Using my definition techniques for semeai-eye [6], I try to define nakade [shape] for arbitrary positions, regardless of whether the nakade is adjacent and only adjacent to the defender's stones (gaps in the boundary must be possible) and regardless of whether the group's eyespace equals the nakade or has further regions. This is a typical characteristic of life and death problems: one can try to transform one part of the eyespace into a nakade and eliminate the eye-building potential of the other parts.


A _nakade_ is a region of connected intersections so that

* if each intersection adjacent to the region is occupied by the defender's stone with an outside liberty and the players play only within the region, the defender moving first can necessarily fill all but one of the intersections of the region,

* if each intersection adjacent to the region is occupied by the defender's stone with an outside liberty and the players play only within the region, the defender moving first cannot necessarily permanently partition it into at least two regions,

* if the initial position is the starting position, the players may play anywhere and either player tries to prevent the other's new independent life, neither player can force occurrence of a seki or ko ban involving the region, and

* if each intersection adjacent to the region is occupied by the defender's stone without any outside liberty, the players play only within the region, and either player tries to prevent the other's new independent life, neither player can force occurrence of a seki or ko ban involving the region.



Each bullet point is studied separately. Each relies on assumed hypothetical conditions, which idealise the enviroment and localise the study of the region. An impossible condition is skipped (no outside and no inside liberties). "Necessarily" is an informal alternative word for describing the same as "force" in its mathematical sense. In the second bullet point, "the defender moving first" avoids unstable eyes, which would occur if the defender moved second in that bullet point. Each of the third and fourth bullet points needs to be applied possibly twice, once for each instance of "neither player" moving first trying to force.

I am not convinced yet that the semi-formal draft is final, all conditions are needed and no further condition is needed. However, I think that the draft must be much closer to a good accurate definition of nakade than seen earlier anywhere in the literature or the web.

Comments?

Your use of "nakade [shape]" shows you are aware of the problem that informal western use of nakade is corrupt. Moreover, since a nakade is just a "move inside" it can be used in cases other than depriving a bulky shape of two eyes, for example a cut or placement after ishinoshita.

If a piece of research is to be serious, I think you should keep the potential to involve oriental researchers using the term properly. Maybe you need to resurrect Davies's term "bulky".

I do not care if Western use is a "corrupt" derivation of Asian use of the word. There are different uses, and it does not matter if an Asian or Westerner uses them. What matters is whether a particular use with a particular meaning makes sense in a given context. There are applications for referring to a shape and other (possibly related) applications for referring to a play. One such use refers to a play I prefer to call "creating a nakade [shape]". Informally among Westerners, such is sometimes called a "nakade [play/move]" or "nakade play/move" spoken explicitly.

My current study purpose refers to regions that cannot be partitioned. So when you mention "just a move inside", this must be a different use of the word nakade, which, at the moment I am not studying. (It is also interesting for studying, but for other reasons: to discuss inside versus outside.)

A placement after ishinoshita (its exciting form) and other things must be considered to see whether a definition for nakade shape works properly there.

Have Asian researchers studied nakade shape (Western use) to find an accurate definition, with which results thus far? For my current study, I need not rely on linguistic findings.

"Nakade" has been used so much that I do not see a need for "bulky". (I see a need for another term for a related concept, but that would be another topic.)

Yes, of course, Asian researchers have looked at this topic. The Japanese can go back a few hundred years.

Although he was only a Japanese 9-dan, the Meijin Inoue Dosetsu Inseki (of Igo Hatsuyoron fame) produced a huge collection of problems which were designed less for solving and more as ordered and graduated tuition sets on various life & death topics. Unfortunately only about a tenth of the book survives, but this includes the basic work on nakade (properly used) and sekis.

In the case of nakade, Inseki goes up in order from 4-point shapes to (from memory) 16-point shapes in 102 positions. The problems are not too hard, especially if you do them in order.

From the known titles of the missing portions, we can infer that he possibly covered also aspects to do with sealing positions in before making the nakade (for example, he had a category of oki-hakasu, which appears to mean sealing in with a net-like move before making the inside placement (oki).

There is also the intriguing but unknown tobiashida, which has to mean a "jumping net/geta").

It is significant, in that it shows how thorough Inseki was in his cataloguing, that he covers things likes kozukushi (i.e. bent four in the corner).

This book was the Yoshin Teiki. It may not read like a PhD thesis, but it is highly entertaining and useful, and of course historically significant. (I hope to present it soon as a SmartGo book but at the moment I am still getting to grips with its .gobook formatting language - not easy for a bear of little brain.)

It seems the whole empty board is a RJ_nakade_ .

_________________
I think I am so I think I am.

What you describe about Asian researchers' findings, it appears to provide nothing for defining nakade.

Instead, they created examples of a variety of classes of problems about life+death or other tsumego then somehow, IIUYC, resulting in nakade shapes. All interesting, and all deserving later definition research about related other (more advanced) concepts and terms, but at the moment I am studying "only" the result, when a nakade shape already exists, to identify this fact and distinguish it from non-nakade-shapes.

When referring to 16- or 17-point nakades, it is not what I want to call "nakade shape", but "shape of a nakade string", which exists inside the greater nakade shape including also the adjacent empty intersections and sometimes the defender's stone(s) inside.

When nakade shape is defined. it is trivial to derive definitions for nakade-creating play (before the play, it is not a nakade shape, after the play it is a nakade shape) and of nakade-strings (especially of the attacker's stones) as the strings in the region of the nakade shape.

Since you mention bent-4 and Thomas Wolf has extended this topic to what I have called hidden kos, I want to exclude shapes with kos by definition (as you can also infer from my draft). This may be my preference, because ko shapes deserve conceptual classes of their own. To start with, the following I do not want to call a (non-ko) nakade (and it is not a strong eye):

Click Here To Show Diagram Code

[go]$$B Hidden ko necessary for attempted failure to force partition
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X X X . . . .
$$ | . . X , X . . . .
$$ | . X X O X X . . .
$$ | . X . . O X . . .
$$ | . X X O . X . . .
$$ | . . X X X X . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B Visible ko necessary for forced partition
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . X X X . . . .
$$ | . . X , X . . . .
$$ | . X X O X X . . .
$$ | . X O . O X . . .
$$ | . X X O . X . . .
$$ | . . X X X X . . .
$$ | . . . . . . . . .[/go]

cyclops, the whole 19x19 board is not a nakade shape, because, for either player being the defender, he can partition the region. Note that "each intersection adjacent to the region is occupied by the defender's stone with an outside liberty" is an applicable condition by occupying none such intersection, because none exists. This empty set of surrounding stones is different from a contradicting requirement of surrounding stones having neither outside nor inside (and thus no) liberties. Presumably the definition wording can make the intention clearer, but conceptually I do not think that the empty position creates a problem for the definition.

I think it does more than enough. Almost everyone knows what a chair is. What they have been taught and have experienced through constant repetition creates what is tantamount to a definition in their unconscious brains. If you ask an individual for a formal definition, that is to use his conscious brain, he would probably struggle to be comprehensive, and he would be quite likely to pick out different salient points than another individual. E.g. one person may reason that the number of legs is what matters, and will say that, among seats, one leg means a shooting stick, three means a stool, four a chair and six a sofa. But his brain actually knows better than that, and so if you ask him to go and sit on a stool and there was only a four-legged chair which temporarily had three legs because one was broken, he would look askance. Likewise, a chair-shaped object with four legs and on which you sit might actually be a commode, and because it has a higher - or perhaps better, a lower - function, most people would probably not class it as a chair. And so we can go on finding exceptions - a chair with a solid base, a bean-bag chair, a bar stool with one leg or a bar stool with four, or a garden swing. In every case the flaws in the conscious brain's definition would be easily exposed, but for virtually every person told to sit on a chair, the unconscious brain would unerringly direct his bottom to the correct surface.

Now if you do the constant repetition of seeing a nakade situation explained, especially if the repetitions are ordered and graduated, your unconscious brain will set up a neural network pretty fast - a first approximation will happen instantly - and will end up storing a (hidden) definition that will be amazingly close to the definition the same or a similar exercise produces in someone else's brain. This will be useful because then the two people can talk meaningfully about nakades. But there is an even more useful aspect: the unconscious brain is fantastic at storing away all these neural networks without any apparent work by the owner of the brain, whereas remembering formal definitions and/or lists requires a lot of often very unsuccessful work by the conscious brain.

In short, the Inseki approach is likely to be the more receptive, tractable, reliable and useful approach for most people.

Of course it is possible to imagine situations where the hidden definitions of the unconscious brain need to be made explicit, and perhaps made more accurate - a computer program is the most obvious example. But even here it is worth remembering that it is possible to become more precise and less accurate. Indeed, in something as complex as go, i'd say "likely" rather than "possible".

It is not sufficient for all purposes and everybody if the classic Asians' subconscious awareness of nakade by means of examples sufficed for them. A formal definition is needed so that everybody can always decide whether something is a nakade and so that everybody knows what everybody else is speaking about, without spending many years in vain for attempts of coming to an agreement, while still overlooking basics (see Sensei's Library).

(I do not doubt that, if(!) everybody studies many examples, their - subconscious or conscious - thinking can almost agree. The point is to overcome a) the necessity for everybody to study many examples for each concept, before everybody can join an almost-agreement, and b) the only almost quality of an agreement. If there are different uses, then each use can get its accurate, instead of only almost accurate quality. I also do not doubt that formal definitions require different thinking than - subconsciously or consciously - referring to a set of many previously studied examples, but, as soon as the relevant formal definitions are found, their use can be explained also to those having difficulties with direct textual understanding of definitions, so that also they can get an understanding like that they would otherwise get only after spending much more time on studied many examples. Needless to say, it was hardly the study of examples in classic problem collections that raised my understanding of nakade significantly, but much more the study of basic shapes, such as those shown but neglected in classic collections, for the purpose of drafting a definition. Concerning "the unconscious brain is fantastic at storing away all these neural networks without any apparent work by the owner of the brain", it applies also to the storing by the subconscious thinking of what before is thought consciously and, e.g. in my case, explicitly and formally.)

When you say "the Inseki approach is likely to be the more receptive, tractable, reliable and useful approach for most people", of course, I disagree, because a) everybody starts as a beginner, and as a beginner he does not first want to read all the classics just to understand well enough what a nakade is and b) the examples-driven approach has led to many years of failure to even express reasonably enough what nakade is. (I have to criticise Landman, too, for his failure to specify the first moving player for his specialised concept.)

Hi John,
What you just posted resonated with me at some very deep levels, I guess I always thought so sub-consciously... Now, seeing it vocalized at a conscious level makes me think...



... and I think the above hits the nail right on the head. Come to think of it - I don't know formal definitions for pretty much none of the items I use every day... and yet I can not only function surrounded by those items, but I can also manipulate the world around me with certain degree of competence. What's more, I am not sure if knowing formal definitions would give me any more competence or not.

For example: would I be more comfortable sitting in a chair if I knew how it is formally defined? Would I be able to buy a more comfy chair? Would I be able to better fit a chair into a particular interior design concept, were I an interior designer? Or would I even be able to create a better chair, were I a carpenter?

Would I be able to play Ko better if I understood the formal definition. Or would my level of play increase if I understood a formal definition of 'nakade'? And so on... substitute pretty much any other item or idea, same thing...

As a matter of fact, a lot of progress and improvement was due to people denying and defying widely accepted (even if informal) definitions, and so in turn redefining the world around them as they go. Example? 20 years ago, the definition of a 'phone' did not include a camera or 'apps'... So what is the value of trying to define 'phone' in a formal way?

Having said the above, there are also some other thoughts that bounce around my tired brain.

1. Researcher's approach:

Maybe there are two parallel ways of looking at things: the user and the researcher. As a user, it might not matter to me how a 'chair' is defined. Or, more on-topic: as a Go player, I might not care to read a pages-long definition of Ko... I can play Ko and comfortably discuss positions involving Ko while being blissfully unaware of any formal definitions. When I say to another Go player: look at the Ko on the top - we know what we mean, even if we have never seen Ko being formally defined. Same goes for 'nakade' and a lot of other Go terms. Or most of real-life items.

I actually got scared when I read RJ mentioning research into 'outside and inside moves' or some such. Brr... But that's just me!

To a researcher - this formalization might be of great importance. Not because otherwise they feel lost in the subject (not sure about RJ here, and I often wonder) but because such formal approach allows then to take the next step, and build on top of prior work. It also allows cataloguing. So, in a sense of pushing the overall knowledge a step further, it has a tremendous theoretical value. Theoretically.

For example:
An average human will instinctively understand that it does not matter if, at a supermarket, we scan the soap first and the shampoo next, or the other way around - the total will still be the same. No need to formalize this idea. A mathematician, however, might, and does, find a lot of value in having a formal and well defined way to describe this principle.

So is this divisiveness about the value of formalized Go research simply a division between a theoretician and a player? What's the value of each approach?

2. Aims of research:

Now, generally, a research is a good thing, but in this case - is there any aim other than 'its fun'? Not that 'fun' is an invalid justification - after all, we all play Go for precisely this reason, so I cannot really deny the validity of such thinking. But, if that's the case, its only fair to be aware of it and admit it openly.

If not just 'for fun' then - what is the reward awaiting us at some point along this path? Is it higher skill level attained with greater ease? I am not sure if it has been demonstrated that such 'scientific' approach, in the long run, is any more efficient than the traditional methods. We have had this discussion with RJ quite a few times, and I know which side I have been on (and still am) - but in my more honest moments I have to admit - I simply do not know.

Trying to bite through pages of the so-called 'Go Theory' gives me a head-ache more often than not, with very little, if any, reward in terms of increased understanding. Well, lets be frank - there was no reward whatsoever! But maybe its just me... Maybe I am not diligent enough, have not enough background, or my brain is simply used to dealing with problems in different ways. My guts tell me that all this research can have, at most, limited benefits, like making RJ and a few others warm and fuzzy inside, or, at most, coming with a more precise set of rules - which might or might not be beneficial overall. But again - I simply do not know.

So is this research just for its own sake, or is there a clear, well-defined payoff to be expected at some point? And if so, which point is it? I don't think I have ever seen it spelled clearly by anybody, including the 'researchers'. Other than 'the show must go on' (i.e. we need to keep pushing the formalized knowledge step after step and eventually we will get somewhere, hopefully, and it is understood that this is inherently good.)

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

Why?

(Excuse me if you consider this a derailment. It's a genuine question. You seem to like to post formal definitions of things, but are somewhat less forthcoming with reasons why anyone should be interested, or what kind of purpose they might serve. What have you learnt through writing this definition down?)

RJ, have you perhaps discovered some unknown nakade shapes which the go world is unaware of? It would seem to me that there are only a small limited number of nakade shapes which kills. Or perhaps you found some special exceptions where normal play doesn't work? What is the purpose of making a precise definition of nakade which does not really add to the present knowledge base of nakade shapes?

I mean most people know how to kill an opening move which is mistakenly placed on the first line by a beginner. Do we really need a long precise definition for showing the solution when a simple explanation suffice?

_________________
http://tchan001.wordpress.com
A blog on Asian go books, go sightings, and interesting tidbits
Go is such a beautiful game.

Bantari,

Chair and other non-go, every day objects: formal definitions are not needed for their use.

Ko: the formal definition of ko in general is too mighty in its scope of application and too nasty in the low levels to be useful for becoming stronger because of knowing the full definition well. However, the core condition of global-ko-intersection provides the key idea for what correct ko fighting is all about expressed more clearly than I have seen before. Being aware of this idea clearly can help to improve in strength a bit.

Nakade: the anticipated formal definition is too nasty in the low levels to be useful for becoming stronger. However, teachers bothering to understand the essence of such a definition can improve their related teaching and so help pupils to understand better by seeing on average more relevant examples and their comments with better reasoning. E.g., as a beginner, it is essential to learn that a seki shape must not be confused with nakade.

Weak definitions (phone): As you know, I favour the most complete definitions. (But, allow me this OT remark: many smart capabilities of smartphones do not fulfil the function of a phone, but a new class of tools is created by combining phone, alarm clock, pocket light, camera, PC, watch, internet, Swiss knife, GPS, NSA (SCNR) and other features.) There is also scope for smartnakade concepts in go, but they need different definitions or conceptual backgrounds than plain nakade.

Ko versus nakade definition: Here you miss a point. While in practice every ko is basic, and every ko fight is a basic ko fight, nakade has much greater variety for practical relevance. Of course (or hopefully) everybody recogises the most basic nakade shapes. However, already when such a shape is not tightly surrounded any more, quite a few people are starting to have problems, such as not recognising a seki when there is much space on the outside and the inside almost looks like a nakade.

Inside vs. outside: it is one of the most difficult research fields and scares also me...

The value of research, building on top of prior work, cataloguing, pushing the overall knowledge a step further has a tremendous value not only for the theorists, but also for practical applications. Maybe not always immediately, but surely later. It is the general effect of fundamental research. This is so also for a careful definition of nakade.

Aims of nakade definition research: I am doing this research, because I am in urgent need for its application when teaching life and death more profoundly than by only repeating known standard examples. Life and death suffers from the problem of exploding tree size and reading complexity. They must be pruned as powerfully as anyhow possible. Pruning must start as earlier as possible: at the roots and basics of the problem. Therefore, understanding the fundamentals, such as what is a nakade, very well then greatly eases more advanced reading, such as reading leading to nakade shapes. Every beginner is taught this for the easiest shapes and easy nakades. Beyond absolute beginner level, the same continues to apply: save reading by understanding shortcuts.

Fun: of course, this is one of the aims.

Traditional methods: why. There has been (almost) only one method: teaching by examples:) Even you will admit that more methods can be better than only one method. Careful definitions are a means to then develop more methods.

Go theory: which do you mean? The hard core maths? It is not written for everybody's fast consumption. Rather it is a source for expert teachers devising new widely applicable ideas.

Research profit: see above. It is almost immediate, when I apply it to teaching (but you would already not notice any longer than I am applying it; you would notice only the application consequence).

Research show: uh, lol, we do not need to raise funds for conquering Mars. The show goes on already because the go researchers themselves are having fun and understand the importance for application, regardless of whether you notice that indeed it is a successful application.

1) to apply it as a player

2) to apply it for teaching

3) for the sake of advancing fundamental go theoy research

4) for greater confidence in correct application

5) for generating more relevant applications

6) for accelerating related reading and decision making (such as in almost all life and death problems and middle game positions)

7) for improving the average degree of correctness in related reading and decision making

8) for generating a more general scope of application, e.g., instead of requiring only tightly surrounded nakade, apply with equal confidence to open an loose shapes



a) see above

b) finding an accurate definition is as difficult as I expected

c) semeai-eyes and nakade are not the same thing, because unstable states can be allowed versus are not desired

d) considering / excluding ko is a necessity (simply pretending to ignore kos does not work for a full understanding of nakade)

e) semeai-eyes and nakade share common or closely related aspects

IMO, it is not spread sufficiently widely yet that nakade shapes do not require tight surrounding or can contain several (not: at most one) strings. Presumably I have not discovered a new nakade shape, but (see my study on semeai-eyes) exhibited the relevance of a surprisingly great variety of functionally different basic nakade and eye shapes. My other intended contribution is to raise clarity of awareness of modular applicability: it can be useful to identify nakade in PART (instead of the whole) of the eyespace, which can change dynamically.



Maybe you are caught in the trap of thinking "I am done" when recalling the 9 most basic shapes of nakade strings. As Wolf has discovered, the number of corner shapes is much greater. What I am telling you: there is an almost abitrarily great number of open boundary shapes, in which nevertheless nakade can occur.



E.g., the same exceptions for semeai-eyes are relevant also for recognising what is (not) nakade.



See other message.



Only experts care for the empty board. Nakade is relevant in middle game, LD, semeais etc.

But concretely, how? Can you give me an example of a case that this formal definition has helped you understand, for example? Obviously, if I saw how you were managing to apply these things, I would count it as useful research, or at least research interesting in its own right. If you're just writing down abstract definitions with no clear goal for what to do with them, I'm not convinced that it's useful.

The definition clarifies:

Click Here To Show Diagram Code

[go]$$B The marked region is a nakade
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O B O O . X
$$ | X X . C B B O . .
$$ | X . O O B C . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

As I notice now, the definition fails here, because,

Click Here To Show Diagram Code

[go]$$B The marked region should be a nakade
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O B O O . X
$$ | X X X . B B O . .
$$ | X . O O B O . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

if the defender is assumed to occupy the adjacent intersections,

Click Here To Show Diagram Code

[go]$$B Occupying adjacent intersection
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O . O O . X
$$ | X X X O . . O . .
$$ | X . O O . O . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

the inside string has lost its liberties and is removed. Now, according to the definition (second bullet point), the defender moves first

Click Here To Show Diagram Code

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

and partitions the region into at least two regions.

Click Here To Show Diagram Code

[go]$$B Defender moves second
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O C O O . X
$$ | X X X O C C O . .
$$ | X . O O C O . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

If we alter the definition and, in the second bullet point, let the defender move second, the region is identified as a nakade,

Click Here To Show Diagram Code

[go]$$B The marked region is a nakade
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O . O O . X
$$ | X X X O 1 . O . .
$$ | X . O O . O . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

because White cannot partition it, but this is wrong; an unstable eye is not a nakade shape yet, but a shape in which the attacker's first move can create a nakade shape.

Now how to alter the definition? Require alternate play for the adjacent intersections and allow play also on them? Two or three cases, one for an already surrounded region, one for a not yet surrounded region with / without inside removals?

EDITED

Draft 2:

A _nakade_ is a region of connected intersections so that

* if the players play only within the region and on its adjacent intersections, the defender moving first can necessarily fill all but one of the intersections of the region,

* if the players play only within the region and on its adjacent intersections, the defender moving first cannot necessarily permanently partition it into at least two regions and surround them,

* if the initial position is the starting position, the players may play anywhere and either player tries to prevent the other's new independent life, neither player can force occurrence of a seki or ko ban involving the region, and

* if each intersection adjacent to the region is occupied by the defender's stone without any outside liberty, the players play only within the region, and either player tries to prevent the other's new independent life, neither player can force occurrence of a seki or ko ban involving the region.

The second bullet point applied:

Click Here To Show Diagram Code

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

Click Here To Show Diagram Code

[go]$$W Example 1 typical variation
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O X O O . X
$$ | X X . 1 4 X O . .
$$ | X . O O X 3 2 X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

White cannot partition, so it is a nakade.

Click Here To Show Diagram Code

[go]$$W Example 2
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O B O O . X
$$ | X X X . B B O . .
$$ | X . O O B O . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

Click Here To Show Diagram Code

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

White cannot partition, so it is a nakade.

Click Here To Show Diagram Code

[go]$$W Example 3
$$ ------------------
$$ | . O X X X X X X .
$$ | O O . . . . . . .
$$ | X . O . O O . X .
$$ | . X O O C O O . X
$$ | X X X O C C O . .
$$ | X . O O C O . X .
$$ | X . . . O O . X .
$$ | X . X . . . X . .
$$ | . . . X X . . . .[/go]

Click Here To Show Diagram Code

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

White can partition and surround three parts in the initial region, so it is not a nakade, as it should be.

Draft 2 of the definition seems to make progress.

EDIT:

The next question I am having is whether "play only within the region and on its adjacent intersections" is necessary or bad in the second bullet point.

Click Here To Show Diagram Code

[go]$$W Example 4
$$ ------------------
$$ | O O . X O . . . .
$$ | O O . X O . . . .
$$ | X X X X O . . . .
$$ | O O O O O . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Now I recall why, if the first bullet point is needed at all, it needs its further semeai-eye condition "and do not remove any surrounding stone":

Draft 3 (first bullet point):

* if the players play only within the region and on its adjacent intersections and do not remove any surrounding stone, the defender moving first can necessarily fill all but one of the intersections of the region

Click Here To Show Diagram Code

[go]$$B 2 = pass prescribed by the definition
$$ ------------------
$$ | O O 3 X O . . . .
$$ | O O 1 X O . . . .
$$ | X X X X O . . . .
$$ | O O O O O . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

A black cy3_nakade_ is a set of connected intersections, empty or occupied, surrounded by black stones such that ....
.. A white cy3_nakade is defined mutatis mutandis likewise.


can necessarily???

I can necessarily be confused by your idiom. No idea what you mean apart maybe from the existence of a valid ( unrefutable ) strategy to achieve something.
How would you translate "can necessarily" into German? "Kann unbedingt"?

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