than to White, and is called "reverse komi" (gyaku komi in Japanese). For practical examples, see Pro-am Honinbo Match and Points Rating System.

Fine-tuning 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.

Relation with the value of first move

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.[7] The exact value is not agreed upon, but e.g. in [ext] the world's first environmental Go game, where one could pass in exchange for more points (obtained from the bowl, not from the opponent's prisoner pile), there was one move after the reward for passing dropped from 14 points to 13.5 points, two moves after it dropped to 12.5 points, one move after it dropped to 12 points, and 12 moves after it dropped to 11 points. The (professional) players might have slightly disagreed on the precise value of the first move, but based on this, they seemed to have agreed that the early opening moves have values somewhere between 11 and 14 points. Halving that we get 5.5 to 7 points, which agrees with common values of komi. Note that the game was played in 1998, which was before the introduction of the 6.5 point komi in the 4th LG Cup (1999), and the 5.5 point komi was in common use at the time.

It is then normal that the value of komi be equal to half the value of a move in the opening.

See also: /Discussion#value1stMove

see also: /Value of first move

Komi setting by bidding

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."

Declared komi

Proposed by Denis Feldmann, tournament players register a komi. The komi of a game is then the mean value of both player's declared komi See also [ext] RGG

Komi in other games

Giving komi to avoid impasse isn’t exclusive to Go. In [ext] Janggi (Korean chess) tournaments which don't allow draws, the points given to the second player (‘han’) are called [ext] [komi]. Though generally not to avoid impasse, giving komi is also possible in many card games, not only because they use a turn order, but also in ones with a “contract” to compensate for the disadvantage of being on the side which has to play this “contract”. In trick-taking games, the most celebrated subgroup of these, the komi given to the younger hands or the taker of the (high) “contract” or by the opposite side should be no greater than value of one trick. In [ext] [Doppelkopf] the partnership with the queens of clubs may even receive this virtual trick to compensate for not being guaranteed to hold the highest trumps.

Notes

[1] 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.

[2] 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.

[3] 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.

[4] 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

[6] Some old tournaments (such as the 1961 Meijin, according to GoGoD) used "5 points komi, but white wins ties"--another way of describing what is effectively 5.5 points komi.

[7] 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.

See also


Komi last edited by 2001:14ba:48c9:d600 on November 24, 2024 - 04:23
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