Why not at 'a' or 'b', or even 'c' if one is not concerned about strengthening white for this purpose? isn't even the most common pro joseki response in this situation (that would 'a') To me, it seems as if the choice of is every bit as arbitrary as Lee Changho's lines to the side.



This is the most radical idea yet. So, in this imaginary world where you have to answer of your opponent's moves passively, for the sake of calculating some kind of secure territory figure, are you actually suggesting that if the space is too small to make a living shape after those reductions, then one is then permitted to dance off in the other direction to get more eyespace? If that is allowed, why is it allowed only when the eyespace is too small and not when it is larger?

In my previous post I already showed that passive answers to attacks to the two-space extension result in a dead shape for white. By the argument you give, white will now dance off in a different direction, in which case the two-space extension would be permitted to be analyzed something like this, and not like the 4-point dead shape I showed earlier.

Click Here To Show Diagram Code

[go]$$B Freedom!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . 9 . , . . . . . , . . . . . , . . . |
$$ | . 0 2 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | 6 . 8 , . . . . . , . . . . . , . . . |
$$ | 5 4 O . . . . . . . . . . . . . . . . |
$$ | 7 3 . . . . . . . . . . . . . . . . . |
$$ | . . 1 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Which is it? 4 points or something closer to 9? Maybe I'll ask King Friday when I get off the trolley in the land of make-believe...

(You mean "Black 2" rather than White 2".)

Positional judgement according to my method relies on principles for the nature of reduction sequences. The purpose of setting principles is to ensure the same kind of moves for evaluation of all regions. I think that such consistency for all regions is good, because regions are treated likewise regardless of their shapes.

The principle used for the decision between Black 2 or Black A is [4]: "Subject to the other conditions, the defender's territory is minimised by the attacker and maximised by the defender." Here, the defender moves, so he maximises his territory, while abiding by the other principles' conditions. You might ask why "maximised". It is derived from ordinary strategy due to the game aim: a player wants to maximise his own territory, while the opponent wants to minimise it. Black 2 maximises, while Black A would not maximise.

If Black 2 is one space farther to the right, then Black does not maximise his territory, but offers White a chance to invade at A.

A few of the other conditions I have already explained in earlier messages. Direction change to maintain life plays a role here.



Black B (or C) does not maximise Black's territory, because then White can better reduce as follows:

Click Here To Show Diagram Code

[go]$$W Black wants too much, Black 10 at x
$$ ------------------
$$ | . . . 8 7 9 . . .
$$ | . . . . 6 5 . . .
$$ | . . X x 4 3 . . .
$$ | . . . . X . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Black maximises better if instead he plays at 2.



Such considerations are considered immaterial in territorial positional judgement. Imagine supporting white stones according to these my principles [4]:

"The life of string-connected or directly connected reduction plays does not need further justification.

If the attacker has only remote support by friendly stones, his early reduction plays are accordingly reasonable.

If the attacker has only remote support by friendly stones, his later reduction plays rely on imagining supporting stones that can reasonably be assumed to have been played earlier. Later, more such supporting stones can be imagined."



(You mean "Black 2" rather than White 2".)

Territorial positional judgement does not care for empirical frequency. Quite like life and death status analysis does not care for whether plays elsewhere on the board might be more urgent than locally defending the life of a small group. You also would not question life and death status analysis just because it does not answer the question for globally perfect play, wouldn't you? Analysis sequences serve the purpose of enabling answering analysis questions. They do not (necessarily) suggest perfect play on the whole board. This difference in objectives does not make analysis invalid. We use analyses all the time, because we believe that answering analysis questions is helpful for better developing strategy. Answering analysis questions for territorial positional judgement is a special form of helpful analysis.



Lee, in his book [1], does not offer any justification for his line drawing. I, for my method [4], use principles, such as those mentioned, and explain why those principles make sense for the purpose of making territorial PJ. Principles and explanation are much less arbitrary than no principles and no explanation.



The purpose of territorial PJ is assessment of existing territories. Always allowing direction changes would... (I have already explained in earlier messages.)



This is indeed a question one can come up with. The two-space extension or similar shapes require an exception to one's thinking. The usual go theory thinking about the 2-space extension applies also in PJ: it is considered alive because of having 1 eye and several running directions. The imagined reduction plays do not change the life potential: running directions are replaced by break-through directions.



No, because White need not, because the white group is still alive. Dancing off is an exception only for the last moment of defending threatened life.

Also here, like in every other PJ sequence, the objective is NOT perfect play in ordinary game playing. The objective is territorial PJ of the defender's territory regions.

For Black's moves, apply my principles supposing supporting stones. It is reasonable to assume them, because, at a time when every black reduction move would be played, Black would already have got supporting stones played earlier. The PJ reduction sequences show only the local moves incl. the early local moves, the intermediate timing local moves and the late local moves; the sequences do not show the intermediate moves "elsewhere" on the board. It is a very convinient abstraction to consider only the local moves and ignore (but presume) the remote moves.

You do the same in life + death status analysis combined with endgame value analysis: you consider ONLY the local moves (except maybe for virtual, symbolic ko date moves), but IGNORE the remote moves.

Local-only is what makes local analysis feasible at all. The complexity is reduced so much that it can be done.



1) My principles provide a pragmatic justification for validity.

2) One makes the axiomatic assumption of ignoring global side effects. There is no justification in axioms themselves, because one starts from axioms. One just needs to understand the limitations implied by the made axioms.

A locally analysed life + death problem can, by axiom, be solved locally. Nevertheless, in a real game, global side considerations (such as double threats) can alter a purely local consideration. This does not prevent us from solving local LD problems. Likewise, we need not prohibit local-only territorial positional judgement. (Except that, I recommend whole board reduction sequences with good timing, so that at least the most relevant double threats are considered.)



Axiomatic principles are being offered by me. (I would wish, professionals would offer and state explicitly theirs for PJ, too. I do not share Kirby's view that professional analysis would be better, just because it is suggested by a professional. To be better, there must be explicitly stated principles.)



It was "voodoo", until I have stated the relevant principles for the nature of reduction sequences.



Yes: my principles for the nature of reduction sequences. [4]

There are also ways of calculating influence:

- influence stone difference
- relating excess influence stones to the current ambient temperature
- applying all aspects of my formal definition of influence
- applying only the territory aspect of my formal definition of influence (Takagawa and Ishida appear to have done it implicitly, see GoWorld 41: imagine sequences of best use of thickness, then do territorial PJ)
- quiescience sequences, until most influence is converted into territory, then do territorial PJ



Rigorous ways exist (see above), but it would indeed be an exaggeration to call them "equally rigorous", because more methodical steps are needed.



Because you misinterpret it. You want it to be the global perfect play prediction of the final score. Be more reasonable and use a Current Territory method!

I'm not sure that I properly understand what this is about, but taking a stab at it, I sense two strands.

(1) It's talking about the exact value of a stone in terms that have nothing to do with Yi's book. Specifically, he does not talk about irreducible minimum territory (or current territory = territory so far) or influence, or value of a move. He talks about evaluation rather than counting, about prospective territory and development potential, and he stresses approximation and the practicality. It's fine to talk about the former, but it's necessary to, ahem, draw the boundary lines.

(2) Experience (or intuition) is discounted. This seems unwise. Some pros are demonstrably better than others in the difficult art of making early boundary plays, which means their experience/intuition has a specific value even if we can't explain exactly what it is. In fact, it is often possible to tease out a value post facto by asking an expert laboriously to list the factors he considered in making a snap judgement - see texts such as Daniel Kahneman's recent book on thinking fast and slow. You may object that for go such explanations are lacking. Well, step 1 is surely to read Yi's book, but there are (in my opinion) even better texts for that purpose. One I particularly commend is a long series by Sugiuchi Masao on the transition from the large boundary-play stage to the small boundary-play stage (subtitled as a way of dealing with the "common pasture" of much of the board). I think the approach here encapsulates what is wrong with much of the western approach where an attempt is made to attach static value to positions and also to attach a static value to the transition from LBP to SBP plays. In contrast, Sugiuchi stresses that this transition is a fuzzy and dynamic process where development potential (to use Yi's term) is at the forefront but, more so, where the order of play is the crucial factor. This does not mean order of play in terms of size of moves, but in terms of impact on the position, including safety and thickness. It is informed by counts of prospective territory rather than governed by them, and of course it is much more than the facile "I'm 10 points behind so I have to invade" kind of thinking.

For some reason or other there were quite a few very long series in similar vein, by the likes of Suzuki Tamejiro, Shimamura Toshihiro, Segoe Kensaku and others, in the 1950s, so that there is an abundance of examples that show how old-timer pros think in such cases, i.e. in Kahneman's terms how they explain their intuition. I'm not sure why we seem never to see such articles nowadays but, as a highly speculative guess, this was about the time when time limits changed drastically from things like 13 hours to 5 hours, and there was also a sharp increase in amateur tournaments with very short time limits. Maybe careful evaluation of this type was then considered to have less practical value until Yi re-discovered it. Today's Mickey Mouse time limits may send it back underground.

John,

- Experience can be useful. But for a pro player's experience to be useful for us, there must be a list of experience examples or an explanation how to seek on one's own or alternatively substitute by generalising insight such experience.

- Determination of a particular (current) position's static value(s) does not prevent additional dynamic considerations. Rather it can assist them. Besides, static values become dynamic by observing them at every moment of every dynamic sequence.

Each dynamic sequence is evaluated separately generally with the minimum territory as the basis until you get to the endgame where you can accurately determine the end game plays.

You seem to be confusing what Lee Changho and other professionals are doing with what you want to do which is why you would need to read the book.

oren, please see the answer in the go books forum.

What answer?

This is a logical explanation. I accept it. Thanks.



I still don't get why this exception is a good thing to have. Doesn't it have the effect of increasing the territorial estimate for groups that don't have much eye space?

Robert, with respect, it seems as though you are calculating something that we don't care about. That is why Lee Chang-ho gives a different value to you - he is not wrong, he is calculating something else. I suspect "Territory Value" is some phrase that you have given a rigorous definition, which is all well and good for you, but I disagree that your definition is a useful one, or (equivalently) I disagree that the name "Territory Value" is representative of how I might use the words "territory value" in conversation. I would also say that the territory value (not Territory Value) of the 3-3 stone was 4, and would mean something very specific by that, which is different to what you mean. This is probably why you are having such difficulty communicating with people in this thread. It is up to you to explain to us why we should agree that this is a useful number to calculate before browbeating us into accepting your bizarre calculation.

Why is unreasonable in the 1st diagram but is reasonable in the 2nd one? They are the same armpit hit shape.

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. )

Just kidding...

It is increasing, and bounded above by 361.

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.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

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.

White 1 in the first diagram is unreasonable:

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:

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:

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:

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:

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).

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.

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.

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



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.



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).



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



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



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.)



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?)



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:) )



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?



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).