Komi / Discussion

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Correct Komi

Josh?: Going out on a limb, I suggest that the idea of "perfect play" is a poor way to set komi. Defining perfect play, even a perfect move, is not an easy thing to do, even for a professional. Furthermore, what relevance does perfect play have to "actual play". Even professionals make mistakes. So how useful is this idea for the rest of us?!

I suggestion abandoning the impractical notion of perfect play when setting komi and replacing it with a komi that is determine by the play of two equal opponents. I anticipate at least two objections to this idea: (1) How can you get two perfectly equal players? doesn't this suffer the same problem as requiring perfect play? (2) The play of two equal players could be awful - would you want the komi to be established by awful play?

Firstly, go programs provide can be used to get two perfectly equal players, e.g. get GnuGo to play against GnuGo. Have the programs play one another a large number of times with a given komi and the calculate the ratio of white wins to black wins (I am adopting an idea that as proposed elsewhere on SL, to use the win/loss ratio as a measure of the effect of the komi rather than the actual score. This means that there is no problem with resignation.)

Secondly, when two players of equal rank play they use some value of the komi (depending on the rule set used), but this komi does not change if the players are 9 kyu or 9 dan. So if the komi is correct for both 9 kyu and 9 dan that suggests that the komi is appropriate for perfect play, awful play, and everything in between! If that is the case, why is it problematic to base the komi upon the awful play of two evenly match players -- we assume it anyway! This brings me to what I consider the big question mark in my proposal: That the komi is independent of the players rank, it is only the difference in the ranks that is important. Is this actually true? I don't know if it is but, again, I think that computer go programs can assist. There are several versions of computer programs that play go and they play at different strengths. Above I describe a procedure for estimating the komi using one go program. Find the "fair komi" for each program. Does the "fair komi" differ between programs? I expect that there will be differences but I am curious to see what the difference would be like. If the difference is small, then the case for having a "one-size-fits-all" komi seems good and therefore it also seems that using a go program, weak though it may be, could provide a better approach to determining the "fair komi".

I realize that I could be stirring up a hornets nest, but I am interest in what objections people have to this idea or what improvements they could foresee. Also, if anyone knows of any data relevant to this approach, that would be interesting to see here as well :-)


illich: I did a little research using gobase.org.
I selected games on 19x19 with 5.5 komi. The results are:

Total: 12607 decided games
Black wins: 6701 games (53.15%)
White wins: 5906 games (46.84%)

Black wins by 0.5: 369 games (2.92%)

So when you move games B+0.5 to W+0.5, it will be very close: 6332:6275. This means that komi of 6.5 is fair.

OneWeirdDude: It means no such thing! Strong players will ease back with they are winning, because it is better to guarantee a 5-point win than have a 20-point lead and risk losing it all (or keeping a 0.5-point lead versus risking a 1.5-point lead, for that matter); but they will stir up trouble if they are losing, because if their opponent, who is ahead, makes no mistakes, he wins, so the losing player will want to give his opponent more opportunities to make mistakes. Conclude, therefore, that the above method is not reliable for determining correct komi.

There is one brief analysis of komi and winning percentages at [ext] http://homepage.ntlworld.com/daniel.gilder/komistats.html and another at DougsGoBlog#toc2.

I have heard that more pro games are won by B in ING rules which use (effectively) 7.5 . This suggests the perfect komi in chinese scoring is at least 9. Since this is a scary amount of points to give W for the privilege of moving first, I would like to see much better statistics.

Searching GoBase at komi 8 gives 172 for B, 138 for W. Searching at komi 7.5 gives 483 for B, 566 for W. I did not filter for tournament games only, so this may include games where the stronger player is W.

togo: I have never seen any statistic using the point difference of matches. Of course that would be wrong, not only for komi estimation but for everything.

Roy: Keep in mind that a substantial fraction of these games -- maybe half, or even more -- are "walkovers": the stronger player was going to win, holding Black or White, at any contemplated komi. As sente is determined randomly, we can expect the stronger player to have sente half the time; so subtracting the walkovers makes the effective difference due to komi quite a bit larger. If about half the games are walkovers, that would subtract about 3152 games from both Black's and White's komi-relevant wins, leaving a ratio of 3549B/2754W, or 56.3% B and 43.7% W. I.e., more than a quarter of the time when komi is relevant, B is winning because it is too small! That is a very large advantage, and is unlikely to be fully neutralized by a 1-point change in komi. Given the history of komi having to be periodically increased as Black's winning percentage increased over time, and the recent results of 6.5 komi games still showing Black with a slight edge, I suspect that in 20 or 30 years' time komi will have to be increased yet again, to 7.5. That should be the end, though, as it agrees pretty well with the value of handicap stones measured in pro-pro handicap games.

Rising Komi Indicates Better Players

Peterius: Is it fair to assume that if komi has been increasing over the past 50 years, go players have gotten better overall and that their first move is worth more than it used to? Would this mean that the greatest player 100 years ago might be a 2 dan now?

  • DrStraw Hhm! Are you sure it is not an indication that players have got weaker because when playing as white they need more komi?
  • Roy? It just means they learned how to overcome the komi by a more aggressive fuseki for Black. I.e., Black just started playing more like White had to play in the days before komi, and vice versa. For example, Shusaku's kosumi is considered too slow now, but was a powerful weapon for Black in the absence of komi.
  • Jeff When teaching Go, I put pairs of beginners on 5x5 with zero komi for the first few games. This results in a 50/50 winning percentage. Perfect play at 5x5 yields 24 komi, but at their level 24 komi would result in 100% win rate for black. As they grow in skill, I adjust komi as needed, because their moves start to take on meaning (and thus have more value).

Relationship with value of the first move

Continuing the theory : I'm 6k, so I think the average value of my moves is about 1 point behind the professional's ones (15 stones is about 200 points, and a game is about 200 moves long). Well then I guess the komi that professionals set is half a point too much for me ! Well I don't know about you, but in that case, I prefer playing white, with a decisive advantage of half a point !

Velobici: IMHO its not that amateurs play moves that are 1 point (or N points) less efficient than professionals. Consequently, over 200 moves end up 200 points amateurs are 200 points behind. Rather, amateurs play some moves that are professional level and some that are just horrible. The just horrible moves (errors) are the ones that mark us as amateurs. By reducing the magnitude of our errors, we improve...still we make moves that are somewhat less horrible in the midst of moves that are professional level. Once we stop making horrible moves, all our moves are professional level and we play like Jie Li.

That is obviously correct as such, but you can still say that statistically 6k loses about 1 point per move, so the calculation above makes sense. Theoretically he may not lose any points for the first move (say, he plays 3-4), but we could think of the statistical one point loss coming from the fact that he doesn't know how to use the stone properly later in the game. Still continuing the thought you could say that if correct komi for 9d is 7, then for 30k it would be about 6. Which implies that in practise the same komi is actually good enough for players of all strengths. Of course, statistics from games would be a better way to prove this.

If someone thinks that fair komi is exactly the same for all players, then it may be interesting to note that, for nearly random players (who know only enough not to fill their own eyes), fair komi is actually very close to 0. This is easy enough to test with a computer program.

It is generally considered that 17 stones is a fair handicap between two equal players where black can kill all white stones. This indicates each stone is worth 361/17 or about 21 points so that komi would be 10.5. It is to be admitted that this is not proof for 1 stone, but it is indicative.

Anonymous: It takes me 35 stones to kill at white stones from Many Face of Go. Does that mean I'm 18 stones weaker than Many Face of Go?


  • In my opinion,
    • Komi = First Stone (miai value)
    • 2x Komi = First Stone (deiri value).
  • People seems to love using deiri value more because deiri value is directly related to the score.
    • First Stone Miai Value = 7 moku (- 1 territory).
    • First Stone Deiri = 14 moku (- 1 territory).
    • Komi = 7 (Area) = 6.5 (Territory).
  • The 6.5 is the value for jigo under territory scoring, but is that possible?
  • According to Mathematics
    • Passing first move = 2x Komi + 1
    • 2x First move = 2x Komi + 1, unless white does not get first move after black pass first move.
      • Therefore, First Move = Komi + 0.5.
      • This is the reason why Komi keeps on increasing.
  • According to the Rules
    • White wins jigo so:
      • Komi = First Move + 0.5
  • Combine the two elements of mathematics and rules:.
    • Komi = Komi + 1.
      • The results show that black wins jigo until komi is correct.
      • The correct way to say is that Roundup(Komi) = Rounddown(Komi+1).
      • It's a play on half integer versus integer.
  • Statistics shows black win jigo (0)
  • Rules say white win jigo (1)
    • Both Statement does not contradict, so in is hypothetically said that 0 = 1, but it is only a play on numbers.
    • Another way to interpret is 0 = 1 until komi = true komi.
      • 0 = 1 is a metaphor that komi is too small.
      • 0 = -1 is a metaphor that komi is too large.
  • Comments End.

anonymous: You're trying to prove 0 equals 1 (Komi = Komi + 1) ?

  • Passing first move = 2x Komi + 1
    • Passing first move means Black passes his first move.
  • 2x First move = 2x Komi + 1
    • 2x First move means Black gets two plays, White passes her first move.

So probably 0 doesn't equal 1 after all.


kokiri: I know it's only 6 1/2 points or so, but somehow, when I'm white and receiving komi, it seems as though I can play 3/4 of the game badly, be losing by 10 points on the board, then wake up, play a decent yose, and win by a couple.

Take the following game below, through 40 moves, I've generated 2 weak groups, given up about 30 points of territory and don't seem to have any great prospects of my own.

Fast forward to the end of the game - I've been plastered around the board by black, have failed to do anything much apart from hang onto one corner and taken about a grand total of 6 points outside the fourth line, yet with the magic 6.5 points I win by a 2.5points.

I also think that, as a low kyu player, using komi is a bit of a waste of time because I don't feel good enough to take any real advantage of the first move.

Anonymous: I agree that lower level players do not need komi because I usually get a score differences in the twenties to thirties when playing other beginners.

Alex Weldon: (In reply to kokiri) Uh. I disagree with this. I'm a little stronger than you, 1 dan at the Toronto Go Club, 3 kyu on KGS, but not much stronger. I find that 6.5 komi is not enough to compensate for Black's first move advantage, at my level and with my fleet-footed style of play. For instance, there's a guy at the Toronto Go Club named Harry, same rank as me, similar style. We've played a total of 10 games and EVERY time, whoever had Black won by at least 10 points on the board. 10 games is too much for that just to be fluke. So, if you think 6.5 komi is too much, you should just start playing more aggressively and play to get/keep sente.

kokiri fair enough, I feel that my go (and those I play with) isn't really consistent enough for komi to really be relevant; maybe it's good practice for sometime in the future, though.

Moves 1 to 10  

W8 is, I feel a mistake, if black plays the joseki from a to build thickness to the left it looks good, but fortunately black plays at B9.

AndyPierce: For what it's worth, I think W8 is fine and W10 is the mistake. W8 works well with white's two hoshi stones at the top of the board but 10 seems to be in the wrong direction to maximize this potential. Since black seems determined to only play on one side of the board, why not help him make his mistake by pressing him down with moves at b and c? The splitting move at W10 seems rather to encourage black to develop up the right side, hurting W4's potential, and to give black a nice moyo on the lower side as well.

Moves 11 to 20  

B1 - Black seems to be trying to build on both sides which feels a bit greedy - however I let him get away with it through to W10

Moves 21 to 30  

I was a bit surprised by B3 in reply to W2 but it seems to devalue my prospective moyo, and build black's bottom left.

W4 seems a good enough way to enter the bottom.

Moves 31 to 40  

Giving up the 2 stones in the corner gives some good aji for yose, and W10 is a decent attack on blacks group, but on the whole I seem to have handled black's area with a heavy hand, and I've not invested any effort around my own hoshi stones.

End position - White wins by 2.5  

The end: in addition to the two bottom corners, black's managed to create a decent profit on the top, and I have only one corner (albeit big) in exchange.

I win by 2.5 points, but my overall feeling was that I was being pushed around a lot for most of the game, and got the 'W' as a result of a few lucky yose.

I'm not saying this always happens - clearly I often play badly for the first 1/2 game and then lose by 40, but in cases like this one it just seems that the wrong player won.

IlyaM: Hmm, not sure why it makes komi bad. Playing good end game is an important skill too. If your opponent got too relaxed to play end game carefully because he leads in the middle game you should rightly punish him ;) I myself played a similar game just yesterday - my opponent was leading a lot thanks for me helping him to build huge moyo and thanks for me failing to reduce him properly. But I played a slightly better end game and managed to win by 2.5 points. My opponent said after game he thought he was leading ;). BTW we played without komi because of rating difference. Probably if there was no komi in your game you'd try to play even better end game to catch up :)

geno: I think this is a definitional issue. 'komi' isn't 6.5 points, it's whatever compensates for black getting the first move, whatever makes the game even. It's usually points, but in theory it could be dancing hotties, Heian-era go master spirits, whatever. :-) If you're not getting an even game, change the komi.

kokiri if I get a couple of dancing girls as komi, you can take black every time ;)

Alex Weldon: I think you mean that you'll want to take Black. The dancing girls are there to distract Black. :-)

geno: Unless they perform the rare and exotic dance move known as the 'reverse komi', but the dancers have to be very flexible. 8-)

Nacho: What if black is a girl?

Seriously, though, I think that if komi is irrelevant (as kokiri said somewhere), then why should you care? And if it isn't, then you have to agree that having the first move seems (statistically at least) to give an advantage to black. Maybe you could argue that komi is too low; or too high, but that's a different discussion.
And about that "lucky yose" thing, IMHO there is no luck in go, only mistakes by one or the other player. If you make a mistake, and it goes unpunished because your opponent didn't see it, it isn't luck, is a mistake. And also, yose is all about calculations; how can you have luck? That probably means you are better at yose than your opponent. Someone (I don't remember who, anybody?) said something like "I'm a great believer in luck, and I've found that the harder I work, the more I have"

DougRidgway A true fair komi will depend on the strengths and styles of the players. Some suggest using auction komi to adjust appropriately.

Neil: Why should players with different styles get compensated for weaknesses?

geno: Well, they shouldn't necessarily. If your goal is to make an even game -- and at this point we have to start talking about what we mean by an even game -- then obviously we've defined the problem so as to require some sort of compensation (except in the presumably rare circumstance where the two players are exactly equal, and I'd be inclined to generalize that circumstance by calling it 'zero compensation' rather than 'no compensation').

So what is an 'even game'? Do we mean even statistically? (Over what population? Over what period in history? Et cetera.) Do we mean even between two players in some particular match? The statistical or general or black-first concept leads us to talk about komi, and the particular or specific or player-strength concept leads us to talk about handicap.

The problem is that handicap is more than an order of magnitude less fine than komi, so I think people naturally want to use komi for handicapping different players if the skills are really close. "Hikaru is not a full stone less strong than Akira, just a few moku." And since the komi is defined as half of the statistical moku difference between black and white over some population (Komi Go / Discussion), it feels like it's okay to talk about one moku as some (fluctuating?) fraction of a stone.

It might be useful to think of 'statistical-komi' and 'skill-komi' if you wanted to get really theoretical. Or we could say 'no komi is ever handicap; komi is always statistical' and just start talking about 13ths of a stone. Which would be cool: it would be jargony, like jewelers talking about their kind of stones in troy ounces or carats or something. :-)

Changed 'handicap-komi' to 'statistical-komi'. My apologies; I'm one of those people who has trouble proofing his own writing. -- geno / 2004-01-30

Neil: I thought we were talking about the compensation for going second, not handicaps to aid weaker players. Taking the skills of the players into account makes sense if you're trying to handicap a game. Helping out one player against the other does not make sense in a test of skill, though.

Alex Weldon: I think you're misunderstanding what Doug suggested. He doesn't mean that one player should get greater or lesser compensation depending on his style of play... the idea behind auction komi is that some pairings (like me vs. Harry at the Toronto Go Club as I mentioned higher up on this page) tend to increase/decrease the value of going first. So, for a game between Harry and me, proper komi would be over 10 points, since out of the 10 games we've played, Black always wins (regardless of who is which colour), and Black's smallest win was around 11 points (on the board). Meanwhile, other players might favour complicated fighting, which reduces the value of going first. Therefore, in a pairing between two fighting-oriented players, maybe komi should be lower. Auction komi handles this in a very natural way, by letting players pick what they think komi should be, and giving Black to the player who values it more.

Neil: Everyone plays the same game. The value of going first doesn't change. I think it's an abuse of the auction idea for a player to change his bid from game to game. The only reason to have an auction, by my understanding, was to accommodate different people's opinions of the one true value of the first play.

Bill: I used to think that, Neil, but I was wrong. The variability of play typically affects both the variability of the results and the median result (komi). Unless you are positing perfect play, both style and strength affect the komi.

Neil: So let's stop calling it a compensation and start calling it a handicap.

Bill: It's not a handicap when it is used between (roughly) equal opponents. (OC, komi can be used as a handicap or as part of one.)

PS to Arno: I think there's some bug somewhere. I posted the four paragraphs above with the summary "why, the 'even game', and some epistemology", noticed the extra lines in the diff, posted a minor edit with the summary "fixing more of those mysterious extra lines? a bug?", and the primary edit vanished from Recent Changes. I had a similar problem that Hu noticed a couple of weeks ago.

aLegendWai: Hi. I have some other feelings about komi (= receive extra points at start in order to compensate the advantage of being Black).

First I think komi is important because black is really in an advantage of getting/keeping sente. It is obvious in the early game because black can try its black to keep sente and occupy big points. It is the advantage of black. This advantage will undermine as the game goes on.

In ancient games which komi system didn't occur, if you are weaker than the player, one kind of handicap game is to be black. It is worth noticing that black wins more than white in even game in the past. So the advantage of being black is obvious.

I admit there is a difficulty to assess how manys points komi should be. But we do need to assign some extra points to white in order to offset the advantage from getting/keeping sente. If you wish to play a 'real' even game, a komi system is appropriate.

Second, however, I don't like the 0.5 komi system (Japanese rules). The dot(.) and the five (.5) look ugly in my view :P. In a 19*19 board game, you get 1-point from one territory. You can get 1-point from one prisoner. But you have no way to get 0.5 point.

0.5 point is to avoid a draw game. But why do we need to avoid a draw game? Assuming the whole number of komi (eg 6) can accurately offset the advantage of sente. So if it is a draw game, it implies both players are equally strong. But under 0.5 komi system, it is never possible. Equally strong players will not deserve a draw. One player must lose/win.

In ancient games, draw is perfectly acceptable.

On the other hand, let's talk about why 0.5 komi system is needed. The most important thing is it must be able to distinguish between the winner and the loser. If a draw game occurs and it is in a competition, a rematch is needed. Although a forceful win/loss is very unfair to equally strong players, "a waste of time and money to the hosts" has to be counted.

So no 0.5 komi system should be advocated at least in a friendly match.

Every time I win a game by 0.5 point, I don't feel the winning is honourable. It is a draw indeed. I haven't defeated the opponent in the game. (PS: A joke: someone once asked me why you don't set the komi as a whole number. You are just looking for trouble. Yes right, but unless I am the host :)

My ideas anyway. You may agree or disagree. :P

willemien I made a separate page for the discussion of the relationship between komi and the value of the first move at komi/value of first move i will copy this discussion to there after reorganising, please post newer comments on that page and not on this page.

Value of komi equals value of first move?

On the other hand there are theories which claim that the value of the first move is only the value of komi. This idea is based on the fact that if you play a game where everything is played out and there is only one position left with reverse sente, you count the territory in that area as if no player played there yet. And if one of the players played there, you count it just like the change of the points - the value is not doubled because the value of sente is zero points in that moment (we have assumed that everything else was played out!).

When playing the first move the position is similar: The first move is a sente move, which gives you six points after all. Everything else is played out (you can play only this sente move and nothing else). The score in the beginning is 0:0 as both players have no territory. And with the first move the score changes to 6,5:0 (considering *standard* komi). So we can count the difference as 6,5-0=6,5 points. If you consider the value of the first move as 13pts, you would get 13-0=13, which is not true, because black will theoretically win by 6,5, not 13 points! The fact that black can pass and white takes the advantage just means that passing is worth minus komi points. It is just like if your opponent threatens to cut off your ten stone group connected with bamboo joint and you defend. Will you get twenty points in that situation? No. Only not playing there is worth minus twenty points. (Value Theory by FieldMouse?)

Dieter: I've read the above twice and I cannot understand it. Can your rephrase?

xela: It looks to me like a misapplication of endgame theory ("gote plays are worth half of sente"). It's not clear, but I don't think I agree with it.

Anonymous: Somebody deleted someone else's post.

Anonymous: Well, it seems to make sense by miai counting that komi should equal the value of the first move. If there is no komi, black wins by (say) 7 points if he moves first, and if white moves first he wins by 7 points. So the game is a switch, {7 | -7}, with position value 0 and move value 7. If you then add in the komi of 7, the result is a {0 | -14} game, i.e. if black plays first it's a jigo, and if white plays first he wins by 14 points. The value of the game is then -7 and the move value is still 7 (komi does not change the value of the move). By deiri counting, you get the move value of 14, as expected. I think this is just another manifestation of the difference between miai counting and deiri counting.

Komi / Discussion last edited by PJTraill on May 3, 2019 - 01:50
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