Territory Value of the 3-3 Stone

[oren]

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.

[RobertJasiek]

Black has no points in the corner, but the 4-4

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.

This is an extreme example, but the point is, as the game changes in the surrounding board, the value of stones change.

Yes.

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.

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

[skydyr]

It seems just as accurate to say that the 3-3 point doesn't enclose any territory, because after a few white moves, black is left without a living shape.

Wrong, because that would NOT be a sente reduction sequence. The attacker's sente in the sequence is one of the requirements (as well as the defender's requirement to block the sente moves (except when an exception applies)).

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

[RobertJasiek]

your diagram shows white playing two moves.

Which diagram, please?

[oren]

your diagram shows white playing two moves.

Which diagram, please?

Your first post. And sorry, I meant black.

[Kirby]

...
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, 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.

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.

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:

..
My point was, what he meant by "worth 4 points" and what you think he means by "worth 4 points" could be quite different, this is the issue with arguing against something you haven't read.

[RobertJasiek]

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

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.

[Shinkenjoe]

We should write a mail to yi changho.

[Bill Spight]

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.

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.

[RobertJasiek]

just because you didn't read any justification for Lee's method does not mean that justification does not exist.

Can you find any in MJK's translation?

you are not asking it from Lee.

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.

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:

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

[Kirby]

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? ...

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.

[dumbrope]

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:

$$B 4 points
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . B . , . . . . .
$$ | . W O . . . . . .
$$ | x x W B . . . . .
$$ | x x W B . . . . .
$$ | . W O . . . . . .
$$ | . B . . . . . . .
$$ | . . . . . . . . .

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?

[oren]

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.

[Kirby]

...

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

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.

[mitsun]

...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...

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.