J89's pass-for-ko: Misinterpreted in the Western Go World?

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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by kvasir »

Gérard TAILLE wrote: It seems not clear how you handle this famous double-ko "abuse"
Let's take a slightly different position:
Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . .
$$ | O O . . . . .
$$ | a O . . . . .
$$ | X O . . . . .
$$ | . B O O O . .
$$ | B B B B O . .
$$ | O B . B O . .
$$ | . O X O X . .
$$ | O O O O X . .
$$ | . O X X X . .
$$ | O O X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
In this position, due to the liberty at "a" and the double-ko "abuse" then black marked stones become uncapturable (=> alive). How do you correct this result?

First, in step 1 of the first iteration we get that the marked stones are alive.
Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . .
$$ | O O . . . . .
$$ | . O . . . . .
$$ | X O . . . . .
$$ | . X O O O . .
$$ | X X X X O . .
$$ | O X . X O . .
$$ | . W X W X . .
$$ | W W W W X . .
$$ | . W X X X . .
$$ | W W X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]

The intention was that the marked stones can not be removed in the second iterations because they are marked alive in the first iteration, so now we can show that the black stones are dead in step 1 of the second iteration.
Click Here To Show Diagram Code
[go]$$W :b4: :b6: :b8: pass to not help white
$$ | . . . . . . .
$$ | O O . . . . .
$$ | 1 O . . . . .
$$ | 5 O . . . . .
$$ | 3 X O O O . .
$$ | X X X X O . .
$$ | 9 X 7 X O . .
$$ | 2 W X W X . .
$$ | W W W W X . .
$$ | . W X X X . .
$$ | W W X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Maybe we should take it to another thread, as was so kindly suggested, but I hope I am communicating my meaning.

Edit ==========
Now I realize that we get a double-ko seki because some of the black stones are marked alive in iteration 1. I am not sure this is a problem or unexpected, how about white needing to play the approach move to capture? Anyway it was a good point.
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

Comparison of different rulesets

RulesetJ89(1989)J2003J89(<= 2007)GT territory rule
Ko banCapture into a ko-shape prohibits recapture into that ko-shape.Capture into a ko-shape prohibits recapture into that ko-shape.Capture into a ko-shape prohibits recapture into that ko-shape."Permanent prohibited ko" prohibits the repeated capture into a specified ko-shape.
Lift of ko ban
____________________
** with former ko ban
Pass for individual ko ban allows immediate recapture into individual ko-shape**.Pass allows immediate (global) recapture into all ko-shapes**.Pass for individual ko ban erases that ko ban. Recapture into any ko-shape** is disabled, until after all ko bans have been erased.(Not applicable.)
Genuine double-ko cycle

:w1: :b2: :wx: :b1: :w2: :bx:
Impossible. :b1: is prohibited.Enabled, but optional.Impossible. :b1: is prohibited.(Not applicable.)

:w1: :b2: :wc: :b1: :w2: :bc: would be optional.
Double-ko cycle

:w1: :b2: :wx: :bx: :w2: :b1: :wx: :bx:
Enforced. Owner = :white:
Abuse not expressly excluded!
Would result in chôsei for any other :white: formation on the board.
Impossible, as :bx: is unavailable.

:w1: :b2: :wx: :bc: :w2: :b1: :wx: :bc: would be optional.
Optional.

:w1: :b2: :wx: :black: :w2: would be impossible, as :w2: is prohibited.
(Not applicable.)

:w1: :b2: :wc: :bc: :w2: :b1: :wc: :bc: would be optional.
J89 L&D Example 16
Extended moonshine-life & double-ko (one solid eye each)
Intended result: :white: :white: dead; :black: :black: alive.

Abuse of double-ko cycle results in seki!
:white: :white: dead; :black: :black: alive. :white: :white: dead; :black: :black: alive. :white: :white: dead; :black: :black: alive.
J89 L&D Example 17
Bent-four + outside ko-shape & double-ko (one solid eye each)
Intended result: :white: :white: dead; :black: :black: alive.

Abuse of double-ko cycle results in seki!
:white: :white: dead; :black: :black: alive. :white: :white: dead; :black: :black: alive. :white: :white: dead; :black: :black: alive.
J89(1989) L&D Example 18
Bent-four & double-ko (solid eye inside; nested ko-shapes outside)
Intended result: :black: :black: dead; :white: :white: alive.

Abuse of double-ko cycle results in seki!
:black: :black: dead; :white: :white: alive. :black: :black: dead; :white: :white: alive. :black: :black: dead; :white: :white: alive.
J89(<= 2007) L&D Example 18
Bent-four & irremovable ko-threat
(= Bent-four & double-ko (nested ko-shape inside))
./. :black: :black: dead; :white: :white: alive. :black: :black: dead; :white: :white: alive.Seki.
Black sending three, White returning two
Moonshine-life vs. moonshine-life
Seki.Seki.Seki. :black: :black: dead; :white: :white: alive.

:white: claimed "permanent prohibited ko".
_____________________________________________
Legend:
:w1: :b1: ko capture / recapture into ko-shape #1; :w2: :b2: ko capture / recapture into ko-shape #2.
:wx: :bx: "pass-for-ko" (any kind).
:wc: :bc: genuine "pass".
:black: genuine move.
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by jann »

Gérard TAILLE wrote:
jann wrote:This is a longstanding question in J89 which has two possible answers:
  1. Maybe passing for each ko is only required once for each player (see here)
  2. Or the problem was overlooked by J89 authors, and will be fixed in the future (with some hack like requiring a normal pass of either player before passing for a ko a second time)
1)
If you use "pass once per ko" then black can pass immediatly and wins the game because the two white marked stones are dead in the confirmation phase

2)
Click Here To Show Diagram Code
[go]$$B
$$ +---------------------–-
$$ | 2 X X O X O . . . O X O . O . |
$$ | X O 1 O X O . . . O X X O O O |
$$ | O O X X X O . . . O X . X O X |
$$ | O X X O O O . . . O X X X X . |
$$ | . O X O . . . . . O O O O X X |
$$ | . O X O . . . . . . . . O O O |
$$ | O X X O . . . . . . . . . . . |
$$ | O O O O . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . |[/go]
without using "pass once per ko", in order to win, black must continue at least one move.
After :b1: :w2: then black passes and wins the game.
Nice position, thank you. Even if harmless here since the result is the same (B can force the reinforcement with the same play either way), this does show a case where the attacker might need to play the same ko twice in confirmation.
Alternating systematically a "ko ban requiring an explicit pass-for-ko" and a "normal ko ban" seems to resolve the problem.
That idea sounds more complicated and conceptually less sound than my #2 alternative above. Anyway, the Nihon Ki-in is probably aware of the problem by now and will choose an official solution in their next version.
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by jann »

Cassandra wrote:J89(<= 2007)
If would be nice if you could use more descriptive names for your inventions.
Pass for individual ko ban erases that ko ban. Recapture into any ko-shape** is disabled, until after all ko bans have been erased.
Would this mean I cannot recapture in a ko until I passed for all my potential recaptures? Or until both players passed for all their potential recaptures? I think I misunderstand something since neither seems to work. Maybe you mean players can also pass for potential recaptures of the opponent?
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

jann wrote:
Pass for individual ko ban erases that ko ban. Recapture into any ko-shape** is disabled, until after all ko bans have been erased.
Would this mean I cannot recapture in a ko until I passed for all my potential recaptures? Or until both players passed for all their potential recaptures? I think I misunderstand something since neither seems to work.
One fundamental (but implicite) Japanese understanding seems to be that ko-fights shall not play any decisive role during status confirmation for determining the L&D-status of groups.

We have learned that it are the double-ko, in conjunction with a third ko-shape, that are potentially problematic.

If recapture into any ko-shape (with former ko-ban) is disabled, as long as there are still unlifted ko-bans on the board, nobody will really want to capture into a double-ko. Unless they wanted to discourage their opponent from recapturing into a third ko. But this is never a topic in the L&D examples.

The player, who wanted to recapture into a third ko, would never capture into a double-ko, as he can be very sure that his opponent will never lift the ko-ban for "his" ko-shape to recapture.

Thus said, my interpretation of the current J89 legal text has the same effect as my earlier loose saying "There is NO double-ko during status confirmation."
Only after ALL former ko-bans have been lifted, the board returns to the status of after the game stopped, i.e. there are no active ko-bans on the board, similar to the beginning of status confirmation.

As a matter of course, if a player fills a ko-shape, the respective ko-ban (that his opponent is likely to never lift) is also erased. Just because the ko-shape has vanished.
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by jann »

Cassandra wrote:The player, who wanted to recapture into a third ko, would never capture into a double-ko, as he can be very sure that his opponent will never lift the ko-ban for "his" ko-shape to recapture.
But his opponent will flip a double ko once, and not pass there afterwards - and this would be enough to prevent him from recapturing into the third ko permanently?
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

jann wrote:
Cassandra wrote:The player, who wanted to recapture into a third ko, would never capture into a double-ko, as he can be very sure that his opponent will never lift the ko-ban for "his" ko-shape to recapture.
But his opponent will flip a double ko once, and not pass there afterwards - and this would be enough to prevent him from recapturing into the third ko permanently?
Yes.

But in J89's L&D-examples "flipping a double-ko once" would only lengthen the sequence. The "opponent" will simply capture through after the players "pass-for-ko".
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by jann »

Sorry still unclear for me. How would this work in moonshine life for example? Black tries to take ko(s) on the left, then flips the right once and doesn't pass there to keep a permanent non-passed-for ko on the board, blocking the ko(s) at the left as well?
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O . O . O X O . O |
$$ | . O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

jann wrote:Sorry still unclear for me. How would this work in moonshine life for example? Black tries to take ko(s) on the left, then flips the right once and doesn't pass there to keep a permanent non-passed-for ko on the board, blocking the ko(s) at the left as well?
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O . O . O X O . O |
$$ | . O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
It will be White's turn.
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O 1 O . O X O . O |
$$ | 2 O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W :w3: pass-for-ko
$$ --------------------------------
$$ | T X X X X X O O O . O X O . O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | . X X X X X O O O . O X O 4 O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X 5 X O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W :b6: pass
$$ --------------------------------
$$ | 7 X X X X X O O O . O X T X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O T O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Wm9 :b8: pass; :b9: pass
$$ --------------------------------
$$ | O X X X X X O O O . O X T X O |
$$ | T O X 1 O 3 X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O T O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Wm9
$$ --------------------------------
$$ | O . . . . . O O O . O X T X O |
$$ | . O . O O O . O O . O X X O O |
$$ | O O . . . . . O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O T O |
$$ --------------------------------[/go]
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by jann »

Cassandra wrote:
Click Here To Show Diagram Code
[go]$$W :b6: pass
$$ --------------------------------
$$ | 7 X X X X X O O O . O X T X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O T O |
$$ --------------------------------[/go]
But how is 7 legal when there are ko bans on right? Weren't "recapture into any ko-shape** is disabled, until after all ko bans have been erased"?
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

jann wrote:
Cassandra wrote:
Click Here To Show Diagram Code
[go]$$W :b6: pass
$$ --------------------------------
$$ | 7 X X X X X O O O . O X T X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O T O |
$$ --------------------------------[/go]
But how is 7 legal when there are ko bans on right? Weren't "recapture into any ko-shape** is disabled, until after all ko bans have been erased"?
White is simply too fast.
:razz:

Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O 1 O . O X O . O |
$$ | 2 O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
:b2: captures into a ko-shape.
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | M X X X X X O O O . O X O . O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
:ex: is forbidden for White.
Click Here To Show Diagram Code
[go]$$W :w3: pass-for-ko
$$ --------------------------------
$$ | M X X X X X O O O . O X O . O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
:w3: plays a "pass-for-ko".
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | T X X X X X O O O . O X O . O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
This lifts the ko-ban in the upper left corner.

There are only :et: on the board, while all former :ex: have disappeared.
This implies that ALL former ko-bans have been lifted.
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | . X X X X X O O O . O X O . O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
This "resets" the board.
Each side is free again to capture into any ko-shape available.
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by jann »

B 2 flips the double ko in reply to W's first (connecting) move, before taking the ko at left corner?
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

jann wrote:B 2 flips the double ko in reply to W's first (connecting) move, before taking the ko at left corner?
After sunrise, it's a bit too late now...
;-)

Honte told me on our late evening walk yesterday that you would come up with this variation for sure. :D
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Cassandra »

jann wrote:B 2 flips the double ko in reply to W's first (connecting) move, before taking the ko at left corner?
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O 1 O . O X O 2 O |
$$ | . O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
:b2: captures into the double-ko at right.

White now has two options, both of which lead to success.


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

Option :w1:
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O O O . O X M X O |
$$ | 3 O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O O O . O X M X O |
$$ | O O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X 4 O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X . X O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W :b6: pass
$$ --------------------------------
$$ | O X X X X X O O O . O X . X . |
$$ | O O X 5 O 7 X O O . O X X . . |
$$ | O O X X X X X O . . O O X X . |
$$ | . O O O O O O O . . O X X . . |
$$ | . . . . . . . . . . O X . X . |
$$ --------------------------------[/go]
White's group left the board ...
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O . . . . . O O O . O X . X . |
$$ | O O . O O O . O O . O X X . . |
$$ | O O . . . . . O . . O O X X . |
$$ | . O O O O O O O . . O X X . . |
$$ | . . . . . . . . . . O X . X . |
$$ --------------------------------[/go]
... BEFORE Black's group disappeared.

Thus, Black's group at the left is dead, while White's group at the right is alive.


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

Option :w2:
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O X X X X X O O O . O X M X O |
$$ | 4 O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X 3 X O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | M X X X X X O O O . O X M X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O M O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W :b6: pass; :w7: pass-for-ko (left)
$$ --------------------------------
$$ | M X X X X X O O O . O X M X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O 5 O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W :b8: pass; :w9: pass-for-ko (right)
$$ --------------------------------
$$ | T X X X X X O O O . O X M X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O O O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | T X X X X X O O O . O X T X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O O O |
$$ --------------------------------[/go]
Only :et: on the board, NO :ex: remaining!
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | . X X X X X O O O . O X . X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X . O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O O O |
$$ --------------------------------[/go]
Reset of the board.
Click Here To Show Diagram Code
[go]$$Bm10
$$ --------------------------------
$$ | . X X X X X O O O . O X . X O |
$$ | X O X . O . X O O . O X X O O |
$$ | O O X X X X X O . . O O X 1 O |
$$ | . O O O O O O O . . O X X O O |
$$ | . . . . . . . . . . O X O O O |
$$ --------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Bm10
$$ --------------------------------
$$ | 2 X X X X X O O O . O X . X . |
$$ | X O X . O . X O O . O X X . . |
$$ | O O X X X X X O . . O O X X . |
$$ | . O O O O O O O . . O X X . . |
$$ | . . . . . . . . . . O X . . . |
$$ --------------------------------[/go]
White's group left the board ...
Click Here To Show Diagram Code
[go]$$Bm10 :b12: pass; :b14: pass
$$ --------------------------------
$$ | O X X X X X O O O . O X . X . |
$$ | M O X 4 O 6 X O O . O X X . . |
$$ | O O X X X X X O . . O O X X . |
$$ | . O O O O O O O . . O X X . . |
$$ | . . . . . . . . . . O X . . . |
$$ --------------------------------[/go]
... BEFORE Black's single stone at left disappeared.

:b12: = "pass-for-ko" will not help either (typical for a single ko-shape), as White has the connection at :wx: at her hands.
Click Here To Show Diagram Code
[go]$$W
$$ --------------------------------
$$ | O . . . . . O O O . O X . X . |
$$ | . O . O O O . O O . O X X . . |
$$ | O O . . . . . O . . O O X X . |
$$ | . O O O O O O O . . O X X . . |
$$ | . . . . . . . . . . O X . X . |
$$ --------------------------------[/go]
Black's group at the left is dead, while White's group at the right is alive.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Matti
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Re: J89's pass-for-ko: Misinterpreted in the Western Go Worl

Post by Matti »

Many years ago I discovered a patch for the "pass-for-ko rule. Even with it there wolud be other flaws in the J1989 rules, so I didn't bother to release it. Anyway:

In the confirmation phase:
  • A player may not recapture a ko before making a pass to recapture that particular ko.
    A player may not recapture a ko for the second time before making two passes to recapture that particular ko.
    A player may not recapture a ko for the third time before making three passes to recapture that particular ko.
    Etc.
This keep the double ko seki alive. If there is additional stuff attached, a player may rotate the double ko seki n times to gain n tenukies to resolve the thing.
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