Life In 19x19

Kirby wrote:What was the proof that the correct value of komi is not smaller than zero?

Wouldn't it just be that, if there is any advantage to playing second, Black's first move could be "Pass," and he could recapture that advantage? (Or both players' optimal play is "Pass" and komi really is 0.)

Kirby wrote:

HermanHiddema wrote:Although there is no proof for the correct value of komi, there is proof that it exists and that it is not smaller than 0. The correct komi is well-defined, it is the amount of points by which black wins if both players play perfectly (which may be 0). Given that the definition of correct komi is basically "the amount of compensation white needs to get a draw if both players play perfectly", then obviously, by circular reasoning, with the correct komi perfect play leads to a draw.

What was the proof that the correct value of komi is not smaller than zero?

If putting a stone on the board would cause black to lose by 1 or more points, he would pass instead, and could then by symmetry achieve the same score against any first move by white. White would therefore also pass, and the score difference would be 0.

amatterof wrote:

Kirby wrote:What was the proof that the correct value of komi is not smaller than zero?

Wouldn't it just be that, if there is any advantage to playing second, Black's first move could be "Pass," and he could recapture that advantage? (Or both players' optimal play is "Pass" and komi really is 0.)

HermanHiddema wrote:If putting a stone on the board would cause black to lose by 1 or more points, he would pass instead, and could then by symmetry achieve the same score against any first move by white. White would therefore also pass, and the score difference would be 0.

Ah yes, of course. I seem to recall having thought about this before, but I had forgotten. Thanks for explaining.

Let us suppose that, with correct play by both players, the result on the go board is 7 points for Black by area scoring. Then, if correct play were known, komi would be 7 and the game would result in a tie. OTOH, if correct play were known, we would not be playing 19x19 go.

Given that, what about Button Go, where at his turn a player can take the button, which is worth 1/2 point. In that case we have to consider two possible ways that Black can get 7 points. In one case Black has 6 more points of territory than White and also gets the last dame; then White will take the button, for a final score of 6.5 for Black. In the other case Black has 7 more points of territory than White, White gets the last dame, and then Black takes the button, for a final score of 7.5. Then a komi of 6.5 or 7.5 would be correct, if correct play were known. We can estimate that there would be around half as many ties as without the button.

First of all, we cannot even be 100% sure that the 6 point komi is correct. When standard komi was first introduced, it was 1.5, then changed later to 2.5, 3.5, 4.5 until in the early 2000's it was changed from 5.5 to 6.5, because black was winning 55.6% (?) of the time, and that difference was deemed large enough to take action on the komi. There is practically nothing to go by except statistics. And if the stronger player happened yo have taken black 55.6% of the time, then the komi change would have been groundless. It could even have been the other way around, meaning they should have probably made the komi even bigger than 6.5. Ultimately, the only "proof" we have of whether komi is correct is whether it stands the test of time. Since we do not have enough years for the universe to live, we can never be sure. And this is were the half-point comes in.

"THE 0.5 IS IN GOD'S HANDS"

If in reality komi is too small, a draw is unfair to white. If komi is to large, a draw is unfair to black. The 6.5 komi does NOT say the komi is believed to be 6 points. It says, "We don't know whether it's 6 or 7, so we might as well make it 0.5 so that our tournament can run smoothly." Whether you agree with this or not is up to you, but the reasoning behind 0.5 is that we don't quite know true komi for sure anyway. By no means does every tournament have 6.5-- some have 6 or 7-- but it's rare in the pro world.

Elom wrote:When standard komi was first introduced, it was 1.5, then changed later to 2.5, 3.5, 4.5

That's news to me, do you have a source? Or are you just making things up?

Elom wrote:in the early 2000's {komi} was changed from 5.5 to 6.5, because black was winning 55.6% (?) of the time, and that difference was deemed large enough to take action on the komi. There is practically nothing to go by except statistics.

Based upon statistics, almost 40 years ago I predicted that Japanese komi would be 6.5 by the turn of the century. Almost! Not too much later an article in the American Go Journal opined that correct Japanese komi was 7, based upon pro statistics with both 4.5 and 5.5 komi. Early in the 1980s (IIUC) Ing set komi for area scoring at 7.5. also based upon statistics. The sense that komi should be around 7 has been in the air for a long time. As pros get better, maybe komi will be shifted upwards, but don't hold your breath.

HermanHiddema wrote:Although there is no proof for the correct value of komi, there is proof that it exists and that it is not smaller than 0. The correct komi is well-defined, it is the amount of points by which black wins if both players play perfectly (which may be 0). Given that the definition of correct komi is basically "the amount of compensation white needs to get a draw if both players play perfectly", then obviously, by circular reasoning, with the correct komi perfect play leads to a draw.

I am always puzzled by this kind of statement. Since "perfect play" is undetermined, how does this make correct komi "well-defined"?

ez4u wrote:

HermanHiddema wrote:Although there is no proof for the correct value of komi, there is proof that it exists and that it is not smaller than 0. The correct komi is well-defined, it is the amount of points by which black wins if both players play perfectly (which may be 0). Given that the definition of correct komi is basically "the amount of compensation white needs to get a draw if both players play perfectly", then obviously, by circular reasoning, with the correct komi perfect play leads to a draw.

I am always puzzled by this kind of statement. Since "perfect play" is undetermined, how does this make correct komi "well-defined"?

A unicorn is well defined.

Bill Spight wrote:Let us suppose that, with correct play by both players, the result on the go board is 7 points for Black by area scoring. Then, if correct play were known, komi would be 7 and the game would result in a tie. OTOH, if correct play were known, we would not be playing 19x19 go.

Not sure that follows. Didn't they "solve: checkers? People still play it...

I hear something similar said long time ago about chess... once there are (cheap) computer programs able to beat any (almost any?) human, there will be no point playing chess.

HermanHiddema wrote:Although there is no proof for the correct value of komi, there is proof that it exists and that it is not smaller than 0. The correct komi is well-defined, it is the amount of points by which black wins if both players play perfectly (which may be 0). Given that the definition of correct komi is basically "the amount of compensation white needs to get a draw if both players play perfectly", then obviously, by circular reasoning, with the correct komi perfect play leads to a draw.

Give the above statement, the 0.5 point added/subtracted to/from komi is indeed unfair. Because then one side, in spite of playing perfectly, might still lose the game - if the other side also plays perfectly.

What's more, there are errors in Go which can cost less than 0.5 points, according to the fraction crunchers. In such case, it is possible with fractional komi that one side played perfectly, while the other did not, and the perfect side still lost. Which seems to go against the whole idea of Go, and be really really unfair.

Why are we so afraid of draws in Go?
I can understand that pro sponsors and organizers have it "easier" when draws are eliminated, but is that really what matters?

Bantari wrote:

HermanHiddema wrote:Although there is no proof for the correct value of komi, there is proof that it exists and that it is not smaller than 0. The correct komi is well-defined, it is the amount of points by which black wins if both players play perfectly (which may be 0). Given that the definition of correct komi is basically "the amount of compensation white needs to get a draw if both players play perfectly", then obviously, by circular reasoning, with the correct komi perfect play leads to a draw.

Give the above statement, the 0.5 point added/subtracted to/from komi is indeed unfair. Because then one side, in spite of playing perfectly, might still lose the game - if the other side also plays perfectly.

What's more, there are errors in Go which can cost less than 0.5 points, according to the fraction crunchers. In such case, it is possible with fractional komi that one side played perfectly, while the other did not, and the perfect side still lost. Which seems to go against the whole idea of Go, and be really really unfair.

It is possible that a player does not play the biggest move, but still gets a perfect result. Consider the case where the only move left with any value is a one point ko. As black, it is my turn, and I can fill the ko, which is worth 1/3 of a point according to endgame theory. Instead, I pass, and my opponent takes the ko. Since I have more ko threats, I then go on to win and fill the ko, and I have lost no points. So, although locally I played sub-optimally, globally that was still perfect play.

Why are we so afraid of draws in Go?
I can understand that pro sponsors and organizers have it "easier" when draws are eliminated, but is that really what matters?

In KO tournaments, it is necessary to eliminate draws. In most other tournaments, it is not, and indeed there are events that have whole komi (Cassandra mentions one earlier in the thread).

But a whole komi is only more fair if it is the correct komi.

Suppose the correct komi is 7. That means that a komi of 6.5 gives an "unfair" result in those games which black wins by 0.5, which should have been ties. A komi of 6, on the other hand, would lead to an unfair result not only in games black wins by 1 point, which should have been ties, but also in all draws, which white should have won by 1. So the application of a wrong whole komi doubles the number of unfair results!

EdLee wrote:

Joelnelsonb wrote:with a perfect game like Chess (bare with me), perfect play on both sides will result in a draw everytime, 100 out of 100.

But this is only your belief, not a proven fact.

Computers have already solved checkers and mancala: yes, they are both draws with perfect play. But not yet for chess or Go -- it's still an open question.

I don't understand your point. Proven or not, it does seem like a reasonable assumption. Play wouldn't be very "perfect" if it led to a loss.

It would, if the game were unfair?

Indeed, for example Connect Four is solved and the first player wins with perfect play from both sides. Whereas tic-tac-toe (noughts and crosses) is solved and is a draw. It depends how much of an advantage the first move gives you. For Chess we don't know yet, though I expect most would agree it is less than in no-komi Go.

Joelnelsonb wrote:with a perfect game like Chess (bare with me)

As for a perfect game to bare with you, I think it would be strip poker.