Territory Value of the 3-3 Stone

[Bill Spight]

$$B half a chance?
$$ ------------------
$$ | o o o o o . . . .
$$ | o o o o o 3 2 . .
$$ | . 5 X 7 9 1 . . .
$$ | . 4 . 6 8 . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B half a chance?
$$ ------------------
$$ | o o o o o . . . .
$$ | o o o o o 3 2 . .
$$ | . 5 X 7 9 1 . . .
$$ | . 4 . 6 8 . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

While we're throwing out theories, I like the half a chance technique. Black has half a chance of playing because we don't know who has sente. After this, the peaceful responses to attacks result in 10 points. Just average with 4 point result if white gets to reduce first. That's 7 points. (Plus lower order terms as maybe after black has half a chance of playing another move. Don't ask me if the series converges. I was a physics major. I summed non-convergent WKB approximations for lunch. )

Oh, Black has much more than half a chance, because of miai. She could also extend towards the left side. However, White could prevent that with, say the shoulder blow on the 4-4.

[dumbrope]

Don't ask me if the series converges.

It is increasing, and bounded above by 361.

Nah. Fringe effects.

At some point, adding more stones to a strong position becomes too small to bother with. So your extensions become far and then interact with other stones on the board. I think the higher order terms would break down pretty soon. Personally, when I play the 3-3 point I am looking to play elsewhere for a while. Hence these fudge factors like the alpha of Yi Ch'ang-ho.

Bill's point is good. 50-50 is too pessimistic.

[RobertJasiek]

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

Click Here To Show Diagram Code

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

$$W reasonable attack and defense
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . 2 . . .
$$ | . . . . . . . . .
$$ | . . 1 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

Why is :w1: unreasonable in the 1st diagram but :w5: is reasonable in the 2nd one?

White 1 in the first diagram is unreasonable:

$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . 1 . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . 1 . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

For this to be a "reduction" at all, it requires the support of a nearby white stone played earlier, like this:

$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . b c . e .
$$ | . 1 . d . . . . .
$$ | . . a . . . . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . b c . e .
$$ | . 1 . d . . . . .
$$ | . . a . . . . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

During the opening, such a supporting stone does not occur, because either White would not approach the 3-3 or White would approach it with a usual approach move at 4-4, 3-5 or 3-6.

During the middle game, it is possible that such a supporting stone occurs because of a fight on the lower left side. However, it is pretty inconceivable that, if that supporting stone has occurred during the middle game, White 1 will be played as a "reduction" to the 3-3 stone, i.e., as a move reducing its territory. It is pretty inconceivable, because White 1 is the kind of reduction one does not play until the endgame. During the middle game, White would first play at a, b, c, d or around e, before playing at 1 as a "reduction".

During the middle game, there is only one conceivable case when White 1 could make sense:

$$W
$$ ------------------
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . X . . . . . . O
$$ | . 1 . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | O O O O O O O O O O

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . X . . . . . . O
$$ | . 1 . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | . . . . . . . . . O
$$ | O O O O O O O O O O[/go]

Namely, when White 1 tries to kill the black stone and White needs to do so. Even then, White 1 is not a "reduction" but a "killing move".

During the endgame, White 1 could occur. However, it would occur only if bigger moves were already played:

$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X X . X X . .
$$ | . 1 . O . O . . X
$$ | . . . . O . . . .
$$ | . . O . O X . . .
$$ | . . . O X . . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X X . X X . .
$$ | . 1 . O . O . . X
$$ | . . . . O . . . .
$$ | . . O . O X . . .
$$ | . . . O X . . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .[/go]

Here, during the endgame, White 1 has enough supporting stones to be played meaningfully; the stone lives, because it is directly connected to the previously played white stones.

White 1 would not occur (as a "reduction") before the bigger endgame or middle game moves. It would be unreasonable to consider an earlier White 1 as a "reduction" nevertheless.

As surely you notice, this is not an empty quarter of the board any longer.

*************************************************************

White 1 in the second diagram is reasonable:

$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . 1 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . 1 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

This White 1 is a reasonable reduction of the black corner formation, because White 1 is a joseki move. Now, that was easy:) More to the point, White 1 can be a reasonable "reduction", because it lives easily. Either because of earlier supporting stones further below down the left side, or because White 3 will defend White 1 in gote (as a middle game reinforcement, not as a positional judgement reinforcement), or because White wants to make privilege exchange and play elsewhere with White 3. In this case, the reduction 1 sets the strategic directions with a preference for White on the left side and a preference for Black on the upper side.

White 1 actually "reduces", because an exchange of White 1 for a common joseki answer Black 2 prevents Black 1 from building a corner enclosure, which would be worth more for Black (provided White 1 is or will be supported somehow).

[RobertJasiek]

I still don't get why this exception is a good thing to have.

It is an exception in the restricted context of methods applied for positional judgement. In a broader context, it is not even an exception:

1. Your stones must live.

2. With your living stones, you can make territory.

Having and maintaining life are a presupposition for making territory.

Doesn't it have the effect of increasing the territorial estimate for groups that don't have much eye space?

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

Click Here To Show Diagram Code

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

Reconsider your objection. Black 2 would never choose to die like this. Locally, Black always replies to the reduction White 1 by maintaining the black group's life by playing at 3.
I.e., Black changes the direction.

[RobertJasiek]

it seems as though you are calculating something that we don't care about.

It is your choice not to care about the most precise of the available positional judgement methods;)

That is why Lee Chang-ho gives a different value to you - he is not wrong, he is calculating something else.

1) In the specific example of a 3-3 stone in an empty quarter, Lee's "calculation" consists of counting up to 4 the number of intersections enclosed by his straight line drawing. Of course, this calculates something else: it is elementary school calculation of a 2x2 square:)

2) But, apart from counting the intersections within the square, WHAT IS Lee's "something else" that he calculates?! It cannot be the secure territory intersections, because there are more than four of them in this corner. What it can be is the subset of the secure territory intersections being within the drawn square surrounded by the straight lines. Now, FOR WHICH PURPOSE would one ever consider such a subset? How could such a subset be compared to other territory regions on the board, where one counts ALL secure territory intersections (and not just an arbitrary subset)? What is wrong with forming such a subset is that it does not have any good meaning for applied interpretation! It does not help that Lee does not make a mistake in counting 2x2 = 4.

I suspect "Territory Value" is some phrase that you have given a rigorous definition,

No. It is an informal phrase. The (more) formal terms are "territory count" (invented by the CGT people) and "current territory" (motivated by Cho Chikun, defined by me).

I disagree that your definition is a useful one,

Cho, Lee, Shikshin and I consider it useful. It is your free choice to disagree:)

or (equivalently) I disagree that the name "Territory Value" is representative of how I might use the words "territory value" in conversation.

This is not equivalent to what is the definition of current territory.

I would also say that the territory value (not Territory Value)

Sure. Usually, one writes terms with lower case letters. (There are exceptions, e.g., to introduce to the reader the fact that the phrase is meant to be a term.)

of the 3-3 stone was 4, and would mean something very specific by that,

WHAT is it that you mean by that? After answering this question, how do you apply your meaning to every other territory region? Why does it make sense to consider all the regions on the board with your meaning?

(FYI, considering current territory allows consideration of all regions of a player, because the sente requirement allows construction of global reduction sequences with meaningful timing. Can your other meaning achieve the same or more?)

which is different to what you mean. This is probably why you are having such difficulty communicating with people in this thread.

The difficulties arise because the 3-3 in an empty quarter is difficult, because 1) it does have an empty enviroment and 2) it requires a direction shift. So, for readers in this thread not having grasped the basics of positional judgement sequences yet, it is more difficult to understand the basics together with the advanced conceptual details also needed for assessing the 3-3.

It is not surprising that earlier professional players (IIRC, such as Kajiwara or Cho) just made "random" declarations of the kind "is worth 5 points [of territory]", which were probably motivated by the komi used at those times.

(It is particularly strange that Lee falls back to 4 komi times:) )

It is up to you to explain to us why we should agree that this is a useful number to calculate

Because the number is meaningful, because it is calculated due to application of the (same) principles, with which territorial positional judgement is possible for every position and every region in it. Do you or do you not agree to the (partial selection of the) principles for positional judgement I have cited so far? Do you or do you not agree that having principles at all is better than voodoo guessing of which are the territory intersections? BTW, the first principle for the nature of reduction sequences in positional judgement is:

"Reduction sequences are imagined." [4]

The second is:

"Maintain the attacker's sente." [4]

Do you or do you not agree to these principles?

before browbeating us into accepting your bizarre calculation.

The calculation is not bizarre, but just an application of the methods always applied, except that here a) one really needs to recall that maintaining life indeed is a presupposition of territory and b) principles for supporting stones justifying reasonable reductions or exhibiting unreasonable reductions require more careful application than in easier examples with almost settled territory boundaries (where the same principles apply, but everybody understands faster why they do apply).

[RobertJasiek]

removed contents of double post

[RobertJasiek]

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.

[RobertJasiek]

$$W continuation
$$ ------------------
$$ | . . . . . . . . .
$$ | 8 . . . . 6 5 . .
$$ | 7 4 X . . X . . .
$$ | . 3 . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

[why is] :w5: [...] reasonable in the 2nd one?

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:

$$W continuation
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . 5 . .
$$ | . X X . . X . . .
$$ | . O . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

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.)

[dumbrope]

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.

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.

[billywoods]

It is your choice not to care about the most precise of the available positional judgement methods;)
...
Cho, Lee, Shikshin and I consider it useful. It is your free choice to disagree:)

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

But, apart from counting the intersections within the square, WHAT IS Lee's "something else" that he calculates?!

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).

This is not equivalent to what is the definition of current territory.

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.

how do you apply your meaning to every other territory region? Why does it make sense to consider all the regions on the board with your meaning?

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.

Do you or do you not agree to these principles?

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.

[RobertJasiek]

oren, RBerenguel think that one, most or all diagrams in
http://www.lifein19x19.com/forum/viewto ... 44#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.

$$W upper left corner, 3-3 stone
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

No stone is added.

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

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. (*)

$$W reasonable attack and defense
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . 2 . . .
$$ | . . . . . . . . .
$$ | . . 1 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

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).

$$W continuation
$$ ------------------
$$ | . . . . . . . . .
$$ | 8 . . . . 6 5 . .
$$ | 7 4 X . . X . . .
$$ | . 3 . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

Same as *.

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

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.

$$W upper left corner, 3-3 stone
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

No moves are added.

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

Click Here To Show Diagram Code

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

Same as *.

$$W upper left corner, 3-3 stone
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

No moves are added.

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

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.

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

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.

$$B Black's points
$$ ------------------
$$ | . . . . . X . . .
$$ | X X . . . X O . .
$$ | O X X X X X . O .
$$ | O O . O O . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .

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.

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

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 (*).

$$B White's points
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . X . . .
$$ | X X . . . . . . .
$$ | O O O . . . . . .
$$ | . . O X . . . . .
$$ | . . O X . . . . .
$$ | O O O . . . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .

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.

$$B
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . X . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

No moves are added.

$$B
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

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

No moves are added.

[RobertJasiek]

I suppose that's not much harder than calculating common endgame sizes

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.

[RobertJasiek]

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

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.)

[...] that stone [...] will surround 4 empty intersections, and they will be those 4 intersections in the corner.

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.

definition [of current territory]. You must justify its usefulness before anyone will adopt it.

E.g., Cho Chikun and Lee Changho have used it and almost all my related principles for decades:
http://www.lifein19x19.com/forum/viewto ... 12#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.

What is the territory value of a lone tengen stone, or a lone 5-7 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.)

If you come up with any precise answer for that under your definition, what you're doing is nonsense.

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;)

Do you or do you not agree to these principles?

I do not. Nobody plays go by sticking a stone in a corner

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.

and then leaving it there until one move before it dies

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."

and defending minimally,

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).

so your principles do not calculate anything useful.

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

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

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.,

$$B assumed privilege exchange
$$ -----------------------
$$ | . . . . . . . . . . .
$$ | . . . . . . X O . O .
$$ | . . . . . . X O . . .
$$ | . X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .

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

$$B wrong assumption
$$ -----------------------
$$ | . . . . . . 1 . . . .
$$ | . . . . . . X O . O .
$$ | . . . . . . X O . . .
$$ | . X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .

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:

$$W assumed privilege exchange
$$ -----------------------
$$ | . . . . . 2 1 3 . . .
$$ | . . . . . 4 X O . O .
$$ | . . . . . . X O . . .
$$ | . X X X X X X O . . .
$$ | . X O O O O O O . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .

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:

$$B current territory: circles
$$ -----------------------
$$ | C C C C C x . . . . .
$$ | 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 . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .

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.

which under any reasonable calculation makes it 4 points per stone.

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.)

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.

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.

That is why I propose that you stop trying to precisely axiomatise something that is necessarily vague and undetermined.

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).

[Bantari]

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.

[RobertJasiek]

we also need to calculate the value of that approach stone to have an overall picture.

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.

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?

No, see above.

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.

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

the distinction between 4 or 8 points at such early stage is simply meaningless.

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.

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.

Yes.

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

Nice observation:)