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 Post subject: Re: Japonese counting
Post #101 Posted: Sat Aug 14, 2021 3:03 am 
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Gérard TAILLE wrote:
Let's try to progress slowly. What is for you the result of example 11?

See my posting above.

The White group under consideration is surrounded by a "TWO-EYED life" (at least this can be assumed for sure) Black group.

Thus, the rest of the board can be considered to be completely empty.
Nothing outside Black's unconditionally alive wall can stop Black from capturing White's stones inside.
Therefore, White's group under consideration is "dead".

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 Post subject: Re: Japonese counting
Post #102 Posted: Sat Aug 14, 2021 3:05 am 
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jann wrote:
Cassandra wrote:
It is completely irrelevant for the status of :wt: that White could capture Black's stones with a. Just because no group in the upper left is under consideration now.

As I wrote earlier you seem to misunderstand what it means to "enable" a new live stone. If you cannot carry out a capture without enabling something (that wasn't originally possible) elsewhere, that is not a valid capture in J89. Spatial locality means nothing - that's why pass-for-ko (with global enabling) was invented for.

The problem with double kos and ko passing is one of the oldest well known defects of the text. But because it would break almost anything it is safe to assume that such perpetual ko passing loop is not allowed - even if the rules authors overlooked the problem.

Other than that, there are several beasts where the ko pass rules change local outcomes and require protecting moves that would not be necessary in normal go. Those are, I think, accepted consequences of J89.


I agree with you Jann, spatial locality means nothing in J89. J2003 tries to define spatial locality but it is another issue.

Concerning the famous "enable a new live stone" I have real difficulty to understand the meaning.
Let's take the well known first example given in the rule, to try and get a better understanding
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . B B O . . . |
$$ | O B B O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

What is the status of the marked stones?
In the rule I see
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | 1 B B O . . . |
$$ | O B B O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | 1 . . O . . . |
$$ | O 2 . O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

and it is said "Black is now able to play 2, a stone which cannot be captured".

Where is my point? Surely black :b2: cannot be capture but in any case (I mean even if white does not try to capture black), black is able to prove she can occupy this point by the sequence:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | 1 B B O . . . |
$$ | 2 B B O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . O . . . |
$$ | O 3 . O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

That means that you are not enabling something that wasn't originally possible are you?
If it is true that means that the four marked stones in the first diagram are dead.
By the way the white stone in the corner is also dead isn't it?
The final conclusion is the same (seki or anti-seki) but the intermediate results are completly the opposite.

Note : surely the wording of 7.2 is not clear but it is not my point.
My point is : what do we really want to say?

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 Post subject: Re: Japonese counting
Post #103 Posted: Sat Aug 14, 2021 3:40 am 
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Gérard TAILLE wrote:
Where is my point? Surely black :b2: cannot be capture but in any case (I mean even if white does not try to capture black), black is able to prove she can occupy this point by the sequence:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | 1 B B O . . . |
$$ | 2 B B O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . O . . . |
$$ | O 3 . O . . . |
$$ | X O O O . . . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]


Then Black has to play this sequence BEFORE the game stopped.

During status confirmation, it does not have any meaning that Black played the move :b3: at a point where a Black stones was present before, because this move is part of a sequence for confirming the status of a °WHITE" group.

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 Post subject: Re: Japonese counting
Post #104 Posted: Sat Aug 14, 2021 3:43 am 
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Cassandra wrote:
These "TWO-EYED life" groups enclose and / or seperate areas of the board, which contain groups of still undetermined life-and-death status.

Each of these areas is one "locality", and has to be considered on its own.

Designing rules like this may be possible. J89 chose a different way: ko passes (hoping for a similar effect). You can have either explicit localization or passing for kos, but not both.

Quote:
I am with you with your understanding of "enable". But this is NOT covered by the legal text.

I hope that we can agree that the primary concerns of the rule were "snap-back" and "nakade".
As I already mentioned before, an addition would have been helpful that the "new stone" had to be established on a board point that had been occupied by the (then captured) group under status consideration earlier.

The very example (ex 4) you quoted earlier shows this is not correct. The new stone can appear elsewhere, where no capture happened from. What matters is logical connection - made possible by the capture.

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 Post subject: Re: Japonese counting
Post #105 Posted: Sat Aug 14, 2021 3:50 am 
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RobertJasiek wrote:
Cassandra wrote:
Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . X . X O X . |
$$ | X X X O O X X |
$$ | O X O O X X . |
$$ | . O . O O X . |
$$ | O O O O O X . |
$$ | X X X X X X . |
$$ | . X . . . . Q |
$$ -----------------[/go]

what is the status of :wt: ? [...] common sense must apply.

:wt: in your example is NOT attached to the double ko.


Common sense is not needed. My J2003 interpretation of J1989 treats it correctly:

The big white string is uncapturable due to the infinite alternating sequence B[kkPP]*, where k is ko capture and P is ko-pass. White triangle is neither uncapturable nor capturable-1. Its local-2 is:

Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . X . X O B C |
$$ | X X X O O B B |
$$ | O X O O B B C |
$$ | . O . O O B C |
$$ | O O O O O B C |
$$ | B B B B B B C |
$$ | C B C C C C W |
$$ -----------------[/go]


White triangle is not capturable-2. Therefore, it is dead.

Robert, it is not quite clear to me what capturable-2 means. Can you help me through the following examples by just give me the status of the white stones?
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]

what is the status of white marked stones?

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | O O O O O O O O O |
$$ | . O O O O O O O . |
$$ | O O O O O O O O O |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]

and now what is the status of white marked stones?

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 Post subject: Re: Japonese counting
Post #106 Posted: Sat Aug 14, 2021 3:57 am 
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jann wrote:
The problem with double kos and ko passing is one of the oldest well known defects of the text. But because it would break almost anything it is safe to assume that such perpetual ko passing loop is not allowed - even if the rules authors overlooked the problem.

I think that you are mistaken with stating that "it would break anything".

As a matter of course, there must be a difference between the status of an "isolated" double-ko, and a combined position where a double-ko is (only) a part of.
And also as a matter of course, there could be a difference between the status of a group that has four liberties, and a group that has only three.
Similar to the difference between the status of an "isolated" bent-four, and a combined position, where a bent-four is (only) a part of.

Also as a matter of course, better solutions than the current Article 7, 2. text are quite conceivable.


And I do not think that the rules' authors overlooked the problem. Otherwise they would not have invented "life / death after the dissolving of a seki".
If the position was a seki during status confirmation, nothing could be dissolved.
And the property of a position before the game stopped is complete irrelevant during status confirmation.
It seems more likely to me that they did not have any (other) valid idea how to solve the problem of limiting "no-result" results of a game.

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 Post subject: Re: Japonese counting
Post #107 Posted: Sat Aug 14, 2021 4:26 am 
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Cassandra wrote:
"Pass-for-ko" is NOT a global issue, but a LOCAL one!


The J89 local-per-basic-ko-recapture is flawed. The J2003 ko-pass-for-all-basic-kos-of-a-player corrects the flaws. Both ko rules are hybrids between local and global.

Quote:
"TWO-EYED life"


J89 does not rely on two-eyes. It required J2003's completion with capturable-2, my conjecture and Chris Dams' proof of the equivalence of the WAGC Rules two-eye life model to the J2003 capturability life model.

Quote:
These "TWO-EYED life" groups enclose and / or seperate areas of the board [...] Each of these areas is one "locality", and has to be considered on its own.


Although it is possible to design (and Pauli and I have written such) rules in this manner of partitioning the board by two-eye-alive groups, J89 has not done so.

Quote:
NOTHING beyond the border of (a) "TWO-EYED life" group(s)


Note: an unsettled position need not have settled borders due to existing two-eye-alive groups.

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 Post subject: Re: Japonese counting
Post #108 Posted: Sat Aug 14, 2021 5:50 am 
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RobertJasiek wrote:
J89 does not rely on two-eyes.

I did not post about J89, but about territory rules.

RobertJasiek wrote:
Cassandra wrote:
These "TWO-EYED life" groups enclose and / or seperate areas of the board [...] Each of these areas is one "locality", and has to be considered on its own.

Although it is possible to design (and Pauli and I have written such) rules in this manner of partitioning the board by two-eye-alive groups, J89 has not done so.

Your "local-x" reach beyond the border of "uncapturable" groups?

Regarding J89:
The status confirmation is done for each group independently, no one's result affecting each other's.
Therefore, you can alternatively do "if they cannot be captured by the opponent" first for ALL groups.
Thereafter, you can apply "or if capturing them would enable a new stone to be played that the opponent could not capture" for ALL groups that did not match the condition of the first run.
You will realise that the first run has partitioned the board.
And the second run presumably a bit more.
A bit, but not difficult, thinking will reveal, which of the identified "alive" groups can become two eyes, and which not.

Quote:
Quote:
NOTHING beyond the border of (a) "TWO-EYED life" group(s)
Note: an unsettled position need not have settled borders due to existing two-eye-alive groups.

A super-large seki on the board?

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 Post subject: Re: Japonese counting
Post #109 Posted: Sat Aug 14, 2021 6:12 am 
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Cassandra wrote:
Regarding J89:
The status confirmation is done for each group independently, no one's result affecting each other's.

You keep saying this, but is not correct. See LD ex 11, clearly remote groups are considered together.

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 Post subject: Re: Japonese counting
Post #110 Posted: Sat Aug 14, 2021 8:46 am 
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jann wrote:
Cassandra wrote:
Regarding J89:
The status confirmation is done for each group independently, no one's result affecting each other's.

You keep saying this, but is not correct. See LD ex 11, clearly remote groups are considered together.

Sorry, but this is an example that demonstrates exactly what I wrote.

Black 1 starts the status confirmation for White's group at the top, White 2 starts the status confirmation for Black's group in the upper right corner.

You must not expect the authors of J89 to have consulted a specialist in education.
ALL the examples (and there are several) that contain a combination of two positions, each of which is surrounded by an independently alive group, are pedagogical nonsense.

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 Post subject: Re: Japonese counting
Post #111 Posted: Sat Aug 14, 2021 8:51 am 
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Local-2 of a player's string is bounded by HIS stones of uncapturable or capturable-1 strings. Therefore, local-2 can sometimes reach beyond the opponent's uncapturable strings.

A multi-stage analysis is a principally possible rules design. For achieving an unequivocal partition of a settled position, multiple threats must be handled by the definitions, e.g., by minimality or maximality of sets of a player's strings including a particular string.

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 Post subject: Re: Japonese counting
Post #112 Posted: Sat Aug 14, 2021 9:31 am 
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RobertJasiek wrote:
Local-2 of a player's string is bounded by HIS stones of uncapturable or capturable-1 strings. Therefore, local-2 can sometimes reach beyond the opponent's uncapturable strings.


OK that was what I guessed but I was not quite sure.
As consequence is it correct to say

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]
The white marked stones are living because they are local-2 connected

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | O O O O O O O O O |
$$ | . O O O O O O O . |
$$ | O O O O O O O O O |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]
The white marked stones are dead because they are not local-2 connected.

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 Post subject: Re: Japonese counting
Post #113 Posted: Sat Aug 14, 2021 2:33 pm 
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Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]
The white marked stones are living because they are local-2 connected


Therefore, Black optimising the score should not have passed.

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 Post subject: Re: Japonese counting
Post #114 Posted: Sat Aug 14, 2021 2:55 pm 
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RobertJasiek wrote:
Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]
The white marked stones are living because they are local-2 connected


Therefore, Black optimising the score should not have passed.


Yes Robert. A quite unexpected result due to the special procedure defined in J2003.
Let's imagine a real game with such position with white to play. White pass and this looks like the last trap of the game. Note that this move (the white pass) costs nothing to white.

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 Post subject: Re: Japonese counting
Post #115 Posted: Sat Aug 14, 2021 3:22 pm 
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Cassandra wrote:
jann wrote:
Cassandra wrote:
Regarding J89:
The status confirmation is done for each group independently, no one's result affecting each other's.

You keep saying this, but is not correct. See LD ex 11, clearly remote groups are considered together.

Sorry, but this is an example that demonstrates exactly what I wrote.

Black 1 starts the status confirmation for White's group at the top, White 2 starts the status confirmation for Black's group in the upper right corner.
You must not expect the authors of J89 to have consulted a specialist in education.
ALL the examples (and there are several) that contain a combination of two positions, each of which is surrounded by an independently alive group, are pedagogical nonsense.


Oops you do not like very much the J89 at least as it is presented do you?
Taking the examples of the rules : you do not want to see unfinished positions, you introduced a quite unexpected loop in case of double ko, you reject all examples with independant groups, you do not accept "enable new stone" which is not under the group considered ...
Note that you introduced yourself the example 16 which is surely an unfinished position.
What is your prefered go rule? An area one?

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 Post subject: Re: Japonese counting
Post #116 Posted: Sat Aug 14, 2021 9:34 pm 
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Gérard TAILLE wrote:
Oops you do not like very much the J89 at least as it is presented do you?

The presentation includes the legal text, a commentary on the legal text, and "examples of confirmation of life and death".

Everything would have been fine, if ALL INTENDED results of the examples could have been derived by applying the legal text and its commentary only. But this is NOT the case.
Quite apparently, the authors of the rules tried to summarize contradicting (!!!) DESIRED results in a uniform system, but unsurprisingly failed.

The authors unnecessarily damaged the overall impression of their ruleset by not strictly following their own rules, when trying to "solve" position that are very, very unlikely to ever appear in a real game.

It is not "unnatural" at all that a given ruleset will trigger a few "beasts", which results seem to contradict "common sense" (probably different beasts for different rulesets). But it should be logical closed in itself.

But J89 is NOT.
It is said "The results in the following examples WOULD be reached through confirmation of life and death."
Not "MUST".

Quote:
Taking the examples of the rules : you do not want to see unfinished positions,

I doubt that it makes sense to utilise unfinished positions for trying to "prove" the existence of "beasts", as you (and others) did.

Unfinished positions are not bad per se. But they must be interpreted as a helping hand for the user. As a warning that something unexpected will happen after the game stopped, showing that it would be better for one side or the other to play on. But quite apparently, the text was not intended for beginners.

Quote:
you introduced a quite unexpected loop in case of double ko,

Strict application of the legal text is "unexpected" for you?

Indeed, that loop is not shown in the "solution" sequences of the examples. But quite apparently, the authors took it for granted.
Please compare the comment on "no result", where only the very first move of the loop is shown.
As a matter of course, it would have been better in the pedagogical sense, if the loop sequence had been shown explicitly, until the real repetition of the starting position. But quite apparently, the text was not intended for beginners.

The beginning of this loop is introduced in example 11. But the sequence for the position at the right (both this position and the moves played there are completely independent from the position and the moves played at the left, as you can easily prove by changing the order of moves) is not yet finished!!!
It does not make any sense to pass for a specific ko, if you do not intend to capture just this specific ko thereafter.
You will have to recapture both ko to reach the starting position at the right. Only then you can be sure that none of the large groups there can be captured.

Quote:
you reject all examples with independant groups,

All these examples lack the hint
"We know very well that some 'experts' will want to fool unexperienced players during status confirmation. Therefore, we will show you here that anything that exists on the board INDEPENDENT of the group under consideration is completely irrelevant for this consideration."

It is the same, if you pass in a sequence of a status confirmation, or if you occupy a random point on the board outside the position in question.
After the result of the status confirmation has been obtained, the sequence(s) used vanish(es) again into thin air.

Quote:
you do not accept "enable new stone" which is not under the group considered ...

I think that this is a matter of taste. But you should be consistent with its application.

Either you understand this feature as a REBIRTH of (parts of) a group that has already existed on the board before. Then is should be self-evident that you are bound to the previously occupied board points for placing that "new" stone.

Or, otherwise, you will have to accept a "new" stone anywhere inside the area that contains non-independent, non two-eyed-life groups connected to each other.

Quote:
Note that you introduced yourself the example 16 which is surely an unfinished position.

Examples 16 to 18 include "unfinished" positions of a very special kind.

Under strict application of the legal text, all these positions are seki.

You have three choices now:
Either this seki does not affect the outcome of the game. Then everything is fine for both players.
Or one of both players will ask for a resumption of the game and start a triple-ko sequence before the game stops.
Or one of both players will accept his loss of the game.

Quite apparently, option #2 was an undesirable one.

Quote:
What is your prefered go rule? An area one?

Territory rules are fine.

I doubt the applicability of that scoring method during actual play.
I do not like the "beasts" that are typical for area rules.
And my memory is not strong enough to remember everything that has been happened during a long game.

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 Post subject: Re: Japonese counting
Post #117 Posted: Sun Aug 15, 2021 4:37 am 
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Sometimes it is difficult to understand what you really mean Cassandra but it is clearer with your last post.
Yes Cassandra there are a lot flaws in J89 and we are all aware of that.
Though I don't share some of your opinion (for example I like beasts because I often found them fascinating) I agree with you on a number of points.
Maybe the most important point is to be able to recognise indepency between groups.
You are right Cassandra for a go player in one way it make sense to say that two areas are independant because they are surrounded by two eyes groups but in another way we know that ko links all areas by means of ko threats.
Without introducing explicitly dependency or independency in the rule, J89 introduces the pass-for-a-ko concept which is really a way of introducing independency in the rule. Yes it is not a great success I agree with you. In J2003 we can see another way to introduce dependency or independency, by using local-2 concept. My feeling is it is a great progress. OC it is still not perefect:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . W X . X . X |
$$ | W W W W X X X X X |
$$ | X X X X X X X X X |
$$ | O O O O O O O O X |
$$ | . O O O O O . O a |
$$ | O O O O O O O O X |
$$ | X X X X X X X X X |
$$ | W W W W X X X X X |
$$ | . . . W X . X . X |
$$ -----------------[/go]

In my view the independency between the two white marked groups as nothing to do with which side will take the dame at "a".
Anyway, as I said, J2003 is a great progress.

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | O X . X . O . |
$$ | . O X X X O O |
$$ | O . O O X X O |
$$ | O O O . O X O |
$$ | X X O O X X O |
$$ | . X X O O O . |
$$ | X . X X X O O |
$$ -----------------[/go]

BTW, by using only your own understanding of japonese rule (I mean not the J89 as it is strictly written ;-)) do you think white should add a move in the position above?

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 Post subject: Re: Japonese counting
Post #118 Posted: Sun Aug 15, 2021 6:27 am 
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Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$B Confirmation phase
$$ -----------------
$$ | O X . X O 1 O |
$$ | . O X X X O O |
$$ | O O O X O O O |
$$ | . O 2 O O X X |
$$ | O O O X X X . |
$$ | X X X X . X X |
$$ | . . . . . X . |
$$ -----------------[/go]

then because white has not passed for the ko :b1: it will follow
Click Here To Show Diagram Code
[go]$$B Confirmation phase
$$ -----------------
$$ | O X . X . X O |
$$ | 3 O X X X O O |
$$ | O O O X O O O |
$$ | 5 O O O O X X |
$$ | O O O X X X . |
$$ | X X X X . X X |
$$ | . . . . . X . |
$$ -----------------[/go]
:w4: pass
and the white stones are all captured

I would claim that :w2: lifts the ko ban on recapturing :b1:, just as in normal play. The :b1: stone is not "hot" anymore after white plays :w2:, so white is free to capture :b1: on :w4:.
I suppose that by choosing the word "pass" in the J89 rules they just meant that :w2: cannot fight the :b1: ko by playing some ko threat elsewhere. But :w2: is not a ko threat, so there is no problem in that regard.
At least I would assume that this was the intention of the J89 rules, even if it could be interpreted otherwise.

So white does not have to add a move.

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 Post subject: Re: Japonese counting
Post #119 Posted: Sun Aug 15, 2021 7:39 am 
Judan

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I have consulted Chris Dams' proof of equivalence of WAGC-life and J2003-life, and it holds if local-2 is modified as local-2-alternative to be "surrounded" by either player's uncapturable or capturable-1 strings. I have not checked all rules test examples though.

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 Post subject: Re: Japonese counting
Post #120 Posted: Sun Aug 15, 2021 8:02 am 
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RobertJasiek wrote:
I have consulted Chris Dams' proof of equivalence of WAGC-life and J2003-life, and it holds if local-2 is modified as local-2-alternative to be "surrounded" by either player's uncapturable or capturable-1 strings. I have not checked all rules test examples though.

Robert, I have in mind a beast that shows that neither the local-2 nor your local-2-alternative seem to give the expected result (only for the status of the strings of stones, not for the result of the game!).
If you are interested I can show you here this position but, because it looks like a beast, I am not sure you will have time to spend on it.
OC, if somebody else is interested (certainly not Cassandra who does not like beast ;-) ) I will show here this position.
Tell me please.

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