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Re: Why is white dead? II

Posted: Mon Jul 15, 2019 11:42 pm
by jlt
To confuse you even further: things are clear when a group consists of only one string. In the diagram below, "a" and "b" are eyes because they are adjacent to the black string, and only to it.

Click Here To Show Diagram Code
[go]$$B
$$ ------------
$$ | a X b X O .
$$ | X X X X O .
$$ | O O O O O .
$$ | . . . , . .
$$ | . . . . . .[/go]
When there are two strings:
Click Here To Show Diagram Code
[go]$$B
$$ -------------
$$ | a B B O . .
$$ | # b B O . .
$$ | # # O O . .
$$ | O O . , . .
$$ | . . O . . .
$$ | . . . . . .[/go]

"a" and "b" are eyes because each of them is adjacent to each black string and only to them.

A group can have two eyes that look like false eyes:

https://senseis.xmp.net/?TwoHeadedDragon
Click Here To Show Diagram Code
[go]$$B
$$ . . . . . . . . . .
$$ . . O O O . . . . .
$$ . O X X O O O O . .
$$ . O X a X X X O O .
$$ . O X X O O X X O .
$$ . O X O O . O X O .
$$ . O X O . O O X O .
$$ . O X X O O X X O .
$$ . O O X X X b X O .
$$ . . O O O O X X O .
$$ . . . . . O O O . .
$$ . . . . . . . . . .[/go]
There are two eyes because the black group consists two strings, and "a" and "b" are empty intersections which are adjacent to each of these two strings and only to them.

On the other hand, in the original diagram there are three strings
Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . X X X . . , . . |
$$ | a W W X . . . . . |
$$ | @ . W X , . . . . |
$$ | @ @ X . . . . . . |
$$ | . @ X . . . , . . |
$$ | Q X X . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]
but Black cannot play immediately at "a" so we can suppose that "a" is white, so we get two strings
Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . X X X . . , . . |
$$ | W W W X . . . . . |
$$ | W b W X , . . . . |
$$ | W W X . . . . . . |
$$ | c W X . . . , . . |
$$ | Q X X . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]
The eye "b" is adjacent to only one string, so the group doesn't have two eyes. Another way of seeing this is to fill external liberties with enemy stones
Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X . . , . . |
$$ | W W W X . . . . . |
$$ | W b W X , . . . . |
$$ | W W X . . . . . . |
$$ | c W X . . . , . . |
$$ | Q X X . . . . . . |
$$ | X X . . . . . . . |
$$ +-------------------+[/go]
and see that the lower white group is in atari.

(All the above is pretty obvious for experienced players, however it is not uncommon for SDKs to confuse false eyes with real eyes during a game... including me...)

Re:

Posted: Tue Jul 16, 2019 11:13 am
by Pio2001
EdLee wrote:I like how Pio merged sensei's two separate cases "on the side" and "at the corner" into one "by the 2nd line", but it's still nice to include both a side diagram and a corner diagram
The idea is not mine Image

It comes from the book Level Up! volume 4 (Lee Jae-Hwan, Yoo Chang-Hyuk). :cool:

Re: Why is white dead? II

Posted: Tue Jul 16, 2019 12:19 pm
by Jika
@ jlt: String-theory!! Cool.

Re: Why is white dead? II

Posted: Tue Jul 16, 2019 12:54 pm
by Joaz Banbeck
There are two ideas mentioned above which I think are even better if explicitly placed together:
Pio2001 wrote:...
There are only three kind of false eyes.

The false eye by the large diagonal :



The false eye by the one point jump :



And the false eye by the second line :

...
jlt wrote:... Another way of seeing this is to fill external liberties with enemy stones
Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X . . , . . |
$$ | W W W X . . . . . |
$$ | W b W X , . . . . |
$$ | W W X . . . . . . |
$$ | c W X . . . , . . |
$$ | Q X X . . . . . . |
$$ | X X . . . . . . . |
$$ +-------------------+[/go]
and see that the lower white group is in atari...
If you use jlt's idea of filling liberties on Pio's diagrams, they look like this:



...and this:



...and this:



Once the string of black stones is completely surrounded, black can either save it by filling in his 'eye', or white can take it, in which case if becomes a ko. And it is a ko that - as demonstrated earlier in this thread - black cannot win.