Ok. But more deligent case studies can extend evaluation of the methods further to the earlier game. Please go ahead:)

The point I am trying to make is that the OP is aggressive, suggesting that the Jasiek method is absolutely superior, even going so far as to say that the OP-provided justification (which was created by you) for the alternative method is a mistake:



It would seem to me that it would make more sense to take an aggressive stance after having the proof in place that the Jasiek method is superior.

With an open board like this, the arguments appear speculative at best.

I would think that a more reasonable approach would be to explain, "This method exists by Lee Changho to evaluate the territory of the 3-3 stone. I feel that, in some select cases that I can provide here, a closer estimate might be obtained by this Jasiek method." And then you could give examples of cases where your estimate is closer to reality than the Lee Changho method.

But to claim absolute correctness of the Jasiek method, or to even discuss Lee Changho's mistakes on justifications that he did not even provide... This seems incorrect.

_________________
be immersed

Back to the discussion on the actual value of a 3-3 stone, it's also interesting to note that the value in points of a stone can change throughout the course of the game.

A classic example is the value of a 4-4 stone:

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Of course, white can play at the 3-3 point, and take away the corner territory that black has. For example:

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . 9 0 . . . .
$$ | . . 1 2 . . . . .
$$ | . . 3 X . . . . .
$$ | . 5 4 . . . . . .
$$ | . 7 6 . . . . . .
$$ | . . 8 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$Wm11
$$ ------------------
$$ | . . . . . . . . .
$$ | . . 1 O X . . . .
$$ | . . O X . 2 . . .
$$ | . . O X . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Black has no points in the corner, but the 4-4 is still considered to be an acceptable play, because even with an invasion of the 3-3, black has outward influence, and will likely get points in other areas of the board. And in fact, early in the game, this is probably better for black than white. White gets a few points, but black has potential extending toward the center of the board.

Given this, we might estimate some value for the play at the 4-4 point. You could say, given the territory black can make eventually from the resulting influence of a 3-3 invasion - combined with the possibility of enclosing this corner, etc... We might have some value X for the amount of points we estimate for the 4-4.

But as the game progresses, this changes. Imagine the same 4-4 point, but there are other white stones that are strong, surrounding:

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . O .
$$ | . . . . . . . O .
$$ | . . . . . . . O .
$$ | . . . X . . . O .
$$ | . . . . . . . O .
$$ | . . . . . O O . .
$$ | . . . . . . . . .
$$ | . . . . . O . . .
$$ | O O O O O . . . .[/go]

Now, if white invades, assuming same play by black:

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . O .
$$ | . . O O X . . O .
$$ | . . O X . X . O .
$$ | . . O X . . . O .
$$ | . O X . . . . O .
$$ | . O X . . O O . .
$$ | . . X . . . . . .
$$ | . . . . . O . . .
$$ | O O O O O . . . .[/go]

Black could even be killed. So in this type of situation, the value of the 4-4 has changed.

This is an extreme example, but the point is, as the game changes in the surrounding board, the value of stones change. What is possible early on in the game starts to become impossible later on as moves are played.

Because of this, it's difficult to give a static value to a group of stones, because it depends highly on the placement of stones in other areas of the board.

_________________
be immersed

For the sake of the 3-3 stone's territory assessment.



The justification is on a level of informal reasoning according to the current state of the art for my used methodology. The justification is not on a level of mathemetical proposition proving.

Do you think that the informal reasoning is not justification? You have found valid objections. But if you apply such a kind of arguments, then every informal go theory by everybody ends up as "not justified" in your opinion, and only mathematical proofs count.



Lee's line drawing is without any justification. Most of his method for the 3-3 consists of this line drawing. Therefore, most of his method for the 3-3 is without any justification.

Compare my method for the 3-3: I provide at least informal justification. Doing so is superior to not doing so.



Yes. For example, my argument that predominating opinion considers the 3-3 to be more territory- than influence-orientated. You would certainly criticise every player for relying on such a speculative argument when making strategic planning in his games, wouldn't you?



The 3-3 point in an empty quarter of the board is the only case, for which I have made my claim.



Eh? I allow for a small error. To recall, the claim is for the 3-3 in an empty quarter.



Not providing either justification attempt(!) is worse than no justification for the line drawing at all. It is good to ask for justification. You ask it from me. I ask it from Lee. Discussing potential lines of justification is not something "incorrect", but is appreciated since Socrates at least. It is one of the few good things I have learnt at school all the time: discussion by considering potentially interesting arguments is important and good. I am really surprised that you, who you like discussion, seem to think differently.

That's pretty much what the traditional method does. As the game goes on, territory solidifies, so that counting solid territory gives a more and more accurate estimate of the value of a position. The question is how good it is earlier in the game. **{Footnote.}



Cho Chikun's or Lee Changho's or Ishida Yoshio's methods are pretty much the same traditional method. Since virtually every pro uses the same method, their differences in evaluation depend upon their differences in judgement. It is not like one method has been tested against another and has a superior track record. I suspect that Fawthrop's method is superior to the traditional method, but pitting him against Lee Changho is not going to decide the issue.

* As for precision, if I want an estimate that is good to 1/2 stone (7 pts.), then I want an estimate that has a higher precision, because of the errors of estimation. So a point estimate is about the right level of precision. In the endgame, OC, I want calculations to a fraction of a point.

** It can be valuable to estimate solid territory. If I am behind in solid territory by, say, 10 pts., then I can ask how I get more than that from the less settled parts of the board. But as a method of evaluation, the traditional method pretty well sucks. For instance, suppose that an initial stone on the 3-3 is worth 13 pts., and the traditional territory estimate is 4 pts. Where are the other 9 pts.? Hard to say. But I can estimate 4 pts. in the corner plus 4 pts. on either side, for 12 pts. of territory. Where is the other point? Even if it's hard to say, that's not so much of a problem.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

So what I've learned about positional judgement and counting from Japanese books so far is to assume what territory can be said to be solid and use the inside to count. From that position about 4 points makes sense for a 3-3 stone. Assuming the 3-3 stone doesn't die, you can expect about 4 points in the corner assuming black plays purely defensive moves. 8 points seems too high to me, but you can use whatever you like.

Robert, your diagram shows white playing two moves. You would not assume that under the position judgement of an area when just evaluating the points in the corner under a 3-3 stone by itself.

The 4-4 has 7 points of current territory, but its territory is insecure. To make the territory secure (prevent White's invasion), Black needs to play a second move.



Yes.



Nevertheless, one can consider the current position as a static position and determine its static (estimate of a) territory count.

But isn't the initial white move you presented (5-3 point) gote?

Which diagram, please?

Your first post. And sorry, I meant black.

Yes, more information is added by providing informal justification. But just because you didn't read any justification for Lee's method does not mean that justification does not exist.



No, you are not asking it from Lee. You are publicly criticizing the methodology without asking him, when it's entirely possible that you are not aware of the point he was even trying to make:

_________________
be immersed

The "sente" in a positional judgement sequence is judged in its context of the defender accepting it as sente usually by following his duty of blocking (or exceptionally by switching direction and maintaining life).

Do not think of ordinary game playing sente.

The PJ sente simply looks for whether there is or is not something to be reduced. If the boundary is already blocked, then adding another "reduction" stone in front of it is PJ gote.

We should write a mail to yi changho.

Nobody is talking about giving a static value to a stone or group. The initial plays gain around 14 points, but by the end of the game the players may have around 240 stones on the board and around 120 pts. of territory in total. Then each stone is worth on average around 1/2 pt. of territory. The value of a stone typically declines over time, as more stones are played.

That being the case, it is easy to see how a method of counting secure territory, which rarely changes (for instance, in a furikawari), could arise. Everything else is up for grabs. However, that fact does not make the count of secure territory a good estimate of the value of a position. For that you need to assess points that only partially belong to one player or another. True, no one has figured out the best way to do that, but that does not mean that not doing so at all is better than doing so imperfectly.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Can you find any in MJK's translation?



Are you suggesting that all readers of all books may not criticise their authors for not writing something, if the readers do not first ask the authors about it? Contrarily, I think that books must speak for themselves, especially books meant to teach the something.



See MJK's translation of the relevant citation of the book.

No. I am just suggesting that it is more likely that you have either misinterpreted or misunderstood Lee Changho's intention than his having made a mistake in such a common scenario.

A third grader that's just learned algebra can question the math behind Gödel's Incompleteness Theorems, but when he doesn't even have a proof that Gödel is incorrect, his argument doesn't have much merit. You can use casual arguments to say why you think Lee Changho is wrong, but I'm more inclined to believe a pro's casual argument than an amateur's. If you can actually prove what you're saying, then you have an argument. Until then, I can only guess that you're trying to sell more books.

With the lack of dialog with Lee Changho, it's highly likely that you are missing his intention or meaning. There's even a chance that, given the same set of base underlying assumptions/axioms, you both agree on the point value in the corner.

That being said, the discussion is not worthless. More important than the "correct" value in the corner is probably the underlying analysis. However, I think we should give more thought as to why Lee Changho came up with the value of 4, as there is likely something that hasn't been properly analyzed and/or missed. He is a pro, after all, and we should not be so quick to dismiss his conclusion.

You could compare this to studying joseki. You might be convinced that the joseki move is wrong. It's useful to think about. But usually, if you think about the position for long enough, you can see why the pros were correct in saying this was joseki.

I think the same is true here. It may seem that 8 is a more reasonable answer. But I think there's something we're missing.

_________________
be immersed

I suppose this thread is as good as any to ask a question about something I've never understood. Almost all discussion on territory assessment assumes these kinds of forcing moves:

Click Here To Show Diagram Code

[go]$$B 4 points
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . B . , . . . . .
$$ | . W O . . . . . .
$$ | x x W B . . . . .
$$ | x x W B . . . . .
$$ | . W O . . . . . .
$$ | . B . . . . . . .
$$ | . . . . . . . . .[/go]

This reminds me of something my mom used to say when seeing those commercials for underarm deodorant. I'm talking about the ones where they show people applying it their forearms rather than their underarms. She would say, "they should show people putting it on their underarms!" I would ask why, and she'd say: "because maybe stupid people will see this and not know where to put it!"

The fact is that in a real game, it is hard to imagine a position where the marked black moves are optimal, whether it's in the middle game, endgame or opening. I've never seen any "justification" for why this type of analysis is valid. The best that has been stated seems to be that if it's applied equally to both sides, then one might guess it is fair. No proof is ever offered. Maybe stupid people will see this kind of thing in a book and assume black's moves are good.

So I think as long as this kind of voodoo is state of the art in positional analysis, then pretty much everyone is just waving their hands.

Is there a better justification for the kind of diagram shown above than the fact that professionals have thought this way in the past?

During positional judgement you want to know how many points you have solid and the rest is guessing from the flow of the game. The reason you see those types of moves is to understand the limits that can be taken and everything inside is solid territory. What happens outside later will change the calculations.

My interpretation is that, while you don't know what kind of stone formations will occur in the areas of the marked black stones - many possibilities could develop - you know that no matter what happens there, you can minimally get the territory obtained by the exchange of the marked black and white stones.

It could be the case that white plays in that area first and ends up with a lot more territory. Or maybe black plays further back. But whatever develops there, you can count on getting the territory obtained by that exchange in the worst case.

You can decide to not play that exchange in order to do something worth more points, but this gives a lower bound on the points.

_________________
be immersed

I agree completely. It would be very useful to be able to calculate an accurate "present value" for a local position. However, that value would have to be the total value, including both territory and influence.

Unfortunately, the only value which is somewhat amenable to calculation is the irreducible minimum territory, assuming the opponent gets lots of limiting moves in sente. So that is what professionals like to calculate, or at least write books about. But without an equally rigorous way to evaluate the influence value of a position, the territory value is pretty much just meaningless hand waving.

The case of a single move on an empty board is an unusual case where the total value is known, but the split between territory and influence can be argued. We have a century of experience to say that the total value of a single corner stone is around 12-14 points. Trying to calculate an accurate value for just the territory component of that value is rather pointless -- why worry about calculating part of the answer with poor accuracy when the complete answer is known?

So if someone says the san-san stone is worth 4 points territory plus 8 points influence, I am willing to listen to their theory. Same for a claim of 8 points territory plus 4 points influence. But if someone says the san-san stone is worth X points territory plus an unknown and unspecified amount extra, they are just hand waving.