removed contents of double post

As a general note about what is needed for evaluating the 3-3 territorially.

1. One needs to choose a conceptual kind of territory.

2. One determines the value of the used conceptual kind of territory in the studied position.

3. One interprets the determined value.

Concerning (1), I use 'current territory' and (for moyos) 'half territory' for that purpose. Lee seems to use current territory, except single corner stones, for which he determines only part of the current territory, and except moyos, for which he writes 'plus alpha'.

Concerning (2), it must be possible to determine the value in practice. E.g., if one chooses "the score after perfect play" as the conceptual kind of territory, it is impossible to determine a value in practice. Likewise, it is impossible for CGT-like endgame calucations performed for a position in the opening or middle game. Contrarily, current territory (territory remaining after sente reductions) can be calculated in practice. It often suffices to consider only one move sequence per player.

Concerning (3), there are also turn, influence, aji etc., which are also relevant for positional judgement. The determined territorial value must be interpreted in this context.

Why does not one not use a combination of convex hulls and (for regions adjacent to the edges) straight lines to the edges? Because it is less precise than current territory, because privileges (guaranteed sente reduction exchanges) would be overlooked.

Why does one use reductions, with the attacker starting? Because it is the predominating opinion that this gives more reliable values than such calculated from, for example, expansions and the defender starting. Why? By using reductions, the shapes are settled near the already existing stones; by using expansions, the shapes are settled "far" from the already existing stones; near shape settling is more reliable than far shape settling.

As you might recall, Redmond (maybe also some Edo players, who had enough thinking time?) uses a different method for territorial positional judgement: he imagines to continue the game to the end with test sequences ending in played out ordinary endgame sequences. Surely this is a possible alternative, but it has clear disadvantage: it is very time consuming and requires great skill / confidence to play out complete game sequences. I (and, it seems, quite a few professional players) am more modest by using quiescience sequences only to cool down the current hot fights or middle game ko, before determining current territories.

Oops, I overlooked that you are asking for White 5 here. So here is the explanation. When it is played, the study sequence position looks like this:

Click Here To Show Diagram Code

[go]$$W continuation
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . 5 . .
$$ | . X X . . X . . .
$$ | . O . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

For White 5 to be reasonable as a reduction, it must be a) alive even after Black's answer block (the white stone is alive indeed) and b) justified as a sente move (in the context of positional reduction sequences). To be such a sente move, there must not be a necessity to reinforce in gote the stone to maintain its reduction nature, as soon as Black answers with the block.

For such a reinforcement necessity to be absent, it is necessary to presume that White 5 can rely on a supporting stone or supporting stones. More precisely, such a supporting stone must be there at a typical timing, when White 5 can be expected during the course of a game. It is indeed very reasonable to assume such a white supporting stone at that timing, because 3rd line moves (here: further to the right) or similar supporting stones are played before 2nd line endgame moves during every typical game. Although the local judgement sequence does not show the supporting moves played in between, we can assume them to be played, because this is reasonable timing in a global context.

(You might object that, instead of white supporting stones, there could be black attacking stones further to the right. Yes. PJ by current territory makes the simplifying assumption that favourable white supporting stones occur when White reduces and that favourable black supporting stones occur when Black reduces white regions. Since this is a too idealised world, it is important to update PJ counts regularly. E.g., when Black gets his first attacking stone on the upper right, while White gets his first attacking stone somewhere else on the board for some other region, updated PJ counts becomes urgent. Maybe the count is still about the same, but maybe one player's attacking stones are more efficient than the opponent's? Updated PJ should then identify this.)

Yes, that explains it. I had not considered the reductions for PJ to potentially be thought of as occurring throughout the game. I can see where you are coming from when treating early corner moves differently.

Because of this, it seems your system would require some additional practice. But I suppose that's not much harder than calculating common endgame sizes, which is something I have to do away from the board because I'm not fast enough to do it in byoyomi.

I can see that it's precise, but I can't see that it's useful. I was asking you to back this up.


He is estimating the secure territory enclosed by the 3-3 stone itself, while deliberately failing to account for external factors. That is, if that stone lives until the end of the game, and you do not deliberately sacrifice its territorial value, it will surround 4 empty intersections, and they will be those 4 intersections in the corner. Extra stones may surround more; certain configurations of stones may surround more than the stones themselves; if that stone dies, it will surround less; if white is allowed to reduce more than he should be able to locally for black's global advantage, it will surround less; and so on, but he is precisely not addressing these issues, because they are situation-dependent. In particular, he is obviously not saying "just leave this 3-3 stone alone until it comes under severe local attack, then defend in the most sensible way locally, and you'll get 4 points". That's stupid, because (a) it's false (as you said), (b) that's not how anyone plays (as I am saying).

All he is saying is "these four intersections of this board are the only territorial thing you can be certain of with this single stone right now". This is useful because, for example, the same principle does not apply to a 4-4 stone or a 5-5 stone, which I imagine he would not estimate a territory value for (or at least not in the same way).


Whatever you name it, if it is your definition, you do not get to stomp around saying "this is the definition". It is a definition. You must justify its usefulness before anyone will adopt it.


I don't. It doesn't. What is the territory value of a lone tengen stone, or a lone 5-7 stone? If you come up with any precise answer for that under your definition, what you're doing is nonsense.


I do not. Nobody plays go by sticking a stone in a corner and then leaving it there until one move before it dies and defending minimally, so your principles do not calculate anything useful. Besides which, you claim that the 3-3 stone gets you 8 points, but it doesn't: you have to spend an extra move turning it into 8 points (otherwise eventually it dies), which under any reasonable calculation makes it 4 points per stone. Besides which again, if you do not simultaneously manage to come up with definitions for the territory value and the non-territory value of a stone or a group, you're still not really talking about go. I also cannot propose any better, of course. That is why I propose that you stop trying to precisely axiomatise something that is necessarily vague and undetermined.

oren, RBerenguel think that one, most or all diagrams in
viewtopic.php?p=143244#p143244
fit the description "[Black] playing two moves" or "adding a stone [of the same player] and changing the score". Let me explain why this is not the case. I understand the suggested descriptions as "Black plays two moves in a row". Please tell me if you have doubts also about alternating(!), imagined, evaluation sequence moves.

Click Here To Show Diagram Code

[go]$$W upper left corner, 3-3 stone
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

No stone is added.

Click Here To Show Diagram Code

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

Alternation, so Black does not play two successive moves. White starts to reduce the black stone's region. The score is not changed, because this is an imagined evaluation sequence only. (*)

Click Here To Show Diagram Code

[go]$$W reasonable attack and defense
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . 2 . . .
$$ | . . . . . . . . .
$$ | . . 1 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Same as *. In particular, the score does not change because Black maintains life instead of dying (which would change the analysed score dramatically in White's favour).

Click Here To Show Diagram Code

[go]$$W continuation
$$ ------------------
$$ | . . . . . . . . .
$$ | 8 . . . . 6 5 . .
$$ | 7 4 X . . X . . .
$$ | . 3 . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Same as *.

Click Here To Show Diagram Code

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

No moves are added.

Click Here To Show Diagram Code

[go]$$W upper left corner, 3-3 stone
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

No moves are added.

Click Here To Show Diagram Code

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

Same as *.

Click Here To Show Diagram Code

[go]$$W upper left corner, 3-3 stone
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

No moves are added.

Click Here To Show Diagram Code

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

Moves 1 and 2: same as *. Move 3 is not meant to comply with proper judgement sequence principles.

Click Here To Show Diagram Code

[go]$$W reduction of Black's region
$$ ------------------
$$ | . . . . . . . . .
$$ | 6 . . . . 4 3 . .
$$ | 5 2 X . . X . . .
$$ | . 1 . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .[/go]

Here, you might think that White 1 violates the rule of alternation. Explanation: the previous diagram creates a position to be analysed; this diagram then analyses the position with an imagined sequence. It is valid to let an analysis sequence start with the same player who played last in the sequence creating the position to be analysed. It is not only valid, but very useful. If you have never used it before, start using it now!

It is like playing a game to create a position, then studying a group's life and death status. In analysis sequences for that purpose, it is possible that the first move is of the attacker and that he is the player having made the last move in the game sequence and creating the studied position.

Analysis is an abstraction, in which a position can be studied for either player to move first in that analysis position.

The same is done in particular when the type of analysis is 'territorial positional judgement'. E.g., also every local endgame judgement can be done with either player moving first in the (local) study position.

Click Here To Show Diagram Code

[go]$$B Black's points
$$ ------------------
$$ | . . . . . X . . .
$$ | X X . . . X O . .
$$ | O X X X X X . O .
$$ | O O . O O . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .[/go]

No moves are added.

Click Here To Show Diagram Code

[go]$$B reduction of White's region
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . X . . .
$$ | . 3 . . . . . . .
$$ | . 4 O . . . . . .
$$ | . . 6 5 . . . . .
$$ | . . 8 7 . . . . .
$$ | . 2 O . . . . . .
$$ | . 1 . . . . . . .
$$ | . . 9 . . . . . .
$$ | . . . . . . . . .[/go]

Here, we analyse a different position. Otherwise same as (*).

Click Here To Show Diagram Code

[go]$$B White's points
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . X . . .
$$ | X X . . . . . . .
$$ | O O O . . . . . .
$$ | . . O X . . . . .
$$ | . . O X . . . . .
$$ | O O O . . . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .[/go]

No moves are added.

Click Here To Show Diagram Code

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

No moves are added.

Click Here To Show Diagram Code

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

No moves are added.

Positional judgement requires some practice, but is learnt much more easily than calculation of endgame sizes, because the theory is much easier. This is so because PJ can afford rounding to, say, 0.5 points, while endgame decisions, at every move, benefit from distinguishing move sizes only 0.5 apart. PJ is mainly sente (apart from a few mostly trivially easy remaining gotes), while endgame allows sente / reverse sente / gote more easily and requires related decisions. PJ considers a few regions, while endgame considers many small regions and many endgame moves lead to new small regions easily. In summary, endgame is much more complex.

If you try to ask more specifically about this, then I can try to answer. (Please note that I attend the congress from July 26 to ca. August 12 and my answer might be delayed by that period.)



Ok, this might explain Lee's thinking. Unfortunately, the identification of only those intersections that, in the end, will likely still be surrounded ones does not inform about the total amount of territory protected by the 3-3 point. In every other shape with more stones, the current territory essentially conincides with the number of intersections that will likely still be surrounded in the end. In case of the 3-3 stone or in every other, infrequent case of required direction change for the sake of maintaining life, there is no such identity between the current territory and the number of intersections that will likely still be surrounded in the end.



E.g., Cho Chikun and Lee Changho have used it and almost all my related principles for decades:
viewtopic.php?p=143612#p143612
It is just that the 3-3 is a case, for which Lee makes an exception of not determining the current territory for that stone.



0 points of current territory!

(On an (almost) empty board, such a stone has the miai value of (about) 14 points, but this says nothing about territory.)



I am so sorry that I am able to identify "0 points of current territory" for a center stone and to declare that such a stone creates only influence;)



This sounds like a disagreement of application of the principles for the case of a single corner stone, but does not really sound like rejecting the principles entirely.



This is not what my principles imply for the 3-3 stone. In fact, my principles imply that Black answers an imagined White kakari-reduction by extending on the other side. Accidentally, already Black's first analysis move is a last (reasonable) move to change direction for maintaining life.

Nevertheless, this does not amount to "leaving it there until one move before it dies". Rather it mounts to: "During an actually played game, Black can leave the 3-3 stone alone for a long time, because he has the miai of answering White's kakari by extending on the other, the left or upper, side and so maintaining life. Also during a PJ analysis sequence, Black maintains the life of his corner stone in the same manner."



This is a common, misleading description. Black's defense is MAXIMAL, but subject to the other conditions for PJ sequences (such as usually blocking in front of the attacker's last reduction move).



Do you say so only for the 3-3 stone, or in general for all positions?



Here, you make a mistake. It is not like Black needs to spend an extra move, but it is as follows: there is the possible privilege exchange White 1 (kakari) for Black 2 (extension). The territory of the 3-3 is evaluated as if the the privilege exchange would already be made.

This assumption of privilege exchanges is the same for all positions. E.g.,

Click Here To Show Diagram Code

[go]$$B assumed privilege exchange
$$ -----------------------
$$ | . . . . . . . . . . .
$$ | . . . . . . X O . O .
$$ | . . . . . . X O . . .
$$ | . X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

in this position one does NOT assume that Black would need to spend one extra move to get 2 extra points, like here

Click Here To Show Diagram Code

[go]$$B wrong assumption
$$ -----------------------
$$ | . . . . . . 1 . . . .
$$ | . . . . . . X O . O .
$$ | . . . . . . X O . . .
$$ | . X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

but one presums that the following privilege is guaranteed:

Click Here To Show Diagram Code

[go]$$W assumed privilege exchange
$$ -----------------------
$$ | . . . . . 2 1 3 . . .
$$ | . . . . . 4 X O . O .
$$ | . . . . . . X O . . .
$$ | . X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Because this privilege exists, Black's current territory in the initial position is:

Click Here To Show Diagram Code

[go]$$B current territory: circles
$$ -----------------------
$$ | C C C C C x . . . . .
$$ | C C C C C x X O . O .
$$ | C C C C C C X O . . .
$$ | C X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Black does not have any current territory on 'x'. Black is not assumed to defend to get these two extra points nevertheless. White is not assumed having to make his privilege exchange prematurely in order to prevent Black territory on x, but is assumed to have the right to do so later. Already this possibility prevents Black from having points on x.



Under any reasonable calculation, the available privilege is considered to exist, and we get 8 points.

(Bill might argue that it is at least 8 points, because alternatively, Black plays first in the corner to build a shimari. However, in PJ of a given position for the sake of evaluating current terrtory, one does not allow for the game to continue. A black shimari move would continue the game. Contrarily, the assumption of a privilege exchange does not continue the game, but merely notices what currently is in the given position.)



As you can see in earlier messages, I have explained that a territory count is only one aspect of PJ and that turn, influence, aji, development potential and directions etc. are other aspects needing judgement.



1) It is vague in its accepted rounding error of, say, 0.5 points. It is sometimes possible to be unsure about the best PJ sequence, and so different opinions can construct different sequences, and their associated current territories can differ by up to ca. 1 point (if the sequences are constructed by strong players).

2) The success of explaining the moves of every related PJ sequence by Cho Chikun or Lee Changho shows that my principles are very good. I am aware that they are still vague and undetermined on a low level, when they use words such as "reasonable", "peaceful" or "passive". However, already the principles themselves provide much guidance for how to interpret these words. Having principles with vague words is much better than being vague entirely because of having no guidance whatsoever. Theory has to start somewhere. Later researchers can then translate my principles into something unreadable, but precise to the level of algorithms;) For the sake of human players' application, the principles are already very useful (for those using instead of rejecting them).

Very exciting discussion. Please allow me to make a few points for consideration.

Point #1.
I think that Robert hit on some very interesting ideas here, not very new, but interesting in the way he tries to apply them. As he says, this is a common way to calculate endgame boundaries and it does seem logical to extend this thinking to other positions. I agree with that, for what its worth. However - as in endgame studies, asking 'what is black count here' is only half of the question - most boundaries apply to both sides, and often one side's loss is another's gain.

What I mean by that is that while it is true that in the position RJ considers (lone 3-3 on empty board) there is a Black privilege of an extension forced by White approach, we also need to calculate the value of that approach stone to have an overall picture. Otherwise we only calculate one side of the board (which can be an interesting exercise by itself.) And it might well be that while Black can count on 8 points considering that, White's approach can be valued at 4, giving the net value of the initial 3-3 stone at 4 points - and then why not just call it 4 points to start with and save yourself all this fuss?

I am not a game theoretician by no means, so I am not sure if the above makes sense, but to my unlearned brain this way of thinking would be the most valuable in terms of actual application. So it might be that Lee's evaluation of 4 points is just a shortcut he applies to land in the approximate same spot.

Point #2.
Nobody, and I mean nobody - not even Lee Changho or Cho Chikun - plays the first move on 3-3 and then takes his abacus and starts calculating points. I think it would be ridiculous to think so, and because of that whatever is said here has at most academic value. At most we can hopt for is an indication of such method can be applied to a more realistic positions. And thus possibly the distinction between 4 or 8 points at such early stage is simply meaningless. Which brings me to my next point:

Point #3.
I can agree that a numeric value can be assigned to each move, right or wrong, early or late in the game. However, for the early moves, fuseki, and especially first corner moves, I think that the main value of the move is not how many exact points we assign to it but rather how it fits into the overall strategy. This is more likely to decide the outcome of the game than the distinction between 4 or 8 dry points for a 3-3 stone. So while the method proposed is surely interesting, I am not convinced of the value of it for this specific example.

Point #4.
Continuing from previous point - Whatever I see in books on positional judgement, whatever methods and numbers, I have always viewed them as some starting points for further consideration, both at the board or in theory. Most examples and positions given are presented to illustrate a specific principle to much weaker players, provide a simple-enough algorithm for unwashed masses, rather than scientifically decide on exact numbers. Its more about an estimate which should be easy enough to actually be ready for application in kyu games. Purely theoretical approach can be constructed, but it might vary from the more practical methods you can use at the board. Examples in life abound.

In theory, theory and practice are the same. In practice, however, not always so.

Point #5.
And lastly - if we all agree that knowing a more precise count allows you to make decisions about future plays better, we also have to agree that professionals are pretty darned strong. So it should stand to reason that their positional estimates are pretty darned good. Question is - do the books they write explain how they do it, or not? And do they explain it fully or, as stated above, just give the first step on the path, the starting point, which the pros then greatly refine in their heads during actual games. And if they refine it - then how? At a guess, I would not be surprised if they do pretty much exactly what RJ is suggesting here (although probably not quite that early in the game) - look at privileges and future plays and account for them as well.

It can also be valuable to consider if their skill is based on empirical or theoretical factors - I would assume its the empirical ones. Which makes me think - if our theory disagrees with our observations, there is something amiss. Might be we need to look closer or might be we need to amend the theory. But eventually they should converge, no? And if they don't, what is more applicable - empirical numbers or theoretical ones, especially if they disagree by such a seemingly wide margin?

Pretty interesting, all of it.

_________________
- Bantari
______________________________________________
WARNING: This post might contain Opinions!!

In the forcing exchange kakari for extension, each player gets 1 new influence stone. The difference of new influence stones is 0. Black's extension shows more clearly the territory the 3-3 stone has already had, while the white stone does not make territory in itself. Or, as Bill would put it, "sente gains nothing". Hence, in the abstraction of a neutral outside position, we can say that the value of the forcing exchange's two new stones can be ignored; their difference of territory and influence values is 0.

This forcing exchange is not like reductions gaining new excess influence value by leaning on a moyo. In that case, the defender plays only on the inside, while the attacker plays only on the outside.



No, see above.



Indeed nobody, only because I don't start with 3-3;)



It is very meaningful. In one corner, there is a 3-3. Elsewhere, there are other shapes. Now, for strategic planning, it makes a difference to have a correct or wrong territory count for the position.



Yes.



Nice observation:)

If your principles are set up to apply to any situation, and there is a situation in which you can't apply them, then I reject your principles automatically! They might be good principles for endgame positions, but that is only essentially because we can play out and evaluate all variations accurately and quickly. A single 3-3 stone is not an endgame position, and there is no use in calculating with it as if it is.


The reason I don't like this is:


...the endgame calculation in this situation is always based on the assumption that (a) white is strong on the outside (as is essentially always the case in endgame, and as you have drawn), (b) black will not sacrifice this group or allow it to be reduced further than necessary (as is almost always the case in endgame).

As for (a), purely practically, in the case of a single 3-3 stone, black will usually not allow white to become so strong on the outside that white can kill on the next move. Regarding (b), I'm sure someone else can give you a whole-board endgame position in which something that looks locally like white's assumed sente privilege (e.g. because if black tenukis, black dies) is actually gote (e.g. because black's best response is to tenuki and allow white to kill for a trade elsewhere). In this case, the 'current territory' - if you like - for black in that corner would (or should, if it's to be useful!) be zero - but you can't tell that locally. I believe this more accurately mirrors the nature of a single corner stone.

I am not sure if I agree with that.
On an empty board with only 3-3 stone, the extension might not be very forced - there are certainly bigger moves elsewhere. Or, if as you suggest, other shapes may exist on the board, the dry points value of the White approach move might not be 0.

In any case - what we have here is very ephemeral: a unrealistic (for you, at least) first stone on 3-3, an unrealistic White approach (possibly on move 2, which would make it completely unheard of), an unspecified existence of outside shapes (maybe they are there and maybe they are not, and who knows how they look like), and your out-of-the-hat assertion that the extension by Black is 'forced' without specifying the outside shapes.

What I am trying to say here is that you are right, as it stands, the three stones on empty board, you might think that your evaluation seems to be spot on. However - this is a very unrealistic scenario. And I still see problems with that.

More about the value of White approach move:
By extension of your own thinking, the White stone has to be counted for at least 2 points - after all, White will not let it die, so eventually it *will* end up with at least 2 1-point eyes. Just like Black will answer attempts to kill the 3-3 which have to be taken into account. At some unspecified time in the future... one could say that the 2 points for the single White stone is White's privilege.

And another thing:
In endgame boundary plays, the privileges are limited by playing out the edges to their conclusion. In early stages, like in this example, can't they be taken a step further to make even more exact calculations? I hinted at that with my previous paragraph, but here is an idea - as it stands, one could argue that it is now White's privilege to either extend from his approach stone (thus making points, just like Black did - which would be a common move and even joseki) or at least use the stone to reduce Black's 8 points. After all, White does have the privilege to use his approach stone *somehow* for his advantage, or the stone would never have been played to begin with, no? So we have to take it into account when calculating the points value of White approach, just as we do for Black.

I consider it exactly as likely for Black to extend after the White approach as it is for White to *then* extend after Black extension. If Black's extension is calculated in when determining the value of 3-3, then White extension needs to be calculated in when determining the value of White approach stone, no?

If we continue this line of thought, Black will then end up with his own set of privileges, which again might change the count, and so on... Not sure how practical this all is, but I see no reason to arbitrarily stop calculating future privileges after Black's first move...

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- Bantari
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Fine, but I do not know such a situation:)



The use strategic decision making. If one knows that the global territory count is T points, one can choose strategy accordingly. If (because one introduces an X for the 3-3's unknown size of extra points beyond the 4 visually trivial points) one knows that the global territory count is T + X, then one can develop one strategy for X = 0, another strategy for X = 1, etc., another strategy for X = 4. Strategies for X = 0 versus X = 4 should be different! Reasonable strategy versus (possibly overplay) fighting strategy.



(a) and (b) can differ in infrequent cases, so I understand your disliking. Usual territorial positional judgement makes simplifying assumptions such as (a) and (b). It allows us to use such PJ at all. Since you don't want it, go with Redmond and read out game sequences to the imagined game ends:)



Sure. For this reason, PJ is designed for the opening and middle game, while the endgame requires 1) endgame calculations or endgame reading or 2) PJ modified by overriding endgame considerations.

PJ is used when pure endgame calculations for the whole board are still too complex to be used.

Good objection, except that you might actually be wrong: if the game starts 3-3, kakari, tenuki, pressing lets the 3-3 sacrifice look bad, IMO.

In an actual game, also a black pincer could be the correct answer. PJ demands a somewhat idealised world.



Supposing good timing for the kakari, and we can assume that White finds some some timing, surely Black must answer. In an actual game, Black can choose his answer from extension and pincer. In current territory PJ theory, Black answers peacefully; this is the extension.



It is unrealistic, because you require the first imagined timing. Theory of privileges is more generous to allow some suitable timing.



Nope. You make a mistake here: Black would be attacking and gain more extra points than the 2 one-point eyes of White's group. White would be generating negative territory. Let us be more generous and assume 0 points for the white stone!



Iterated PJ would become a proceeded game or like endgame calculations. The advantage of PJ to be fast would be lost entirely.

Hi Robert,
I comment on some of the points you make, just for flavor, but my main content is on the bottom, in the PS - so unless you find my intermediate comments of great value, I suggest we just restrict the discussion to the two main contention points I make on the bottom of my post. Otherwise the thread deteriorates to sentence-by-sentence discussion which might just dilute what's important. Especially since my PS pretty much just reiterates the rest of my post, which can simply be seen as an extension of the points I make in the PS.



I dunno... the 3-3 will not be dead after two white moves, and Black will get two moves elsewhere. If White wants to kill the 3-3 he would need to add another stone, which will allow Black to play elsewhere for the 3rd time! This might or might not outweigh the loss of a corner, depending on where the Black moves would be.

This is usually, among other things, why White does not approach the corner on move 2 - it is too small and might not be not sente. Thus the answer might not be forced.



Timing assumes 2 things:
- other shapes on the board, in which case White approach will surely not be worth 0 points, and
- the timing (and side) is chosen by White, wich would also assume that the approach stone has a better value for White than to make Black 3-3 stone stronger.

So I am not sure how you can claim things like 'timing' on White's part and the point value of White's move to be 0. The assumption of 'timing' itself has to imply the value of White approach to be non-zero or White would never have played there.



But then, as said above, the timing should also apply to White's privilege, especially since it is White who picks the time here. You seem to be applying it only to Black's advantage. I understand 'idealizing' a scenario for argument's sake, but I think this is too one-sided.



I think you make a mistake here.
It stands to reason that each White move will balance the Black move more or less (we do not know to what extend unless we know the outside shapes and the exact timing.) And it also stands to reason that eventually White can count on ending up with more (much more?) then only two points out of this stone. I was being generous for Black here.

In any case - this is not really my major objection to what you say.

Generally speaking, I can't get over two issues here:
- as mentioned before, the approach is played at White's timing, so it cannot only favor Black, and
- as mentioned before, you seem to be assuming existence and then non-existence of outside shapes, willy-nilly as it suits you.

To me, logically and realistically, we have to say that:
- either unspecified outside shapes exist, in which case we simply do not know the value of White approach, but assuming White is half-way competent it will surely be more 0 points. With half-way good timing and direction sense, it might even be more than the added value of Black extension,
- or no unspecified outside shapes exist, in which case there is no way White will play the approach on move 2 but take another empty corner which is larger, and wait for proper timing (i.e. unspecified outside shapes) to make the approach - which brings us to the 'either'-part.



Sure, I said so too, but why not at least apply the method to the whole logical and natural local sequence?
Black 3-3, White approach, Black extend, White extend, Black tenuki, White tenuki. Seems like the count should be applied to *this* position, not at some arbitrary intermediate point. I don't think you have addressed that yet.

When I look at the end of the natural sequence described above, I see Black 8 points, White 4 points, net value 4 points - which might be a good number to give the initial Black move.

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PS>
So, to summarize, and give more focus to the discussion, my main points of contention are:

Point #1. The whole outside shapes and timing paradox:
You seem to require the outside shapes for timing to claim forcefulness (as in 'White choses the timing to make Black extension forced') but then deny the outside shapes to dismiss the point value of White approach ('the point value of White approach is zero or even less.') It seems to me that, idealized or not, we should at least be consistent and say that either outside shapes and timing and forcefulness are relevant concepts here, or they are not - and then stick to what we decided. Whatever we decide, though: either White approach is silly and Black extension not forced, or the value of White approach is more than 0 points. One of these positions should be the start of any reasonable analysis of the (partial?) position, I say.

Point #2. The completeness of the sequence:
I don't see how you can decide to calculate points value in the middle of a natural sequence, claiming some moves are forced (Black extension) while others are not (subsequent White extension) with very little, if any justification. It is my feeling that this arbitrariness can create a lot of confusion, if not in this particular example (where the natural sequence is like 2-4 moves long, depending when you start looking) then surely in other cases where natural sequences are much longer. The position needs to be evaluated at the end or such sequences to be useful not at some arbitrary intermediate points to force a specific numerical value.

It seems to me that you are trying to adjust the facts to fit the theory instead of doing it the right way.

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As long as you think those two are the same, it's not really worth discussing. You're taking to different positions and doing positional judgement only on the second.

The two space jump may be played but it's not forced. A one space jump may be preferred or a tenuki may be playable. I'm not arguing 4 points + alpha is absolutely the corner, but it's reasonable to use. You are modifying the position and giving a different score. There's not much surprise there.

But, yet again, why? I can see that these assumptions make your calculations possible, but that's not a good reason to use them, given that they don't bear any relation to gameplay. Please give me an example of how I would use such a calculation. I can't see how attaching the number "8" to the corner in question tells me anything about go. Even if I play in the absurd way that your simplifying assumptions talk about, white also makes points during the kakari / reduction process, which don't seem to have been taken into account.

The basic context of outside shape is to be dynamic and represent (in an idealised form) the attacker's supporting stones occurring in good timing. (Some reduction moves do not get any supporting stones, because a good timing cannot be justified.)



The White extension is a local gote and so breaks the conceptual permanent sente of the attacker. By doing so, you continue the game or perform endgame analysis, but do not perform (the local part of global) positional judgement.



(Answered earlier.)



Currently, the position with only the 3-3 stone is analysed.

This brings is to another principle [4]:
"Usually, the defender is only interested in defending his own territory and is not interested in reducing any adjacent territory of the attacker. Similarly, the attacker is only interested in reducing the defender's territory and is not interested in increasing any of his adjacent territory."

(Note the "usually": if it cannot be avoided in the reduction - blocking process, then exceptions are possible.)

Here, the second half of the principle applies: we do not assume that the White kakari makes / increases White's own adjacent territory.

On average and in an idealised world, the principle is fair, because a) defender and attacker act conversely and b) when the players switch their roles, the same principle applies.

Here, you complain about White not making territory while reducing. But you must be aware that, when the players switch their roles and Black reduces the white regions, then also Black is assumed not to make territory while reducing (some region of White elsewhere on the board).



Consistency lies in the aforementioned symmetries and fairness of the principle.



It lies in the overall design of current territory PJ, which consists of two separate steps: 1) analyse the black regions, 2) analyse the white regions.

Within either step, the players assume and perform their roles of defender or reducing attacker.

This overall design is axiomatic. (And it then allows to calculate the difference of Black's minus White's points.)

Given the overall design and the players' roles in either step, one can then, IMO, derive - from the axioms justification of a kind you are wishing. (No time today to work this out in detail.)

I do not. Please read the first post carefully again. One diagram is for showing how not to do it - the other diagram is for showing how to do it.

Your diagram showing how to do it is incorrect in my opinion.