Loops with a cycle-length of pseudo 6 (contd)


The earth suddenly trembled between rubble and scrub - an earthquake!
There was a huge landslide ahead of us that blocked access to District 6 for all eternity. It is estimated that "He Who Cannot Be Named" had his hands in it magically.

We later heard that GT City's central office building was also collapsed by the earthquake. Thank goodness no one was killed or injured because everyone there was on a research expedition.
There are rumors that GT City will not rebuild its central building, but will leave its ruins as a reminder of a glorious past in which people still believed in the healing properties of "loops". After all, they have more than enough empty office space.

Now let's share what was seen after the earthquake.



##### After the earthquake #####

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

===== GT territory rules =====

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[go]$$B
$$ +-------------+
$$ | 1 X 2 X . X |
$$ | X O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$B
$$ +-------------+
$$ | . 3 . X . X |
$$ | . O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$B
$$ +-------------+
$$ | . Y . Y . X |
$$ | . O Y X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

created a ko-shape.

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[go]$$B
$$ +-------------+
$$ | 4 X . X . X |
$$ | . O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$B
$$ +-------------+
$$ | Q X . X . X |
$$ | . Q X X X X |
$$ | Q O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

created a ko-shape.

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[go]$$B
$$ +-------------+
$$ | Q X . X . X |
$$ | 5 Q X X X X |
$$ | Q O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

captures into a ko-shape.

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[go]$$B pass
$$ +-------------+
$$ | Q X . X . X |
$$ | ? Q X X X X |
$$ | Q O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

passes.
The resulting position is a "critical" one.

White claims for creating a "permanently prohibited ko", making a ko-capture at the shadowed point taboo for Black.

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[go]$$Bm7
$$ +-------------+
$$ | 1 X 2 X . X |
$$ | X O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$Bm7
$$ +-------------+
$$ | . 3 . X . X |
$$ | . O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$Bm7
$$ +-------------+
$$ | . Y . Y . X |
$$ | . O Y X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

created a ko-shape.

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[go]$$Bm7
$$ +-------------+
$$ | 4 X . X . X |
$$ | . O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$Bm7
$$ +-------------+
$$ | Q X . X . X |
$$ | ? Q X X X X |
$$ | Q O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

created a "permanently prohibited ko".

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[go]$$Bm7 pass
$$ +-------------+
$$ | Q X . X . X |
$$ | ? Q X X X X |
$$ | Q O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

Black can only "pass", as the shadowed point has become taboo for him.

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[go]$$Bm11 pass
$$ +-------------+
$$ | O X 2 X 4 X |
$$ | . O X X X X |
$$ | O O O X O O |
$$ | . . X O O . |
$$ | X X X X O O |
$$ | . X . X O . |
$$ +-------------+[/go]

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[go]$$B
$$ +-------------+
$$ | W . W . W . |
$$ | . W . . . . |
$$ | W W W . W W |
$$ | . . X W W . |
$$ | X X X X W W |
$$ | . X . X W . |
$$ +-------------+[/go]

Two eye formation for White, but NOT occupying the entire board.

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[go]$$B
$$ +-------------+
$$ | @ # . # . # |
$$ | . @ # # # # |
$$ | @ @ @ # @ @ |
$$ | T T X @ @ . |
$$ | X X X X @ @ |
$$ | . X . X @ . |
$$ +-------------+[/go]

NO territory for White on the entire board.

White should have taken Black's stones at the top off the board before the game stopped, and occupied the DAME of thereafter.



===== "Two-eyed alive" world =====


As can be seen above, the cycle as a length of 6, but it includes a White "pass", so the cycle length is "pseudo 6" only.

-------------------------

The cycle-length pseudo 6 fulfills the condition

cl = 2 + 4n (n = 0, 1, 2, 3, ...).

Therefore, the last GENUINE move of that (uninterrupted) cycle is forbidden.


Next run:

As can be seen above, White will be able to create a two-eye-formation in the upper part of the board by capturing Black's stones at the top.


-------------------------

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[go]$$B
$$ +-------------+
$$ | a Z b Z c Z |
$$ | Z W Z Z Z Z |
$$ | W W W Z W W |
$$ | T T B W W . |
$$ | B B B B W W |
$$ | . B . B W . |
$$ +-------------+[/go]

Concluding result of status confirmation.

Black should have occupied the DAME before the game stopped, forcing White to take his stones at the top off the board with moves at a, b, and c.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Oops it seems the earthquake has not only attacked the structure of the building of the city but also the foundation of the rule itself.
In either rule, if you look at the marked black group you see two eyes at "e" locations and two dame points at "d" locations. => obviouly the game is not finished because you cannot imagine black allowing the existence of these dame with the consequence that the eye points "e" will not be counted as territory.

OK let's assume that black decides to pass
Can white claim for a territory at the top of the board?

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[go]$$B
$$ +-------------+
$$ | . X . X . X |
$$ | X O X X X X |
$$ | O O O X O O |
$$ | C C B O O . |
$$ | X X X B O O |
$$ | . X . B O . |
$$ +-------------+[/go]

Always due to the dame "d" it is not possible because the outside border marked here above is not valid (two empy locations)

With this kind of unfinished game you not even need to start an hupothetical play.

Surely I have to find a safe-deposit-box in order to protect my rule against an earthquake.

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[go]$$B
$$ +---------------+
$$ | O X X X . X X |
$$ | a O X X X X b |
$$ | O . O O X O X |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
$$[/go]

How do you recognise a double ko? Depending of the environment you cannot replace the position above by the following can you?

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[go]$$Bc
$$ +---------------+
$$ | . X X X . X X |
$$ | O O X X X X X |
$$ | O . O O X O . |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
$$ {AR A7 A6}
$$ {AR G5 G6}
$$[/go]

I suppose that...

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[go]$$Bc
$$ +---------------+
$$ | T X X X C X X |
$$ | Q O X X X X Y |
$$ | O C O O X O T |
$$ | O O O C O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+[/go]

... (two eyes vs. one eye) will make you easier understand that Black's group at the top is dead than...

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[go]$$B
$$ +---------------+
$$ | O X X X . X X |
$$ | 1 O X X X X . |
$$ | O 2 O O X O X |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+$$[/go]

... playing in your head.

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[go]$$B
$$ +---------------+
$$ | M X X X C X X |
$$ | X P X X X X M |
$$ | O O O O X P X |
$$ | O O O C O O O |
$$ | . . . O C O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+$$[/go]

Black's group has one genuine, and two false, eyes -- and so is dead. Same result as after Honte's magic spell.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

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[go]$$B
$$ +---------------+
$$ | O X X X . X X |
$$ | a O X X X X b |
$$ | O . O O X O X |
$$ | O O O . O O O |
$$ | X X X O . O . |
$$ | X . X O O O O |
$$ | . X X X X X X |
$$ +---------------+
$$[/go]

Honte's magic wand will clearly disadvantaged black won't it? => it is almost a double ko but it is not really one.

About compositions of four ko-shapes

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

This is the example with four ko-shapes that Gérard kindly provided to me.

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[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X Y O O O |
$$ | O O Y b X c Y O O |
$$ | O O Q Y X Y Q O O |
$$ | e O a Q X Q d O f |
$$ +-------------------+[/go]

The four ko-shapes are a, b, c and d.

All three groups in question have TWO liberties each.
-- White's group at the left has one liberty at e in her eye, and another one in the neighbored double-ko (at a or b).
-- Black's group in the centre has one liberty in the double-ko at left (at a or b), and another one in the double-ko at right (at c or d)
-- White's group at the left has one liberty at f in her eye, and another one in the neighbored double-ko (at c or d).

Thus, we can expect this position being a seki.



##### Honte's magic DOUBLE-KO spell #####

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[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O T Y X Y T O O |
$$ | O O O X X X O O O |
$$ | . O Q T X T Q O . |
$$ +-------------------+[/go]

After Honte used his magic wand...

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[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . B B B B . . |
$$ | . B B B @ @ B B . |
$$ | B B @ @ # @ @ B B |
$$ | @ @ @ # # # @ @ @ |
$$ | @ @ . # # # . @ @ |
$$ | @ @ @ # # # @ @ @ |
$$ | . @ @ . # . @ @ . |
$$ +-------------------+[/go]

... we can easily see that the position is seki.

No wonder that this is the fastest method, as magic was involved.



##### GT territory rules #####


Second fastest is using the GENUINE quadruple-ko cycle.

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[go]$$B GENUINE quadruple-ko cycle
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X 2 X 4 X O O |
$$ | O O O X X X O O O |
$$ | . O 1 O X O 3 O . |
$$ +-------------------+[/go]

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[go]$$B GENUINE quadruple-ko cycle
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O 5 O X O 7 O O |
$$ | O O O X X X O O O |
$$ | . O X 6 X 8 X O . |
$$ +-------------------+[/go]

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[go]$$B GENUINE quadruple-ko cycle
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O X X X O O O |
$$ | . O . O X O . O . |
$$ +-------------------+[/go]

Same position as eight moves before.

Neither side will ever create a two-eye-formation in the lower part of the board.
==> NO territory.

--------------------------

Using the "permanent prohibited ko" feature will neither shorten nor ease the sequences required.
It seems to me that "permanent prohibited ko" will be most useful in ASYMMETRICAL positions.

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O Q X X X O O O |
$$ | . O 1 Q X O . O . |
$$ +-------------------+[/go]

We will start with trying to find out, whether White will be able to create a two-eye-formation at the bottom.

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X O O O |
$$ | O O Y 2 X . X O O |
$$ | O O O Y X X O O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

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[go]$$B Status confirmation for White groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X O O O |
$$ | O O T P X . X O O |
$$ | O O O Y X X O O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

Black also claims "permanently prohibited ko" for .

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X Y O O O |
$$ | O O . O X 4 Y O O |
$$ | O O O X X Y O O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O Q X X X O O O |
$$ | O O 5 Q X O . O O |
$$ | O O Q X X X O O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X O . O O |
$$ | O O O Y X X O O O |
$$ | . O Y 6 X O . O . |
$$ +-------------------+[/go]

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X Q O O |
$$ | O O Y M X Q 7 O O |
$$ | O O O Y X X Q O O |
$$ | . O . O X O . O . |
$$ +-------------------+[/go]

White must not capture into the ko-shape at left.

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[go]$$B Status confirmation for White groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X Q O O |
$$ | O O Y M X T Z O O |
$$ | O O O Y X X Q O O |
$$ | . O . O X O . O . |
$$ +-------------------+[/go]

White must not capture into the ko-shape at left, instead.
White also claims "permanently prohibited ko" for .

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[go]$$B Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O Q X X X O O O |
$$ | . O 9 Q X O . O . |
$$ +-------------------+[/go]

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[go]$$Wm10 Status confirmation for White groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X Y O O O |
$$ | O O Y M X 1 Y O O |
$$ | O O O Y X Y O O O |
$$ | 2 O X . X O . O . |
$$ +-------------------+[/go]

must not capture into the ko-shape at left, instead.


==> NO White territory.


------------------------

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X Y O O O |
$$ | O O X . X 1 Y O O |
$$ | O O O X X Y O O O |
$$ | . O . O X O . O . |
$$ +-------------------+[/go]

Will Black be able to create a two-eye-formation at the bottom?

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X O . O O |
$$ | O O O X X X Q O O |
$$ | . O . O X Q 2 O . |
$$ +-------------------+[/go]

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[go]$$W Status confirmation for Black groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X O . O O |
$$ | O O O X X X Q O O |
$$ | . O . O X T Z O . |
$$ +-------------------+[/go]

White also claims "permanently prohibited ko" for .

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X Q O O |
$$ | O O X . X Q 4 O O |
$$ | O O O X X X Q O O |
$$ | . O . O X . X O . |
$$ +-------------------+[/go]

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O X X Y O O O |
$$ | . O . O X 5 Y O . |
$$ +-------------------+[/go]

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[go]$$W Status confirmation for Black groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O X X Y O O O |
$$ | . O . O X P T O . |
$$ +-------------------+[/go]

Black also claims "permanently prohibited ko" for .
This does not have any effect, as Black must not re-capture into that ko-shape anyway.

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X Y O O O |
$$ | O O X . X 7 Y O O |
$$ | O O O X X Y O O O |
$$ | . O . O X O . O . |
$$ +-------------------+[/go]

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X O . O O |
$$ | O O Q X X X Q O O |
$$ | . O 8 Q X Q M O . |
$$ +-------------------+[/go]

Black must not re-capture at right, instead.

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[go]$$W Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X O O O |
$$ | O O Y 9 X O . O O |
$$ | O O O Y X X O O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X Q O O |
$$ | O O . O X Q 1 O O |
$$ | O O O X X X Q O O |
$$ | . O X . X Q M O . |
$$ +-------------------+[/go]

Black must not re-capture into the lower ko-shape.

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X Q O O |
$$ | O O . O X T Z O O |
$$ | O O O X X X Q O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

White also claims "permanently prohibited ko" for .

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O Q X X X O O O |
$$ | O O 3 Q X . X O O |
$$ | O O Q X X X O O O |
$$ | . O X . X O . O . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O Y X X O O O |
$$ | . O Y 4 X O . O . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O Y X X Q O O |
$$ | . O T P X Q M O . |
$$ +-------------------+[/go]

Black must not re-capture into the lower ko-shape at right, instead.
Black also claims "permanently prohibited ko" for .

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X O O O |
$$ | O O Y 6 X . X O O |
$$ | O O O Y X X O O O |
$$ | . O . O X O . O . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$Bm10 Status confirmation for Black groups; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X X O O O |
$$ | O O . O X 8 X O O |
$$ | O O O Y X X Q O O |
$$ | . O . O X Q M O . |
$$ +-------------------+[/go]

Black must not re-capture into the lower ko-shape at right.


==> NO Black territory.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

"GT territory rule" do not handle loops by trying to recognize them really (I mean recognizing that the same position appeared already in the previous moves). "GT territory rule" looks only to an infinity of "critical" positions. Assuming white claim for a territory at the bottom of the board then it is black to play and obviously black can play only atari moves to which white has to answer by puting a stone on the board => no "critical" positions at all => no "permanent prohibited ko" => the loop cannot be break => No territory.
That's all you can do with "GT territory rule". Remember, if the attacker wants to break a loop she must first prove she can reach "critical" positions an infinite number of time, with the defender playing first in the hypothetical play. Here the attacker cannot even reach only one "critical" position => the loop cannot be breaked.

In J2003 the analyse seems more complicated if not strange: the big white and black groups of stones are all alive, the four isolated stones involved in the ko are dead (they can be captured and no new permanently alive stone can be created) => the four empty locations in the ko are dame (they are not surrounded by only living stones) => the three big alive groups have dame => seki

It seems I wrote a throwback to GT City's Roaring Twenties.

You too still seem to like to remember that "looping" time.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

"HIGHLANDER  2   ––   At the very most there can be one"


Honte's magic DOUBLE-ko spell reduces the number of ko-shapes that are really effective in a formation under status consideration.
The number of ko-shapes effectively remaining will be

1 or 0.



ONE ko-shape:

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | . Q . Q . X . |
$$ | O O Q X X X . |
$$ | X X X X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |[/go]

Effective number of ko-shapes: 1



TWO ko-shapes:

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[go]$$B
$$ +---------------+
$$ | . Y . Y O X . |
$$ | X X Y O O X . |
$$ | Q X O . O X . |
$$ | . Q O O O X . |
$$ | Q O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Two ko-shapes.

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[go]$$B
$$ +---------------+
$$ | . X Y T O X . |
$$ | X X X O O X . |
$$ | T X O . O X . |
$$ | Q O O O O X . |
$$ | O O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

After Honte used his magic wand...

Click Here To Show Diagram Code

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

Effective number of ko-shapes: 0



THREE ko-shapes:

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------+
$$ | . Q O . O . O X . Y O . O |
$$ | Q X X O O O O X Y Q O O O |
$$ | X X . X X X O X Q . O X X |
$$ | . . X , X O X X X Q O X X |
$$ | X X X X X O X . X O X X . |
$$ | O O O O X O X X X O X . X |
$$ | . . . O O O O O O X X X X |
$$ | . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . |[/go]

Three ko-shapes.

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------+
$$ | . Q O . O . O X Y T O . O |
$$ | Q X X O O O O X X O O O O |
$$ | X X . X X X O X T Q O X X |
$$ | . . X , X O X X X O O X X |
$$ | X X X X X O X . X O X X . |
$$ | O O O O X O X X X O X . X |
$$ | . . . O O O O O O X X X X |
$$ | . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . |[/go]

After Honte used his magic wand...

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------+
$$ | . Q O . O . O X X . O . O |
$$ | Q X X O O O O X X O O O O |
$$ | X X . X X X O X . O O X X |
$$ | . . X , X O X X X O O X X |
$$ | X X X X X O X . X O X X . |
$$ | O O O O X O X X X O X . X |
$$ | . . . O O O O O O X X X X |
$$ | . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . |[/go]

Effective number of ko-shapes: 1



FOUR ko-shapes:

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X Y O O O |
$$ | O O Y . X . Y O O |
$$ | O O Q Y X Y Q O O |
$$ | . O . Q X Q . O . |
$$ +-------------------+[/go]

Four ko-shapes.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O T Y X Y T O O |
$$ | O O O X X X O O O |
$$ | . O Q T X T Q O . |
$$ +-------------------+[/go]

After Honte used his magic wand...

Click Here To Show Diagram Code

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

Effective number of ko-shapes: 0

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O . O X a X O O b |
$$ | O O O O X X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$[/go]

Two kos.
Applying Honte's magic wand would be a disaster for white wouldn't it?

Thank you for giving me the opportunity to clarify what a "DOUBLE-Ko" is.

Click Here To Show Diagram Code

[go]$$B Ko at left
$$ +-------------------+
$$ | O . Q Y T Y O O . |
$$ | O O O Q Y X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$B Groups connected to the ko at left
$$ +-------------------+
$$ | Q . Q Y T Y O O . |
$$ | Q Q Q Q Y Y O X O |
$$ | . Y Y Y . Y O X X |
$$ | Y Y Y Y Y Y O . . |
$$ | O O O O O Y O O O |
$$ | . . . O O Y Y Y Y |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

------------------------

Click Here To Show Diagram Code

[go]$$B Ko at right
$$ +-------------------+
$$ | O . O X . X O Q T |
$$ | O O O O X X O Y Q |
$$ | . X X X . X O X Y |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$B Groups connected to the ko at right
$$ +-------------------+
$$ | O . O X . X Q Q T |
$$ | O O O O X X Q Y Q |
$$ | . X X X . X Q Y Y |
$$ | X X X X X X Q . . |
$$ | O O O O O X Q Q Q |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

------------------------

NONE of the groups is connected to BOTH ko-shapes, so Honte's magic DOUBLE-ko spell will have no effect here.



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

The topic above is strongly connected with what a FALSE EYE is.



Honte's spell only works on false eyes.

Click Here To Show Diagram Code

[go]$$B Ko at left => false eye
$$ +-------------------+
$$ | O . O X M X O O . |
$$ | O O O P X X O X O |
$$ | 1 X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

is an atari.
If White captured into that ko, it would be her stone that was in atari.

Click Here To Show Diagram Code

[go]$$B Ko at left => false eye
$$ +-------------------+
$$ | O . O X 1 X O O . |
$$ | O O O O X X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

False eyes in a seki can be filled by EITHER side (or NEITHER side, as with a GENUINE double-ko, to be complete).
Black here.

Click Here To Show Diagram Code

[go]$$W Ko at left => false eye
$$ +-------------------+
$$ | O . O X 1 X O O . |
$$ | O O O O X X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$W Ko at left => false eye; pass
$$ +-------------------+
$$ | O . O 3 O X O O . |
$$ | O O O O X X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

White here.

------------------------

Click Here To Show Diagram Code

[go]$$B Ko at right => NO false eye
$$ +-------------------+
$$ | O . O X . X O O C |
$$ | O O O O X X O B O |
$$ | . X X X . X O X X |
$$ | X X X X X X O 1 . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

is a self-atari!

Click Here To Show Diagram Code

[go]$$B Ko at right => NO false eye
$$ +-------------------+
$$ | O . O X . X O O 1 |
$$ | O O O O X X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$B Ko at right => NO false eye; pass
$$ +-------------------+
$$ | O . O X . X O O X |
$$ | O O O O X X O X 3 |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Black is able to fill the ko-shape.

Click Here To Show Diagram Code

[go]$$W Ko at right => NO false eye
$$ +-------------------+
$$ | O . O X . X O O 1 |
$$ | O O O O X X O X O |
$$ | . X X X . X O X X |
$$ | X X X X X X O . . |
$$ | O O O O O X O O O |
$$ | . . . O O X X X X |
$$ | . . . . O O O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

White is NOT!

==> That ko-shape is a genuine part of White's eye space!

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Honte's magic SINGLE-ko spell   ––   Usually there is NO ko at the beginning of status confirmation!


##### False eyes in status confirmation #####

Probably you already noticed that EVERY ko-shape that effectively remained after the application of Honte's magic DOUBLE-ko spell in my respective posting above is nothing more than only a FALSE EYE:

Click Here To Show Diagram Code

[go]$$B ko-shape
$$ +---------------+
$$ | . Q . Q . X . |
$$ | O O Q X X X . |
$$ | X X X X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |[/go]

Click Here To Show Diagram Code

[go]$$B false eye
$$ +---------------+
$$ | . O M O . X . |
$$ | O O O Z X X . |
$$ | X X X X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |[/go]

------------------------

Click Here To Show Diagram Code

[go]$$B ko-shape
$$ +---------------------------+
$$ | . Q O . O . O X X . O . O |
$$ | Q X X O O O O X X O O O O |
$$ | X X . X X X O X . O O X X |
$$ | . . X , X O X X X O O X X |
$$ | X X X X X O X . X O X X . |
$$ | O O O O X O X X X O X . X |
$$ | . . . O O O O O O X X X X |
$$ | . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code

[go]$$B false eye
$$ +---------------------------+
$$ | M O O . O . O X X . O . O |
$$ | O Z X O O O O X X O O O O |
$$ | X X . X X X O X . O O X X |
$$ | . . X , X O X X X O O X X |
$$ | X X X X X O X . X O X X . |
$$ | O O O O X O X X X O X . X |
$$ | . . . O O O O O O X X X X |
$$ | . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . |[/go]

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

Being a FALSE EYE means that the remaining SINGLE-ko shape is equivalent to a single liberty. Please refer to my previous posting for a more detailled explanation.
Honte's magic wand can be applied on these remaining SINGLE-ko, too! Please note that stones in SINGLE-ko will only move AFTER their collegues in the DOUBLE-ko already did. Please also note that in principle the formations that remain on the bord after Honte's magic DOUBLE-ko spell will not be particularly complicated, so in many cases you will be able to recognize the status without further magic.

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | . O Q T . X . |
$$ | O O O X X X . |
$$ | X X X X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |[/go]

After Honte used his magic wand for the second time...

------------------------

Click Here To Show Diagram Code

[go]$$B ko-shape
$$ +---------------------------+
$$ | Q O O . O . O X X . O . O |
$$ | T X X O O O O X X O O O O |
$$ | X X . X X X O X . O O X X |
$$ | . . X , X O X X X O O X X |
$$ | X X X X X O X . X O X X . |
$$ | O O O O X O X X X O X . X |
$$ | . . . O O O O O O X X X X |
$$ | . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . |[/go]

After Honte used his magic wand for the second time...


There is NO ko at the beginning of status confirmation!

J89 were trying to fix something that wasn't broken at all.

As we now know (https://lifein19x19.com/viewtopic.php?p=267061#p267061), there are exceptions...


##### False eyes during play #####

Please note that false eyes have different properties during play.

Click Here To Show Diagram Code

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

Black to move.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O X X X 2 O 1 O X |
$$ | O O O O O O O X X |
$$ | X X X X X X X X X |
$$ | . . . O O O O O O |
$$ | O O O O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code

[go]$$Bm3
$$ +-------------------+
$$ | O . 1 5 O O X 3 X |
$$ | O O O O O O O X X |
$$ | X X X X X X X X X |
$$ | O 2 4 6 O O O O O |
$$ | O O O O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]

Please note that White's moves are played on the OUTSIDE, which would be irrelevant in status confirmation.

Click Here To Show Diagram Code

[go]$$Bm5
$$ +-------------------+
$$ | O . X X O O . . . |
$$ | O O O O O O O . . |
$$ | . . . . . . . . . |
$$ | O O O O O O O O O |
$$ | O O O O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]

White won the semeai.


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

Honte's magic SINGLE-ko spell is NOT designed for the real world!

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O X X X . O Q T X |
$$ | O O O O O O O X X |
$$ | X X X X X X X X X |
$$ | . . . O O O O O O |
$$ | O O O O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]

Black to move.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O X X X 2 O O 1 X |
$$ | O O O O O O O X X |
$$ | X X X X X X X X X |
$$ | . . . O O O O O O |
$$ | O O O O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O 7 3 5 O O O X X |
$$ | O O O O O O O X X |
$$ | X X X X X X X X X |
$$ | 4 6 . O O O O O O |
$$ | O O O O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]

Please note that White's moves are played on the OUTSIDE, which would be irrelevant in status confirmation.

Click Here To Show Diagram Code

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

Black won the semeai.

_________________
EDITED

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Thomas,
Obviously it is still too early to know how to use Honte's magic wand. Surely it will be used during a confirmation phase (normal play is OC excluded) but what kind of confirmation phase? In GT territory rule the confirmation phase is quite close to normal play while in J89 or J2008 the pass-for-ko or the ko-pass change the analyse. In any case I guess magic wand might be use but only in special conditions which will depend of the confirmation phase used.
The best is to wait still a moment isn't it? Later, depending of how works in detail the confirmation phase you have in mind, surely you will be able to define the conditions to use the magic wand : who can use this wand (the attacker, the defender, both), in which kind of position the wand may be used (existing kos, number of groups involved, two stage ko allowed ...) when the wand can be used (remember in GT rule I defined special moment by using "critical" position) ...

Exceptionnaly I will try to avoid being impatient relating to the use of the Honte's magic. Take all the time needed to progress in your analysis.
Wait and see.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Analysis:

Is finished as you can see from my previous posting. I am waiting for potential counter-examples.
I still seriously wonder if I am really the very first to discover these principles.


----------------------

Usage:

Final board position of "play" ==> Apply "Honte's Magic Ko Spells" on the entire board ==> Board position for "status confirmation" / "territory identification".

That's all.
The number of potential occasions for controversial discussions remaining will be extremely limited. The same applies to both the occurrence of potential applications of any ko-pass variants and to "pass" after ko-captures.
Regardless of which ruleset you apply, you will always get the "J89-intended" result.


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

By the way:
I've heard rumours that Queen rewrote the first two verses of their well-known hit "A Kind of Magic":


No ko, no loop, no capture ban
No golden glance of what could be
It's a kind of magic

One magic spell that shows the way
A Labrador will win this day
It's a kind of magic




___________________
EDITED

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Obviously is nothing!
https://lifein19x19.com/viewtopic.php?p=267023#p267023 had a purpose

Nevertheless:
You seem to expect some kind of "proof".
The inconsistencies in the J89 ruleset largely relate to positions with a triple-ko.
Well, here comes part 1 of the "proof". The diagrams are a continuation of the previous ones for the triple-ko cycles.


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

About Honte's magic spells


##### GENUINE Triple-Ko: enforced cycle #####

Click Here To Show Diagram Code

[go]$$B
$$ ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? X X X X X X X ? ?
$$ ? ? X O X O X . X ? ?
$$ ? ? O . O . O X O ? ?
$$ ? ? O O O O O O O ? ?
$$ ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ?[/go]

------------------------

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . M M M M M . . . . . . . |
$$ | . . . . . . M ? ? ? ? ? M . . . . . . |
$$ | . . . . M M . ? O W . ? . M M . . . . |
$$ | . M M M . . . ? . . X ? . . . M M M . |
$$ | M ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? M |
$$ | M ? O . . ? . M M M M M . ? . O . ? M |
$$ | M ? . X B ? M . . . . . M ? B . X ? M |
$$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M |
$$ | M . . . . . M . . . . . M . . . . . M |
$$ | M . . , . . M . . , . . M . . , . . M |
$$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M |
$$ | M ? W . O ? M . . . . . M ? . O W ? M |
$$ | M ? . X . ? M . . . . . M ? X . . ? M |
$$ | M ? ? ? ? ? . M M M M M . ? ? ? ? ? M |
$$ | . M M M . . . ? ? ? ? ? . . . M M M . |
$$ | . . . , M . . ? . , O ? . . M , . . . |
$$ | . . . . . M . ? X B . ? . M . . . . . |
$$ | . . . . . . M ? ? ? ? ? M . . . . . . |
$$ | . . . . . . . M M M M M . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}[/go]

Let's apply Honte's magic DOUBLE-ko spell to the outer ko-shapes...

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . M M M M M . . . . . . . |
$$ | . . . . . . M ? ? ? ? ? M . . . . . . |
$$ | . . . . M M . ? T W Y ? . M M . . . . |
$$ | . M M M . . . ? Q . T ? . . . M M M . |
$$ | M ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? M |
$$ | M ? T . Y ? . M M M M M . ? T O Y ? M |
$$ | M ? Q X T ? M . . . . . M ? Q . T ? M |
$$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M |
$$ | M . . . . . M . . . . . M . . . . . M |
$$ | M . . , . . M . . , . . M . . , . . M |
$$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M |
$$ | M ? T . Y ? M . . . . . M ? T O Y ? M |
$$ | M ? Q X T ? M . . . . . M ? Q . T ? M |
$$ | M ? ? ? ? ? . M M M M M . ? ? ? ? ? M |
$$ | . M M M . . . ? ? ? ? ? . . . M M M . |
$$ | . . . , M . . ? T , Y ? . . M , . . . |
$$ | . . . . . M . ? Q B T ? . M . . . . . |
$$ | . . . . . . M ? ? ? ? ? M . . . . . . |
$$ | . . . . . . . M M M M M . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}[/go]

Nothing happens to the left and right INSIDE the cycle. This means that the cycle will be left there.

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q , T ? . . . , . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Q . . . . . . . . . . . Y . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Y . . . . . . . . . . . Q . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? T , Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q14}
$$ {AR Q12 Q9}
$$ {AR E12 E9}
$$ {AR Q7 M3}
$$ {AR H3 D7}
$$ {AR D9 D12}
$$ {AR P9 P12}
$$ {AR D14 H17}[/go]

The result is a ko-fight for nothing, as the position is seki anyway.
Both players might prefer continuing with the status confirmation elsewhere.

-------------------------

Let's apply Honte's magic KO-spell to the inner ko-shape...

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? T T Y ? . . . . . . . |
$$ | . . . , . . . ? Q Q T ? . . . , . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Q . . . . . . . . . . . Y . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Y . . . . . . . . . . . Q . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? T Y Y ? . . . , . . . |
$$ | . . . . . . . ? Q T T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR Q12 Q9}
$$ {AR P8 E8}
$$ {AR D9 D12}
$$ {AR E13 P13}[/go]

Status confirmation takes place outside the triple-ko formation!



##### GENUINE Triple-Ko: optional cycle #1 #####

Click Here To Show Diagram Code

[go]$$B
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? X X X X X X X ? ? ?
$$ ? ? X O X O X . X X ? ?
$$ ? ? O . O . O X O C ? ?
$$ ? ? O O O O O O O ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?[/go]

--------------------------

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | . . . , . . . ? . . X C . . . , . . . |
$$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . |
$$ | . ? O . . ? . . . . . . . ? . O . ? . |
$$ | . ? . X B C . . . . . . . ? B . X C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? W . O ? . . . . . . . ? . O W ? . |
$$ | . ? . X . C . . . . . . . ? X . . C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . . ? X B . C . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}[/go]

Let's apply Honte's magic DOUBLE-ko spell to the outer ko-shapes...

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q . T C . . . , . . . |
$$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q . T C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q . T C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T C . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}
$$ {AR J18 J19}
$$ {AR K18 K19}
$$ {AR L18 L19}[/go]

Nothing happens to the left and right INSIDE the cycle. This means that the cycle will be left there.
We chose the lower exit for an exemplary case.

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . Q . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? T . Y ? . . . . . . . ? T . Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q X T B . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . Y . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? T . Y ? . . . . . . . ? T W Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q . T ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . e n . . . . |
$$ | . . . , . . . . . , . . . f o r c e d |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR J19 J18}
$$ {AR K19 K18}
$$ {AR P12 P9}
$$ {AR Q12 Q9}
$$ {AR R12 R9}
$$ {AR L19 L18}
$$ {AR C18 C19}
$$ {AR D18 D19}
$$ {AR E18 E19}
$$ {AR K16 K11}
$$ {AR L17 O14}
$$ {AR L10 L16}
$$ {AR J11 D18}[/go]

Right:
-- Black occupies the shared liberty.
This exits to the ENFORCED cycle.
Left:
-- Nothing can happen there.
This exits to the diagram above.
Middle:
-- Status confirmation takes place outside the triple-ko formation.

-----------------------------

Let's apply Honte's magic KO spell to the inner ko-shape.

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? T T Y ? . . . . . . . |
$$ | . . . , . . . ? Q Q T C . . . , . . . |
$$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . |
$$ | . ? T T Y ? . . . . . . . ? T T Y ? . |
$$ | . ? Q Q T C . . . . . . . ? Q Q T C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? T T Y ? . . . . . . . ? T T Y ? . |
$$ | . ? Q Q T C . . . . . . . ? Q Q T C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? T T Y ? . . . , . . . |
$$ | . . . . . . . ? Q Q T C . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]

Status confirmation takes place outside the triple-ko formation.



##### GENUINE Triple-Ko: optional cycle #2 #####

Click Here To Show Diagram Code

[go]$$B
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? X X X X X X X S ? ?
$$ ? ? X O X O X . X X ? ?
$$ ? ? O . O . O X O O ? ?
$$ ? ? O O O O O O O S ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?[/go]

--------------------------

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | . . . , . . . ? . . X ? . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? S . ? ? ? ? S . |
$$ | . ? O . . ? . . . . . . . ? . O . ? . |
$$ | . ? . X B ? . . . . . . . ? B . X ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? W . O ? . . . . . . . ? . O W ? . |
$$ | . ? . X . ? . . . . . . . ? X . . ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . . ? X B . ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}[/go]

Let's apply Honte's magic DOUBLE-ko spell to the outer ko-shapes...

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q . T ? . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? S . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T ? . . . . . . . ? Q . T ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T ? . . . . . . . ? Q . T ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}
$$ {AR J18 J19}
$$ {AR K18 K19}
$$ {AR L18 L19}[/go]

Nothing happens to the left and right INSIDE the cycle. This means that the cycle will be left there.
We chose the lower exit for an exemplary case.

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . Q . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T B Y ? . |
$$ | . ? Q X T ? . . . . . . . ? Q X T ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . Y . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . . . . . . . |
$$ | . ? T . Y ? . . . . . . . . . Q . . . |
$$ | . ? Q X T ? . . . . . . . . . . . . . |
$$ | . ? ? ? ? S . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . Y . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR J11 D18}
$$ {AR J19 J18}
$$ {AR K19 K18}
$$ {AR P12 P9}
$$ {AR Q12 Q9}
$$ {AR R12 R9}
$$ {AR Q7 Q4}
$$ {AR P3 P7}
$$ {AR L19 L18}
$$ {AR C18 C19}
$$ {AR D18 D19}
$$ {AR E18 E19}
$$ {AR L17 O15}
$$ {AR K16 K11}
$$ {AR L10 L16}[/go]

Right:
-- Black fills the ko-shape in the middle.
This exits to a status confirmation outside the triple-ko formation.
Left:
-- Nothing can happen there.
This exits to the diagram above.
Middle:
-- Status confirmation takes place outside the triple-ko formation.

----------------

Let's apply Honte's magic KO spell to the inner ko-shape.

Click Here To Show Diagram Code

[go]$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T T Y ? . . . . . . . |
$$ | . . . , . . . ? Q Q T ? . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? S . ? ? ? ? S . |
$$ | . ? T T Y ? . . . . . . . ? T T Y ? . |
$$ | . ? Q Q T ? . . . . . . . ? Q Q T ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T T Y ? . . . . . . . ? T T Y ? . |
$$ | . ? Q Q T ? . . . . . . . ? Q Q T ? . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? T T Y ? . . . , . . . |
$$ | . . . . . . . ? Q Q T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]

Status confirmation takes place outside the triple-ko formation.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

OK thomas let me propose the following example with a very very clear double ko.

Click Here To Show Diagram Code

[go]$$W
$$ +-------------------+
$$ | O O . B O a O X . |
$$ | O B B B O O X X X |
$$ | B B B B O X b X X |
$$ | O O O . O O X X X |
$$ | . X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

The white stones at the top are dead because, black to play, none of these white stones are alive.

The question is now the following : are black marked stones alive or dead?

To answer this question you start an hypothetical play with white to play right?
In J89 or J2003 it follows:

Click Here To Show Diagram Code

[go]$$W
$$ +-------------------+
$$ | 3 O 2 B O a O X . |
$$ | O B B B O O X X X |
$$ | B B B B O X b X X |
$$ | O O O 1 O O X X X |
$$ | 4 X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

and black group is clearly alive.

What about Honte's Magic Ko Spell ?
The initial position becomes

Click Here To Show Diagram Code

[go]$$W
$$ +-------------------+
$$ | O O . B O O a X . |
$$ | O B B B O O X X X |
$$ | B B B B O b X X X |
$$ | O O O . O O X X X |
$$ | . X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

and the hypothetical play becomes

Click Here To Show Diagram Code

[go]$$W
$$ +-------------------+
$$ | 3 O 2 B O O a X . |
$$ | O B B B O O X X X |
$$ | B B B B O b X X X |
$$ | O O O 1 O O X X X |
$$ | . X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

and now black group is dead

Sorry, I must have forgotten an "s".
It should read "Honte's Magic Ko Spells".

Apply "Honte's magic DOUBLE-ko spell" on the entire board.
Apply "Honte's magic SINGLE-ko spell" (to be clear) on the entire board (if you consider this being necessary).

---------------------------------


Are you kidding me?

https://lifein19x19.com/viewtopic.php?p=267053#p267053:

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O O . X O . O X . |
$$ | O X X X O O X X X |
$$ | X X X X O X . X X |
$$ | O O O 1 O O X X X |
$$ | . X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

If it would be Black's turn.

Click Here To Show Diagram Code

[go]$$W
$$ +-------------------+
$$ | O O . X Q . Q B . |
$$ | O X X X O Q Y B B |
$$ | X X X X O Y . B B |
$$ | O O O M O O Y B B |
$$ | . X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

The status of Black's circled group in the upper right corner would ONLY be determined by the neighboured compound of two ko-shapes (triangled), if Black had occupied the crossed point to the left.
As it stands, the status of Black's group in the corner is ENTIRELY dependent on the status of White's group at the top.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O O . X W . O X . |
$$ | O X X X W W X X X |
$$ | X X X X W X . X X |
$$ | O O O M W W X X X |
$$ | . X X X X X O O O |
$$ | X X X X X O . O . |
$$ | . X . X X O O O O |
$$ +-------------------+[/go]

The status of White's circled group is determined by the number of its outside liberties!

=> Thus, the compound of Black and White groups in the upper right corner is NOT a double-ko.

Click Here To Show Diagram Code

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

This formation in the upper right corner is NOT a double-ko!


If you want a donkey bridge:
A GENUINE double-ko does NOT have any DAME and so is ALWAYS a (temporary) seki!

--------------------------

In order to answer your question, which is sure to come, just now:

No, "Honte's magic SINGLE-ko spell" does NOT apply here, because each of the two groups is adjacent to TWO ko-shapes that remained on the board after magic spell

And please remember that the potentially critical triple-ko cycles will be next to impossible after .
Therefore, will not be necessary in the overwhelming majority of cases. is not mandatory at all. Most of the players will be able to look even through false eyes

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

It becomes very restricted. Let's take one of your previous analyses:

Click Here To Show Diagram Code

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

Because of the external marked liberty you can no more use magic wand can you?

Click Here To Show Diagram Code

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

is a SHARED INTERNAL liberty of Black's and White's (only single; added for clarity) groups, isn't it?

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

Nevertheless, I can understand your concerns about a combination of two ko-shapes, which are caught in a (potential) semeai.
So, let's return to the "standard" version of a double-ko...

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | . Y . Y O X . |
$$ | X X Y O O X . |
$$ | Q X O . O X . |
$$ | . Q O O O X . |
$$ | Q O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Double-ko, standard version.

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | C B C X O X . |
$$ | B B O O O X . |
$$ | O B O . O X . |
$$ | . O O O O X . |
$$ | O O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Black's group has TWO liberties .

Click Here To Show Diagram Code

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

White's group has TWO liberties .

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | . X Y T O X . |
$$ | X X X O O X . |
$$ | T X O . O X . |
$$ | Q O O O O X . |
$$ | O O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

After Honte used his magic wand...

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | S X X C O X . |
$$ | X X X O O X . |
$$ | C X O S O X . |
$$ | O O O O O X . |
$$ | O O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

There are two SHARED liberties now, and each of the double-ko groups has another exclusive liberty inside. Thus, both groups have THREE liberties now, one more than before.

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | S X X C O X . |
$$ | X X X O O X . |
$$ | Q X O S O X . |
$$ | O O O O O X . |
$$ | O O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Probably we might want to add a supplementary effect to Honte's magic spell, which would be equivalent of FILLING ONE of both ko-shapes.

Click Here To Show Diagram Code

[go]$$B
$$ +---------------+
$$ | S X X Y O X . |
$$ | X X X O O X . |
$$ | C X O S O X . |
$$ | O O O O O X . |
$$ | O O X X X X . |
$$ | X X X . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

The position is SYMMETRICAL, so we could ALSO choose the other ko-shape for this purpose.
This reduces the number of SHARED liberties by one, so we are back at TWO liberties for both double-ko groups.

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

Let's try to analyse the application on GT City's Central Park:

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]

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | O T Y X . O . |
$$ | . O X X X O O |
$$ | O . O O X X O |
$$ | O O O Q T X O |
$$ | X X O O X X O |
$$ | . X X O O O . |
$$ | X . X X X O O |
$$ -----------------[/go]

After Honte used his magic wand...

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | O Y X X . O . |
$$ | . 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]

Supplymentary effect for the UPPER ko-shape.

Click Here To Show Diagram Code

[go]$$B WHITE territory?
$$ -----------------
$$ | O X X X . O . |
$$ | 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]

Me ari me nashi. => 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 Q X O |
$$ | X X O O X X O |
$$ | . X X O O O . |
$$ | X . X X X O O |
$$ -----------------[/go]

Supplymentary effect for the LOWER ko-shape.

Click Here To Show Diagram Code

[go]$$B WHITE territory?; pass
$$ -----------------
$$ | O . X X . O . |
$$ | . O X X X O O |
$$ | O . O O X X O |
$$ | 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]

Me ari me nashi. => White territory!
It does not wonder that the sequences are different, as the formation is NOT symmetrical.


The results are the same as without supplementary effect. => GENUINE double-ko.


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

Click Here To Show Diagram Code

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

Your example with the pretended double-ko in the upper right.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O O . X O Q T X . |
$$ | O X X X O O X X X |
$$ | X X X X O T Y X O |
$$ | O O O . O O X X O |
$$ | . X X X X X O O O |
$$ | X X . X . . O . O |
$$ | . X X X . . O O . |
$$ | X X . . . . . O O |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

After Honte used his magic wand...

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | O O . X O O Q X . |
$$ | O X X X O O X X X |
$$ | X X X X O . X X O |
$$ | O O O . O O X X O |
$$ | . X X X X X O O O |
$$ | X X . X . . O . O |
$$ | . X X X . . O O . |
$$ | X X . . . . . O O |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Supplymentary effect.
Please note that the compound of the two ko-shapes is a symmetrical one here, so we are free to choose which one of these we want to fill.

Click Here To Show Diagram Code

[go]$$W BLACK territory?
$$ +-------------------+
$$ | O O 2 X O O O X . |
$$ | O X X X O O X X X |
$$ | X X X X O . X X O |
$$ | O O O 1 O O X X O |
$$ | . X X X X X O O O |
$$ | X X . X . . O . O |
$$ | . X X X . . O O . |
$$ | X X . . . . . O O |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$W BLACK territory?
$$ +-------------------+
$$ | 3 . X X O O O X . |
$$ | . X X X O O X X X |
$$ | X X X X O . X X O |
$$ | O O O O O O X X O |
$$ | 4 X X X X X O O O |
$$ | X X . X . . O . O |
$$ | . X X X . . O O . |
$$ | X X . . . . . O O |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Two liberties for Black vs. only one liberty for White. => Black territory!

This result is different from that without supplementary effect => The supposed seki is NOT a GENUINE one!


Thus -- when in doubt (or too lazy to do a thirteen minute double-ko analysis, including an intensive internet recherche) -- view the director's cut, extended version
I am sure that you will not get tired of this film. You will not stumble over (critical) double-ko formations in EVERY of your games.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)