Japonese counting

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Aug 17, 2021 5:32 am

Cassandra wrote:
Gérard TAILLE wrote:
$$B
$$ -----------------
$$ | O X . X . O . |
$$ | . 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 . |
$$ | X . X X X O O |
$$ -----------------
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, though the global ko-pass defined in J2003 is also a big progress, it is a pity to see that the status of white stones is still dead stones (=> seki => white should add a move)
I think it was Robert's intention to develop a logically closed and contradiction-free set of rules, which was able to achieve the desired results of the J89 life-and-death examples.
As far as I understand J2003, this particular ko-pass-rule is both appropriate and necessary to fulfill the above-mentioned task.

By the way:
$$B
$$ -----------------
$$ | P X . X . O . |
$$ | 1 O X X X O O |
$$ | O 2 O O X X O |
$$ | O O O . O X O |
$$ | X X O O X X O |
$$ | . X X O O O . |
$$ | X . X X X O O |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | P X . X . O . | $$ | 1 O X X X O O | $$ | O 2 O O X X O | $$ | 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]
It does not matter that White would have to add a move to get rid of the seki in J89 status corfirmation.
During actual play, Black is able to capture with , forcing White to connect at , also gaining that specific point, due to the just won prisoner.

In what context are you Cassandra? In all rules I know, if the exchange

occurs in normal play then all the black stones at the top are declared dead while all white stones are alive. I do not see when this exchange can give black an adding point: it is true that black gains a prinoner but at the same time white gets a point of territorry for the same intersection doesn't she? To be complete black stones

becomes a prisoner but

loses a point of territory.

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 6:58 am

J89, but apparently I was mistaken

+ + + + + + + + + + + + + +

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

If Black does nothing, White has to add a move during "play", in order to avoid "seki" by status confirmation.

White has ten points occupied with dead Black stones => 20 points.
White has six points of unoccupied territory => 6 points.

Black has two points of territory => 2 points.

=> White wins the game by 24 points.

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

During "play", Black plays his kikashi in the upper left.

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

White has eleven points occupied with dead Black stones => 22 points.
White has six points of unoccupied territory => 6 points.

Black has two points of territory => 2 points.
Black got one prisoner => 1 point.

=> White wins the game by 25 points.

It seems that I did not visualise before that capturing one White stone empties the respective point, turning it into White territory.

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Aug 17, 2021 8:22 am

Cassandra wrote:J89, but apparently I was mistaken

+ + + + + + + + + + + + + +

$$W
$$ -----------------
$$ | O X . X . O . |
$$ | 1 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 . |
$$ | X . X X X O O |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W $$ ----------------- $$ | O X . X . O . | $$ | 1 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]
If Black does nothing, White has to add a move during "play", in order to avoid "seki" by status confirmation.

White has ten points occupied with dead Black stones => 20 points.
White has six points of unoccupied territory => 6 points.

Black has two points of territory => 2 points.

=> White wins the game by 24 points.

$$B
$$ -----------------
$$ | O X . X . O . |
$$ | 1 O X X X O O |
$$ | O 2 O O X X O |
$$ | O O O . O X O |
$$ | X X O O X X O |
$$ | . X X O O O . |
$$ | X . X X X O O |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | O X . X . O . | $$ | 1 O X X X O O | $$ | O 2 O O X X O | $$ | 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]
During "play", Black plays his kikashi in the upper left.

$$B
$$ -----------------
$$ | . X . X . O . |
$$ | X O X X X O 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 . |
$$ | X . X X X O O |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . X . X . O . | $$ | X O X X X O 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]
White has eleven points occupied with dead Black stones => 22 points.
White has six points of unoccupied territory => 6 points.

Black has two points of territory => 2 points.
Black got one prisoner => 1 point.

=> White wins the game by 25 points.

It seems that I did not visualise before that capturing one White stone empties the respective point, turning it into White territory.

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]

OK Cassandra, I think we agree now that black, in normal play, cannot have any interest to take the ko in the corner instead of passing to stop the game.
It remains only the question : in normal play, should white add a move before passing?
In J89 and J2003 we proved white should add this move due to the you use of the pass-ko rule.
In viewtopic.php?p=266571#p266571 you claimed that with your own understanding of japonese rule (I mean not the current J89 or J2003 as they are written) white should not add a move and I agree with you because in normal play black cannot save her stones even by playing first! For that reason I think the pass-ko rule, without minimizing the number of advantages it has, has though here a flaw which was certainly not expected.
Do you agree Cassandra?

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Aug 17, 2021 10:36 am

Cassandra wrote: Do you want to behave a final position differently, whether it contains a solidly connected TRIPLE-Ko that is shared by only two groups

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

OK Cassandra let's try to have a common understanding of tripel ko or double.

Let's begin by the solidly connected TRIPLE-Ko which seems the easiest one.

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

In J89 and J2003 (where I am talking about J89 or J203 I am refering strictly to the test and not to the examples because they could be not coherent with the text), my understanding is the following:

In J89 the marked stones are dead because they can be captured and no new stone are enable to be played that the opponent could not capture. All other stones are alive => the left part of the board is seki

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

In J2008 the three single stones are also dead due to the double barrier with black and white marked stones. All other stones are alive => the left part of the board is seki

Is seki the expected result? I do not know but the losing player made a mistake by passing. She would have continue the game by playing the triple ko to reach a NO RESULT game. IOW the result of the confirmation phase is not relevant. In any case the potential losing player can always continue the game to reach a NO RESULT.

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 10:42 am

Gérard TAILLE wrote:For that reason I think the pass-ko rule, without minimizing the number of advantages it has, has though here a flaw which was certainly not expected.
Do you agree Cassandra?

In principle, yes.

However, in my opinion the only "advantage" of such a special-ko-ban rule is to ensure the intended results of several of the life-and-death examples of J89. Otherwise, it would not be needed, in order to create a self-contained, contradiction free rule set.
I consider it extremely likely that for EVERY ruleset "beast" could be created, which status-confirmation result "common sense" did not expect.

But let's return to J89.
I suppose that the inventors of the special-ko-ban rule wanted to avoid "no result" in several TRIPLE-KO cases.
But it seems that they overlooked the effects of their rule on "NESTED" ko shapes (as in the board position you created). The status-assessment of the position reached after two moves (Black captured in the upper left corner, White connected the resulting atari below) -- if THIS position was the final position of the game -- would match "common sense".
As you corrected me, Black's initional move would COST him one point -- if played BEFORE the game stopped.
So, what it the reasoning that he shall GAIN one point without capturing during play -- through status-confirmation?

+ + + + + + + + + + + + + + + +

By the way:

The life-and-death examples in J89 -- treating a compound of bent-four and double-ko -- do NOT cover ALL possible variations of shared double-ko formations. J89 suppresses an example like the following one -- with NESTED ko shapes.

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

To be honest, I have forgotten ("misplaced") the results of my J89-application trials with it. But for sure, at that time I did not dream of some restricting side conditions that prevent any triple-ko cycles.

However, I know that a status-assessment without any special ko-ban-rule will give interesting results (as well).

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 10:56 am

Gérard TAILLE wrote:Is seki the expected result? I do not know but the losing player made a mistake by passing. She would have continue the game by playing the triple ko to reach a NO RESULT game. IOW the result of the confirmation phase is not relevant. In any case the potential losing player can always continue the game to reach a NO RESULT.

I think you hit the nail on the head.

This is just what I meant.

If the three ko shapes are solidly connected, and consequently only two groups involved, the (J89) result of the status-assessment of this triple-ko shape would be SEKI.
=> Probably one player would prefer "no result".

If the three ko shapes are seperated (e.g. into a double-ko and a simple ko), the J89 examples enforce the death of several groups, ruling out the possibility of SEKI.

Does this mean that a triple-ko is not a triple-ko?

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Aug 17, 2021 1:31 pm

Cassandra wrote:
Gérard TAILLE wrote:Is seki the expected result? I do not know but the losing player made a mistake by passing. She would have continue the game by playing the triple ko to reach a NO RESULT game. IOW the result of the confirmation phase is not relevant. In any case the potential losing player can always continue the game to reach a NO RESULT.
I think you hit the nail on the head.

This is just what I meant.

If the three ko shapes are solidly connected, and consequently only two groups involved, the (J89) result of the status-assessment of this triple-ko shape would be SEKI.
=> Probably one player would prefer "no result".

If the three ko shapes are seperated (e.g. into a double-ko and a simple ko), the J89 examples enforce the death of several groups, ruling out the possibility of SEKI.

Does this mean that a triple-ko is not a triple-ko?

Oops there are big differences betweeen a solid triple ko and the following position.

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

Assuming neither player can allow losing her big group at the top the result is not necessarily a NO RESULT as with a solid triple ko.
As you can see black as a serious advantage because black can force a NO RESULT game.
For white it is quite different because she cannot force a cycle in normal play. After:

Click Here To Show Diagram Code: [go]$$W :w3: pass :b4: pass $$ +---------------------------------------+ $$ | . O O . O . O X 1 X O . O X . . . . . | $$ | O X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X O 2 O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

the game stops and white must resume the game to continue the game. If we assume white is not allowed to resume the game an infinite time then the game will definitly stop and the confirmation phase will take place.

In J89 you already showed that a loop can take place in this confirmation phase => white is alive => seki.
If this result is enough for black to win then it will be the result of the game. But if the seki implies a losing game for black then black will choose to play the triple ko to reach a NO RESULT.
Comparing to the solidly connected triple ko it is quite different : the player with the advantage (here black) cannot lose, the result will be either a win of this player or NO RESULT depending of the score in case of seki.

In J2003 it is quite different:

Click Here To Show Diagram Code: [go]$$B w4: ko-pass $$ +---------------------------------------+ $$ | 1 O O 5 O . O X 2 X O . O X . . . . . | $$ | O X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X O 3 O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | X 7 6 . O . O X O 9 O . O X . . . . . | $$ | O X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X 8 X O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

this

for black is here allowed because after the previous

ko-pass, taking the ko at

becomes allowed!
In J2003 all the white stones are dead.

Here again we can ask yourself what is the expected result but I do not know what japonese professionals will decide.

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 2:01 pm

Gérard TAILLE wrote:Comparing to the solidly connected triple ko it is quite different : the player with the advantage (here black) cannot lose, the result will be either a win of this player or NO RESULT depending of the score in case of seki.

I am happy that we agree that the types of triple-ko I mentioned are different.

Positions, which have a one-sided advantage, are usual also in J89. Therefore, it does not matter whether both sides can enforce a NO RESULT, or only one.

If Black cannot lose, as you finally concluded, the only reason left for beating the White stones to death during status-confirmation is to avoid NO RESULT (i.e. no win for Black) in the case that White would win even with this position kept as a seki.
This is exactly what I mentioned as likely motivation of the authors of J89.

But why on earth should it be mandatory for the party, which large triple-ko portion is sandwiched between opponent's groups, to win a game of Go?

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Aug 17, 2021 2:42 pm

Cassandra wrote:I am happy that we agree that the types of triple-ko I mentioned are different.

OC I agree with you. In addition let's look at the example 11:

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

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

In J89 the white marked are still alive because of the loop in the confirmation phase in top right corner.
In J2003 these stones are dead.
Surely it is a failure of J89 isn't it?

More generally J89 fails to handle double ko as I showed you with the example:

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]

By the way, in J2003, you have two different ways for killing white stone marked:

Click Here To Show Diagram Code: [go]$$B :w4: ko-pass $$ ----------------- $$ | . X 2 X O X . | $$ | X X X O O X X | $$ | O X O O X X . | $$ | 3 O . O O X . | $$ | O O O O O X . | $$ | X X X X X X 5 | $$ | . X . . . 1 Q | $$ -----------------[/go]

Click Here To Show Diagram Code: [go]$$B :w4: ko-pass :b7: is allowed! $$ ----------------- $$ | . X . 7 O X . | $$ | X X X O O X X | $$ | 6 X O O X X . | $$ | X O . O O X . | $$ | O O O O O X . | $$ | X X X X X X X | $$ | . X . . . X . | $$ -----------------[/go]

or you can use the following barrier

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

and play

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | 4 X 2 X W X . | $$ | X X X W W X X | $$ | O X W W X X . | $$ | . W . W W X . | $$ | W W W W W X . | $$ | X X X X X X 3 | $$ | . X . . . 1 Q | $$ -----------------[/go]

which seems more in the spirit of J2003!

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 3:56 pm

Gérard TAILLE wrote:
$$B
$$ +---------------------------------------+
$$ | . . X O . W . W X . . . . X O . O X . |
$$ | . . X X W W W W X . . . . X O O X X X |
$$ | . . . X X X X X X . . . . X X O O X . |
$$ | . . . . . . . . . . . . . . X O . O X |
$$ | . . . . . . . . . . . . . . X O O O O |
$$ | . . . . . . . . . . . . . . X X X X X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
Click Here To Show Diagram Code
[go]$$B $$ +---------------------------------------+ $$ | . . X O . W . W X . . . . X O . O X . | $$ | . . X X W W W W X . . . . X O O X X X | $$ | . . . X X X X X X . . . . X X O O X . | $$ | . . . . . . . . . . . . . . X O . O X | $$ | . . . . . . . . . . . . . . X O O O O | $$ | . . . . . . . . . . . . . . X X X X X | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]
In J89 the white marked are still alive because of the loop in the confirmation phase in top right corner.

Look again

J89 translation wrote:If both these positions are present on the board, the seven white stones on the left are dead while the enclosed black and white groups on the right are both alive in double-ko seki.

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 4:07 pm

Gérard TAILLE wrote:More generally J89 fails to handle double ko as I showed you with the example:
$$W
$$ -----------------
$$ | . X . X O X . |
$$ | 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 . |
$$ | . X . . . . Q |
$$ -----------------
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]

I told you already that example 11 is nonsens in the pedagogical sense.

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]

Final position of the game.
Let us do the status confirmation for the marked White stone.

Click Here To Show Diagram Code: [go]$$B :w4: pass $$ ----------------- $$ | . X 2 X O X . | $$ | X X X O O X X | $$ | O X O O X X . | $$ | 3 O . O O X . | $$ | O O O O O X . | $$ | X X X X X X 5 | $$ | . X . . . 1 Q | $$ -----------------[/go]

This is the correct mirror for what is commented in example 11.

passes for the positon under investigation, not for lifting the ko ban in the double-ko!
White's marked stone can be captured, but no new White stone can be played.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . X 2 X O X . | $$ | 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 3 | $$ | . X . . . 1 Q | $$ -----------------[/go]

This sequence would be shorter.

Click Here To Show Diagram Code: [go]$$B :w2: pass $$ ----------------- $$ | . X . X O X . | $$ | 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 3 | $$ | . X . . . 1 Q | $$ -----------------[/go]

White might even do nothing.

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

The marked White stone is "dead".

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

Would be he same here.

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

And also here.

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

is a two-eyed-alive group, so everything inside is independent from every outside.

Cassandra · Post by **Cassandra** » Tue Aug 17, 2021 5:27 pm

Dear Gérard,

you were not right with your conclusions above, regarding J89, but you might have found the clue for solving examples 16 to 18 as intended.

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

Let's try to apply the example 11 commentary on problem 16...

Click Here To Show Diagram Code: [go]$$B :w4: passes for the ko at left $$ +---------------------------------------+ $$ | 1 O O . O . O X 2 X O . O X . . . . . | $$ | O X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X O 3 O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | X O O 5 O . O X O . O . O X . . . . . | $$ | . X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X . X O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | X . 6 X O . O X O . O . O X . . . . . | $$ | . X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X . X O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | X 7 O . O . O X O . O . O X . . . . . | $$ | . X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X . X O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

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

Do you remember this formation at the top?
Looks a bit like example 11, doesn't it?
But example 11's "White's stones at the left are dead, and the two groups at the right are alive in double-ko seki" would not lead to the intended result of this example.

So let's continue ...

Click Here To Show Diagram Code: [go]$$Bm9 :w8: pass for double-ko $$ +---------------------------------------+ $$ | X X O 1 O 3 O X O . O . O X . . . . . | $$ | . X X O O O O X X O O O O X . . . . . | $$ | X X . X X X O X 2 X O X X X . . . . . | $$ | . . . , X O X X X O O X . . . , . . . | $$ | . . . . X O X . X O X X . . . . . . . | $$ | . . . . X O X X O X X . . . . . . . . | $$ | . . . . X O O O O . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Ups, "collapse of the seki"!

+ + + + + + + + + + + + + + +

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

Would be the same here, where example 11 arises earlier as above.

Click Here To Show Diagram Code: [go]$$B :w4: passes for the ko at left $$ +---------------------------------------+ $$ | 1 O . O . O X 2 X O . O X . . . . . . | $$ | O X O O O O X X O O O O X . . . . . . | $$ | X X X X X O X O 3 O X X X . . . . . . | $$ | . . . X O X X X O O X . . . . , . . . | $$ | . . . X O X . X O X X . . . . . . . . | $$ | . . . X O X X O X X . . . . . . . . . | $$ | . . . X O O O O . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

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

Again a clone of example 11

Click Here To Show Diagram Code: [go]$$B :w6: passes for double-ko $$ +---------------------------------------+ $$ | X O 5 O 7 O X O . O . O X . . . . . . | $$ | . X O O O O X X O O O O X . . . . . . | $$ | X X X X X O X . X O X X X . . . . . . | $$ | . . . X O X X X O O X . . . . , . . . | $$ | . . . X O X . X O X X . . . . . . . . | $$ | . . . X O X X O X X . . . . . . . . . | $$ | . . . X O O O O . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

+ + + + + + + + + + + + + +

This procedure would imply that "pass-for-ko" was intended to be done in order of the ko captures.
But this cannot be really true, can it?

Gérard TAILLE · Post by **Gérard TAILLE** » Wed Aug 18, 2021 7:16 am

Dear Cassandra,

Cassandra wrote:
$$W
$$ -----------------
$$ | . X . X O X . |
$$ | 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 . |
$$ | . X . . . . Q |
$$ -----------------
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]
Final position of the game.
Let us do the status confirmation for the marked White stone.

$$B :w4: pass
$$ -----------------
$$ | . X 2 X O X . |
$$ | X X X O O X X |
$$ | O X O O X X . |
$$ | 3 O . O O X . |
$$ | O O O O O X . |
$$ | X X X X X X 5 |
$$ | . X . . . 1 Q |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B :w4: pass $$ ----------------- $$ | . X 2 X O X . | $$ | X X X O O X X | $$ | O X O O X X . | $$ | 3 O . O O X . | $$ | O O O O O X . | $$ | X X X X X X 5 | $$ | . X . . . 1 Q | $$ -----------------[/go]
This is the correct mirror for what is commented in example 11. passes for the positon under investigation, not for lifting the ko ban in the double-ko!

Example 11 is not clear because on the same diagram two positions are presented and we may think they are independant positions. In that sense your are right OC => let's forget this example 11.

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

My diagram above propose only one position which is the position in which the game stopped.
For this position we need to apply the confirmation phase to get the status of all groups.
Assume I begin by analysing white groups, ignoring for the moment the status of black groups of stones.
Seeing in the rule the statement "Stones are said to be "alive" if they cannot be captured by the opponent, or ...", I begin by looking for uncapturable white groups and here is the result:

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

the marked white stones are uncapturable => they are alive.

Now I have to look for the status of the other white groups and I decide to consider the white stone in the bottom right corner.

Variation 1:

Click Here To Show Diagram Code: [go]$$B :w4: pass-for-ko created by :b3: $$ ----------------- $$ | . X 2 X W X . | $$ | X X X W W X X | $$ | O X W W X X . | $$ | 3 W . W W X . | $$ | W W W W W X . | $$ | X X X X X X 5 | $$ | . X . . . 1 O | $$ -----------------[/go]

Click Here To Show Diagram Code: [go]$$B :b7: pass-for-ko created by :w2: $$ ----------------- $$ | 8 X O . W X . | $$ | X X X W W X X | $$ | 6 X W W X X . | $$ | X W . W W X . | $$ | W W W W W X . | $$ | X X X X X X X | $$ | . X . . . X . | $$ -----------------[/go]

Click Here To Show Diagram Code: [go]$$B :b7: pass-for-ko created by :w2: $$ ----------------- $$ | O . O . W X . | $$ | . . . W W X X | $$ | O . W W X X . | $$ | . W . W W X . | $$ | W W W W W X . | $$ | X X X X X X X | $$ | . X . . . X . | $$ -----------------[/go]

and I see white has been able to put on the board new uncapturable stones in the upper left corner (remember that, at this time of the analysis I do not know which black groups may be uncapturable if not two-eyed groups).

For black, let's try another variation to try and prove the white stone in the bottom right corner is dead.

Variation 2:

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . X 2 X W X . | $$ | X X X W W X X | $$ | O X W W X X . | $$ | 3 W . W W X . | $$ | W W W W W X . | $$ | X X X X X X . | $$ | . X . . . 1 O | $$ -----------------[/go]

pass-for-ko created by

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . X O 7 W X . | $$ | X X X W W X X | $$ | 6 X W W X X . | $$ | X W . W W X . | $$ | W W W W W X . | $$ | X X X X X X . | $$ | . X . . . 1 Q | $$ -----------------[/go]

pass-for-ko created by

This loop can continue forever while the marked white stone in the bottom right corner is still not captured.

According to the article 7.1 the white stone in the bottom right corner is capturable but is alive.

In J89 no indenpendancies are defined between groups of stones (in J2003 we have the local-2 concept but not in J89). Indirectly the pass-for-ko rule creates a kind of independancy but it does not work very well here.

What in J89 rule can avoid the white defense above? (this defense does not work in J2003).

Cassandra · Post by **Cassandra** » Wed Aug 18, 2021 9:24 am

Gérard TAILLE wrote:What in J89 rule can avoid the white defense above? (this defense does not work in J2003).

I'm afraid nothing EXPLICITELY mentioned in the text can prevent this.
I think that this is a side-effect of the flawed special ko-ban rule that the authers of J89 were not aware of. I am sure that this special rule was designed for several application cases of triple-ko. Probably double-ko flew under the radar...

What makes things even worse: The explanations of the life-and-death examples support your assessment.

+ + + + + + + + + + + +

Example 1:

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

Status assessment for White's marked stone.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | 1 X X O . O . $$ | Q X X O . O . $$ | X O O O O O . $$ | X X X , . . . $$ | . . X . . . . $$ | X X X . . . . $$ | . . . . . . .[/go]

It can be captured.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | X X X O . O . $$ | 2 X X O . O . $$ | X O O O O O . $$ | X X X , . . . $$ | . . X . . . . $$ | X X X . . . . $$ | . . . . . . .[/go]

White can recapture, so the status is still pending.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | 5 4 . O . O . $$ | Q 3 . O . O . $$ | X O O O O O . $$ | X X X , . . . $$ | . . X . . . . $$ | X X X . . . . $$ | . . . . . . .[/go]

White's stone is captured for a SECOND time.

Does this mean that the J89 story ends here? Reborn but killed again?
NO!!!

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | X O 6 O . O . $$ | 7 X . O . O . $$ | X O O O O O . $$ | X X X , . . . $$ | . . X . . . . $$ | X X X . . . . $$ | . . . . . . .[/go]

White connects.
Black connects.

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

J89 declares the status of White's captured stone as "alive", because two uncapturable new stones could be played.
But are these stones played
-- AFTER White's stone had been captured for the first time, or
-- AFTER White's stone had been captured for the second time?

In the case of the latter, the new uncapturable stones would be irrelevant.
White's stone would be "dead".

Additionally, and this returns to your problem ...

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

... the new uncapturable stones are played at board points, where Black did NOT capture any White stone, and which were occupied by Black before.
I.e. there was NO rebirth of White's captured stone in the narrow sense.

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

If we were fond of "locality", we could swallow a sedative pill:

Everything happened inside the surrounding fencing by "two-eyed alive" groups.

But worse is to come ...

+ + + + + + + + + + + + + +

Example 4:

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

Status assessment for White's stones.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------- $$ | . X 1 2 X X X O X . . $$ | X X O O O O O O X . . $$ | . O X X X X X X X . . $$ | . O X , X X . . . , . $$ | X O X X . X . . . . . $$ | X O X X X X . . . . . $$ | X O X . . . . . . . . $$ | O O X . . . . . . . . $$ | X X X . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]

Black tries to capture.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------- $$ | . X X O . 3 . O X . . $$ | X X O O O O O O X . . $$ | . O X X X X X X X . . $$ | 4 O X , X X . . . , . $$ | X O X X . X . . . . . $$ | X O X X X X . . . . . $$ | X O X . . . . . . . . $$ | O O X . . . . . . . . $$ | X X X . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]

Click Here To Show Diagram Code: [go]$$B $$ +---------------------- $$ | . X X O 7 X 5 O X . . $$ | X X O O O O O O X . . $$ | . O X X X X X X X . . $$ | O O X , X X . . . , . $$ | . O X X . X . . . . . $$ | 6 O X X X X . . . . . $$ | . O X . . . . . . . . $$ | O O X . . . . . . . . $$ | X X X . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]

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

The sequence shown in J89 ends with this final position.
But is is clear from the comment that the sequence during "play" is shown, which resolves the temporary seki.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------- $$ | . X X . X X X . X . . $$ | X X . . . . . . X . . $$ | 8 O X X X X X X X . . $$ | O O X , X X . . . , . $$ | . O X X . X . . . . . $$ | O O X X X X . . . . . $$ | . O X . . . . . . . . $$ | O O X . . . . . . . . $$ | X X X . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]

You will realise that NO uncapturable White stone has been played yet, AFTER White's group at the top has been captured.
Therefore, White needs another move at the left to enable J89 declaring the captured White stones "alive".

Click Here To Show Diagram Code: [go]$$B $$ +---------------------- $$ | . X X . X X X T X . . $$ | X X T T T T T T X . . $$ | @ O X X X X X X X . . $$ | O O X , X X . . . , . $$ | . O X X . X . . . . . $$ | O O X X X X . . . . . $$ | . O X . . . . . . . . $$ | O O X . . . . . . . . $$ | X X X . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]

Again, as in example 1, NO White new uncapturable stone has been played at board point, which was occupied by White's captured stones before.
I.e. NO rebirth in the narrow sense.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------- $$ | . B . . X X X Q B . . $$ | X B Q Q Q Q Q Q B . . $$ | S O B B B B B B B . . $$ | . O X , X X . . . , . $$ | X O X X . X . . . . . $$ | X O X X X X . . . . . $$ | X O X . . . . . . . . $$ | O O X . . . . . . . . $$ | X X X . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]

Contrary to example 1, there is NO "locality" sedative pill available here!

White's "new uncapturable" stone is played OUTSIDE the surrounding fencing by "two-eyed alive" groups.

Cassandra · Post by **Cassandra** » Wed Aug 18, 2021 5:48 pm

Cassandra wrote:By the way:

The life-and-death examples in J89 -- treating a compound of bent-four and double-ko -- do NOT cover ALL possible variations of shared double-ko formations. J89 suppresses an example like the following one -- with NESTED ko shapes.

$$
$$ +----------------------
$$ | . O . X O X O . . . .
$$ | O X X X O X O O . . .
$$ | . X O O O X X O O . .
$$ | X X O O . O X X O , .
$$ | O O O . O X . X O . .
$$ | X X O O X . X X O . .
$$ | . X X O O X X O O . .
$$ | . . X X X O O O . . .
$$ | . . . . X . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
Click Here To Show Diagram Code
[go]$$ $$ +---------------------- $$ | . O . X O X O . . . . $$ | O X X X O X O O . . . $$ | . X O O O X X O O . . $$ | X X O O . O X X O , . $$ | O O O . O X . X O . . $$ | X X O O X . X X O . . $$ | . X X O O X X O O . . $$ | . . X X X O O O . . . $$ | . . . . X . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . .[/go]
To be honest, I have forgotten ("misplaced") the results of my J89-application trials with it. But for sure, at that time I did not dream of some restricting side conditions that prevent any triple-ko cycles.

However, I know that a status-assessment without any special ko-ban-rule will give interesting results (as well).

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

This nested type of a double-ko might be also missing as example 16A ...

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

And this one as example 16B ...

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

And this one as example 18B ...

There might be a reason that J89 does NOT have the SANDWICHED (i.e. inner) group of the double-ko with NESTED ko shapes.

Life In 19x19

Japonese counting

Re: Japonese counting

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Re: Japonese counting