Territory Value of the 3-3 Stone

[billywoods]

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.

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.

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

The reason I don't like this is:

$$B assumed privilege exchange
$$ -----------------------
$$ | . . . . . . . . . . .
$$ | . . . . . . 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]

...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.

[Bantari]

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.

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...

[RobertJasiek]

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!

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

A single 3-3 stone is not an endgame position, and there is no use in calculating with it as if it is.

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.

...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

(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:)

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).

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.

[RobertJasiek]

On an empty board with only 3-3 stone, the extension might not be very forced - there are certainly bigger moves elsewhere.

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.

your out-of-the-hat assertion that the extension by Black is 'forced' without specifying the outside shapes.

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.

the three stones on empty board, you might think that your evaluation seems to be spot on. However - this is a very unrealistic scenario.

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

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.

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!

can't they be taken a step further to make even more exact calculations? [...] one could argue that it is now White's privilege to either extend from his approach stone (thus making points [...] 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. [...] I see no reason to arbitrarily stop calculating future privileges after Black's first move...

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

[Bantari]

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.

On an empty board with only 3-3 stone, the extension might not be very forced - there are certainly bigger moves elsewhere.

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.

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.

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.

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.

the three stones on empty board, you might think that your evaluation seems to be spot on. However - this is a very unrealistic scenario.

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

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.

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.

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!

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.

can't they be taken a step further to make even more exact calculations? [...] one could argue that it is now White's privilege to either extend from his approach stone (thus making points [...] 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. [...] I see no reason to arbitrarily stop calculating future privileges after Black's first move...

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

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.

___________

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.

[oren]

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).

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.

[billywoods]

Usual territorial positional judgement makes simplifying assumptions such as (a) and (b).

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.

[RobertJasiek]

you seem to be assuming existence and then non-existence of outside shapes, willy-nilly as it suits you.

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.)

Black 3-3, White approach, Black extend, White extend, Black tenuki, White tenuki.

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.

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.

(Answered earlier.)

Point #1. The whole outside shapes and timing paradox:
You seem to [...] deny the outside shapes to dismiss the point value of White approach

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).

we should at least be consistent

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

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 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.)

[RobertJasiek]

As long as you think those two are the same

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.

[oren]

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.

[RobertJasiek]

billywoods,

"not bearing relation to game play": This can be said about any analysis, whether positional judgement, endgame analysis, life and death status assessment or something else. Usually, actual game play differs. Nevertheless, we use analysis because it guides decisions. - Besides, you are exaggerating. PJ sequences have relation to game play, as it COULD occur, when taking into account that the intermediate moves elsewhere or in a near environment as close supporting stones occur, too.

"example of using a calculated territory count": (Before the congress, I do not have the time to edit diagrams. So now I can only mention the possibility to read the literature and now give a short draft of usage.) Suppose we have (incl. the komi, of course) determined the territory count T in Black's favour, aji is irrelevant, White has the turn and slightly superior influence and development potential. We can use the information as follows: in the still unplayed parts of the board, White must aim at getting at least T new points more than Black. (BTW, this is straightforward, but I have seen 4d players not being aware of such strategic planning at all.)

EDIT:

It is also useful to know which are and which are not the counting territory intersections! Strategy is related also to gaining new, additional territory intersections. By knowing which one already considers to be territory, one can then meaningfully plan for additional intersections and identify them as such, when they occur.

[Bantari]

I dunno, it still seems terribly artificial and slightly contradictory to me, not to mention one-sided.

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.

Ok, so you seem to be saying that because of some undefined outside shapes White's attack is performed with good timing, but at the same time refuse to acknowledge these very same outside shapes to evaluate the value of White approach. What's more, as you stated above, the value of White approach is less than zero (when I claimed it should be at least 2 points since we assume it will not die, you pointed out at added Black points due to future attacks on it.) Even putting aside the appearance and then disappearance of outside shapes, two questions beg to be asked:

1. Why would White make the approach move, apparently with 'good timing' as you claim, if this move loses White points? It loses points since it strengthens Black (by 'forcing' him to add another stone in good placement) and the actual value of White stone is negative (according to you.) It seems to me that because of this, White approach is a very poor play which should never be made in the first place. So maybe Black actually have a privilege of playing extension on *both* sides of the 3-3 stone and so has much more than 8 points there?!?

2. How come we dismiss any value of White attacking stone but at the same time can firmly claim values from potential future Black attacks? You seem to be using both to evaluate the same sequence. You claim Black profit from both attack (future attacks on White approach stone) and defense (actually answering to the White approach stone) while at the same time deny White any value from attack and any possibility of defense (his own extension.)

I am also not sure about this whole 'conceptual permanent sente of the attacker.' I mean - why would I attack every if you deny me the ability to actually make points out of the attack? Most, if not all, of the attacks either already have a back-end base to support it and make profit, or the attacker will have to come back at some point and play a gote move at some point. Even if your attack kills a group, I would assume a competent opponent does not die in gote... Or the opponent is really weak, which I think we can agree to dismiss here.

Or are you saying that White *will* make some profit out of the attack/approach, but we just conveniently refuse to include this in our calculations?

In general, what I see you claiming is that you came up with an axiom (I calculate this and nothing else, and I do it exactly like that and no other way) - out of your hat from what I see - and then point to that axiom to dismiss each and any objections or questions. And just because your calculation happen to give you some solid number which happens to differ from the usual evaluations, you claim the superiority of your method.

Expanding on the way you do things, what would prevent me to claim that 4-4 stone is worth 18 point by pointing to the following diagram:

$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
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$$ | . . . 5 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 1 . 4 . . . , . . . . . , . . . |
$$ | . . . . 3 2 . . . a . . . . . . . . . |
$$ | . . . . b . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
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$$ | . . . 5 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 1 . 4 . . . , . . . . . , . . . |
$$ | . . . . 3 2 . . . a . . . . . . . . . |
$$ | . . . . b . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

We have here Black 18 points in the corner, we neglect any White profit from the attack, and we can certainly say that White can use 'good timing' to play '2' and that it is certainly Black's privilege to play '3' and '5' and so on... If you have concerns about any possibilities in the corner (which you should also dismiss, like you dismiss the possibilities of further White attacks in your example) then you can add the a-b sequence with the same result.

Anyways - this is how I calculate it, and my calculation has the advantage over everything else I have seen in this respect because it gives you a precise number which is exactly 18 points, no more and no less. It does not rely on artificial 'boxes' or line drawing, and is based on actual play, timing, and guaranteed privileges. Now you have the tool to exactly calculate the board after you play 4-4 and exactly evaluate your strategy after your opponent makes this move.

Or I can use a different sequence and assign different value to a 4-4 point, just tell me a number you want and I will try to come up with iron-clad justification to satisfy your number. Its a virtual world, after all, and the trick is to know - there is no spoon.

[Bantari]

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.)

Alright, I can get along with that. But then Black's 8 points are only half of the story, right? I mean - sure, we can calculate 8 points the way you say, and the number is good, but then we have to calculate the White points and subtract the two numbers to have the real picture. Otherwise, what is the point of it?

To me it only makes sense (or has any practical value) if we calculate both sides and then determine the balance. To know that Black has 8 points without taking into account how much White makes is useless since it does not help me to decide my future strategy. Its like saying: "in this position, Black has 47 points exactly, now what is your strategy" without also telling you how many points White has and all kinds of other things as well. Its useless other than in the neat fact that it gives you a solid number you can hang your hat on.

To me, for a calculation to have any practical value you cannot perform it in the middle of a forced sequence and you cannot only calculate one side.

So, the way I see things is thusly: Sure, Black has the privilege to make the extension one way or another, but this extension is induced by White approach. And White will never make the approach unless it gives him something as well - in particular, arguably, White will never approach without the approach stone having at least as much value as the Black answer adds to the Black count. Therefore, we simply cannot dismiss all the value of White approach when calculating the result. And the result is that either White approach fits well with outside shapes (and this is its value) or White will next play the extension of his own, making his own 4 points which have to be calculated as well.

I absolutely do not see any point of only calculating only the Black side of the equation here and dismissing the White side completely. If we use future rights and privileges (which I think is a great idea in itself) - we simply *have* to apply the same principles to both sides, and we *have* to look at complete sequences when they are natural and/or forced. Otherwise it makes no sense, even if you do get a fixed number.

Realistically, when you evaluate the first move at a 3-3 point, you have to think: what *net* points can I potentially count on in this corner? And to be simplistic, we can look at the most likely scenario, of 'how will it most likely develop' which is this:

$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 1 . 2 . . 4 . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 1 . 2 . . 4 . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

And then you can say Black has 8 points, White has 4 points, so for evaluation of future strategies I have to count the net as 4 points - which gives me the point advantage I will most likely have here due to my 3-3 move. It makes no sense to neglect the value of White '2' (i.e. the natural extension at '4') and what's more, it gives you a skewed result. In real practical game, you will *never* get Black 8 points to White 0 points out of the initial 3-3 stone - especially when you yourself agree that White will pick the right (for him) timing of the approach and the undetermined outside shapes will support this timing.

I think to look at this position as you do can be terribly misleading since it inflates one side of the balance without accounting for the other. Supporting your strategies with such thinking is not advisable, I think.

[Bantari]

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;)

This tells me two things:
#1. You consider yourself the most conscientious counter in the world (if you don't do it, nobody does.)
#2. You do not calculate your opponent's points (surely it must happen that 3-3 is played against you on occasion.)

To #1: Not sure what to say to that. A little more modesty? Ever thought you are overdoing it? Loosen up a tad bit, maybe it will help your game?

To #2: This pretty much fits with the rest of your statements in this thread - of calculating only one side of the position while neglecting and denying the other. So two thumbs up for consistency here. But again, I don't think this approach helps your game much.

[Bill Spight]

Realistically, when you evaluate the first move at a 3-3 point, you have to think: what *net* points can I potentially count on in this corner? And to be simplistic, we can look at the most likely scenario, of 'how will it most likely develop' which is this:

$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 1 . 2 . . 4 . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 1 . 2 . . 4 . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

And then you can say Black has 8 points, White has 4 points, so for evaluation of future strategies I have to count the net as 4 points - which gives me the point advantage I will most likely have here due to my 3-3 move. It makes no sense to neglect the value of White '2' (i.e. the natural extension at '4') and what's more, it gives you a skewed result. In real practical game, you will *never* get Black 8 points to White 0 points out of the initial 3-3 stone - especially when you yourself agree that White will pick the right (for him) timing of the approach and the undetermined outside shapes will support this timing.

If this is how you evaluate then you are saying that it is a 6 pt. double sente (10 - 4 = 6), which is absurd. You cannot even say that the territory part of the value of is double sente. is gote, so to evaluate it by adding plays you either have to add the same number of stones for each player or use the average of two diagrams.