Territory Value of the 3-3 Stone

[cyndane]

I've enjoyed reading this discussion quite a bit. It's very interesting that we can get such different answers to a naively simple question. Bills comment

Precise values? When you get different estimates of 4, 8, and 12, where is the precision?

naturally makes me think that perhaps values should also be assigned an error. Why not call a bare 3-3 stone 8 plus or minus 4? Then all the estimates agree. As the game progresses the measurement of it's territory can change, and the error becomes smaller. Is it a useful way to think?

[RobertJasiek]

I think I'm confused about what exactly you are trying to count,

Globally, it is the

Territory Count = Black's territory - White's territory

(there can be prisoners). In my methodology, the kind of territory being determined is the

Current Territory,

see http://senseis.xmp.net/?CurrentTerritory

Except for not stating the sente condition clearly enough, Cho Chikun also uses current territory as the basis of territorial position judgement. We get

Territory Count = Black's current territory - White's current territory

it seems that if you are granting white all the moves in your additional example in sente, it's hardly ideal play for black.

What is ideal for Black is his maximal defense of his already existing territory regions under certain made assumptions, such as peaceful defense and sente for White.

When White's current territory is being determined, the roles are swapped: Black gets the sente, while White defends peacefully his already existing territory regions.

Without looking at the whole board, it's hard to say that black wouldn't get compensation elsewhere in exchange for being relatively sealed in in gote.

Current territory is NOT (I repeat: NOT) the result of ordinary go playing. When a player's current territory is determined, the study game's objective is exactly this: to determine his current territory.

Think of it as a kind of proof play. When you have a different task, such as determining the life and death status of a black group, you use proof play with the objective for Black to live (or etc.) and for White to kill (or etc.). Other objectives do not exist. Similarly, in territorial positional judgement proof play about a player's territory, the only relevant objective is the determination of his already existing territory.

The move sequences shown do NOT have the objective of increasing the territory. They only have the objective of determining the already existing territory.

Why not choose this joseki as representative to get a value for the 3-3 stone, since it removes most of the potential influence from the equation?

Because you would be determining the current territory of this joseki result, instead of determining the current territory of the 3-3 stone.

The influence of the black joseki stones differs from the influence of the lonely 3-3 stone. Therefore, also the territory must be different. Less remaining influence implies (since it is joseki) more territory. IOW, with the joseki you determine, that the 3-3 stone has less current territory than the joseki result's current territory. It is not clear, how much less.

[oren]

One nice thing about this discussion is that it's finally made me order the Lee Changho book. I'm looking forward to seeing what it has to say in more detail.

[RobertJasiek]

it seems like a weak argument to argue with the pro's estimation - the adversary methodology is an estimation, just the same.

Have you noticed that Lee appears to proclaim "4 + alpha" (for some, by the used method, obviously relatively big alpha), while I proclaim "8" (i.e., I determine the alpha as 4)? A "method" with a rough error is not just of the same quality as a method with an apparently small error, even in your simplistic view.

EDIT:

Then why not discuss the position later in the game, when a pretty full board arises?

It is a principally interesting other study question. (And the methods are applicable again.)

[skydyr]

I think I'm confused about what exactly you are trying to count,

Globally, it is the

Territory Count = Black's territory - White's territory

(there can be prisoners). In my methodology, the kind of territory being determined is the

Current Territory,

see http://senseis.xmp.net/?CurrentTerritory

Except for not stating the sente condition clearly enough, Cho Chikun also uses current territory as the basis of territorial position judgement. We get

Territory Count = Black's current territory - White's current territory

Based on the example at sensei's library, at least, it seems like it's only relevant when a group is relatively sealed in. On the whole board, for example, white could just mirror black's moves in opposite corners, and until the symmetry is broken, after white's moves the territory count should be zero, no?

More to the point, I don't understand why the initial white move you chose is the correct one, and why black's response is correct, when black could just as well respond with a keima or the like, claiming either more territory or the threatened capture of white's original stone. 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.

EDIT:
Also, that page makes it pretty clear that the Current Territory count is only really applicable to the middle game.

[RobertJasiek]

What if black had played twice more in the corner first, then by my reading of your system:

$$W
$$ ------------------
$$ | . X . . . . . . .
$$ | X . 4 3 . . . . .
$$ | . 2 X . . . . . .
$$ | . 1 . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . X . . . . . . .
$$ | X . 4 3 . . . . .
$$ | . 2 X . . . . . .
$$ | . 1 . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

By correct reading of my system, you must apply reasonable reduction moves by White. 1 and 3 approach too closely early in the game. Why? There would be no supporting white stones in the neuighbourhood yet. Therefore, the white moves cannot be sold as sente, because, after your sequence, they are not reasonably alive yet. Reduction plays are reductions only if they are alive! It is a requirement for the white moves to be reductions. Not fake reductions essentially killing themselves.

You could, I suppose, quibble that 1 and 3 are no longer "reasonable reductions", that black can too easily attack those stones, but that objection also existed without the additional stones.

Exactly. Therefore, White 1 and 3 are too close to the 3-3 stone, even without the additional black stones. (As I have said already in my initial post.)

Essentially, you seem to hit upon a loophole in your territory system.

Not a loophole. It is a systematic requirement for reductions having to be reasonable.

It is often the case where switching directions, perhaps sacrificing territory on one side to expand further on the other side, is beneficial.

Not in proof play "determination of a player's current territory. There, direction switching by the defender is infrequently necessary!

You could allow it unconditionally,

No. This would pretty much lead to globally perfect play and not determine already existing current territory, but determine territory existing after additional perfect play.

and get a more accurate estimate

No. Something else would be determined. Accuracy for perfect play of ordinary go playing would be increased. Not the accuracy of the current position's current territory.

Or you could remove it, and accept that when a reduction kills, the number does not take that into account.

Then how?

But allowing a change of direction only when necessary for life creates this sort of situation where a barely living group is worth more than a strong one, because only the weak group is allowed to expand in the other direction to obtain territory.

New territory is not obtained, but already existing territory is being defended as territory. Even though you are sometimes surprised when it is bigger than you thought, because the defender is so cute to survive.

Never has a barely living group, whose only living possibility is a change of direction, less territory than it can show by maintaining life by indeed changing the direction! A barely living group never has only the small territory of its unnecessarily dying shape.

[RobertJasiek]

Why not call a bare 3-3 stone 8 plus or minus 4?

The error is not 4, but - I claim (but cannot prove beyond doubt) - is smaller than the rounding error 0.5.

[Kirby]

Have you noticed that Lee appears to proclaim "4 + alpha" (for some, by the used method, obviously relatively big alpha), while I proclaim "8" (i.e., I determine the alpha as 4)? A "method" with a rough error is not just of the same quality as a method with an apparently small error, even in your simplistic view.

Whose view is the "simplistic view"? Without knowing the exact value, the amount of error is unknown.

So even in your simplistic view, you have not proven that your method provides an apparently smaller error.

[RobertJasiek]

it seems like it's only relevant when a group is relatively sealed in.

For moyos, determine current territory and half territory!

I don't understand why the initial white move you chose is the correct one,

- It is reasonable.
- It lives.
- It minimises while fulfilling the other conditions.

and why black's response is correct,

- It is reasonable.
- It is peaceful (not claiming an unprotected, open side).
- It maximises while fulfilling the other conditions.

or the threatened capture of white's original stone.

That would violate in particular the "peaceful defense" condition.

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)).


EDIT:

Also, that page makes it pretty clear that the Current Territory count is only really applicable to the middle game.

The SL page is just initial food and does not demonstrate all the power of application. See the literature for that.

[Kirby]

...
It is a principally interesting other study question. (And the methods are applicable again.)

There is a difference. Later in the game, the methods can be shown to be correct. When there are many variations, the methods result in simply a guess, no better than other guesses (until you have proven their accuracy).

[RobertJasiek]

There is a difference. Later in the game, the methods can be shown to be correct. When there are many variations, the methods result in simply a guess, no better than other guesses (until you have proven their accuracy).

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

[Kirby]

There is a difference. Later in the game, the methods can be shown to be correct. When there are many variations, the methods result in simply a guess, no better than other guesses (until you have proven their accuracy).

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:

Since both statements cannot be correct, a discussion follows.

This would be Yi Ch'ang-ho's 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.

[Kirby]

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:

$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

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:

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

Click Here To Show Diagram Code

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

$$Wm11
$$ ------------------
$$ | . . . . . . . . .
$$ | . . 1 O X . . . .
$$ | . . O X . 2 . . .
$$ | . . O X . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

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:

$$W
$$ ------------------
$$ | . . . . . . . O .
$$ | . . . . . . . O .
$$ | . . . . . . . O .
$$ | . . . X . . . O .
$$ | . . . . . . . O .
$$ | . . . . . O O . .
$$ | . . . . . . . . .
$$ | . . . . . O . . .
$$ | O O O O O . . . .

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:

$$W
$$ ------------------
$$ | . . . . . . . O .
$$ | . . 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 . . . .

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.

[RobertJasiek]

suggesting that the Jasiek method is absolutely superior

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

even going so far as to say that the OP-provided justification [...] is a mistake:

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.

that the Jasiek method is superior.

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.

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

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?

in some select cases

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

But to claim absolute correctness of the Jasiek method,

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

or to even discuss Lee Changho's mistakes on justifications that he did not even provide... This seems incorrect.

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.

[Bill Spight]

I don't think that people who make precise estimates in the opening are putting too much store in the numbers, but are using them as heuristics.

This makes sense, but it would seem then, that if the "precise estimate" is intended to be used as a heuristic in the first place, it is less meaningful to criticize a "less precise estimate" obtained in a less mathematical manner.

That is to say, if you have a localized position for which you can prove that your precise numerical technique yields exactly the correct answer, then I agree that you can argue of the benefits of using such a calculation above other methods - it provides exactly the correct answer.* {Footnote.}

But if you use a similar method early on in the game, only to come up with a rough estimate in the first place, then I don't see how the method is necessarily superior to other methods of positional judgment.

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.}

When multiple methods of positional judgment (eg. Lee Changho's, Robert Jasiek's, etc.) lead to estimates and not provably correct judgments, it becomes difficult to argue for one method over another in objective terms. As a result, I am inclined to put more weight into estimations that have held track record in game results.

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.