3 L&D problems from an ancient Chinese game

hiyayang · Post by **hiyayang** » Sun Dec 26, 2010 10:38 am

Taken from a year-old post at Tom Weiqi Forum (http://club.weiqi.tom.com/item_111_1456663_0_7.html).

It was an H3 game between Zang Nianxuan (W) and Fang Zuozhou in Qing Dynasty (circa 1700 AD).

Problem #1. Level: Easy (for SDKs?)

Click Here To Show Diagram Code: [go]$$Wc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O . . X X X . . | $$ | . . . . . . . . . . . . . O . O X a . | $$ | . . O . O . . . . . . . . . . X O X . | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

White to play. What's the status of the black group on the right side? Specifically, if white plays 'a', can black live?

Gresil · Post by **Gresil** » Sun Dec 26, 2010 11:05 am

A nice problem!

I can't find anything.

Click Here To Show Diagram Code: [go]$$Wc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . 9 O 5 4 X X X 2 . | $$ | . . . . . . . . . . . 8 6 O . O X 1 . | $$ | . . O . O . . . . . . . . 7 . X O X 3 | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Not this

—the ladder doesn't work.

Click Here To Show Diagram Code: [go]$$Wc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O 4 5 X X X 2 . | $$ | . . . . . . . . . . . . 9 O 7 O X 1 . | $$ | . . O . O . . . . . . . . 8 6 X O X 3 | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Not this

either.

Click Here To Show Diagram Code: [go]$$Bc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O 4 3 X X X X . | $$ | . . . . . . . . . . . . 1 O . O X O . | $$ | . . O . O . . . . . . . . 2 . X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Transposes to the ladder.

Click Here To Show Diagram Code: [go]$$Bc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O 4 3 X X X X . | $$ | . . . . . . . . . . . . 5 O 1 O X O . | $$ | . . O . O . . . . . . . . 6 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The same ladder again.

Click Here To Show Diagram Code: [go]$$Bc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O . . X X X X . | $$ | . . . . . . . . . . . . 4 O . O X O . | $$ | . . O . O . . . . . . . 3 1 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Nah.

Numsgil · Post by **Numsgil** » Sun Dec 26, 2010 11:16 am

@Gresil

Gresil · Post by **Gresil** » Sun Dec 26, 2010 11:40 am

Whoops.

hiyayang · Post by **hiyayang** » Sun Dec 26, 2010 2:09 pm

Nice job, Numsgil and Gresil! Gresil was just one move away from the solution, but he saved me a lot of work posting the variations.

For beginners, here is a variation that most people first thought about and that didn't work (with a correction to one of Gresil's variations):

Click Here To Show Diagram Code: [go]$$Bc Black fails, after white captures the black stone at S6 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . a 8 O 4 3 X X X X . | $$ | . . . . . . . . . b . 7 5 O 1 O X O . | $$ | . . O . O . . . . . . . 6 . 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

At this point, neither 'a' nor 'b' works for black.

White can also play :b6:

at

, to the same effect. Actually, there is a bonus question derived from this:

Click Here To Show Diagram Code: [go]$$Bc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . a . O 4 3 X X X X . | $$ | . . . . . . . . . . . 6 5 O 1 O X O . | $$ | . . O . O . . . . . . 9 7 8 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

How does white escape? Does 'a' work?

hiyayang · Post by **hiyayang** » Sun Dec 26, 2010 2:40 pm

Spoiler alert: Stop here if you want to work on the first problem, as the diagram below contains the spoiler.

Problem #2. Level: Medium

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . . . . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O . . . O X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Black to play. How does the black group extending from lower-right corner to center live? Hint: Running out is not an option.

Gresil · Post by **Gresil** » Sun Dec 26, 2010 2:55 pm

This

seems to work:

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . 5 6 . . X O X . | $$ | . O X . . X X . O X X O 7 O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X 1 X X X O . . | $$ | . . . . X O O . . . O X . . 3 2 4 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Without it black only gets a ko from the atari of M6:

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . 1 2 . . X O X . | $$ | . O X . . X X . O X X O 3 O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O . . . O X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

But can't black live by just extending his eyespace? Does white have a more severe attack than than this :w2:

?

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . . . . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X 3 X X X O . . | $$ | . . . . X O O . . . O X 2 5 . . 1 9 . | $$ | . . . . . . . . . . 8 4 6 7 . . . . . | $$ ---------------------------------------[/go]

hiyayang · Post by **hiyayang** » Mon Dec 27, 2010 6:05 am

Hint (and @ Gresil):

Note that White has a series of sente moves to threaten the black group on the right. For example,

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X 2 . | $$ | . . . . . . O O X X X O X O 6 O X 1 . | $$ | . O O . O O X . O . . . 5 . 4 X O X 3 | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O . . . O X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Therefore, you have to be careful not to play moves that could get either black group killed.

hiyayang · Post by **hiyayang** » Mon Dec 27, 2010 6:09 am

@Gresil:

hiyayang · Post by **hiyayang** » Fri Dec 31, 2010 7:43 pm

Solution to Problem #2: In the actual game the following moves were played, which are believed to be optimal --

Click Here To Show Diagram Code: [go]$$Bc Moves 158 to 167, black to live with ko $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X 0 O . . . . . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O 7 8 . O X . . . 4 1 2 . | $$ | . . . . . 9 . . . . . . . . . 5 6 3 . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$B Moves 168 to 177, 9 at 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . 7 . X O X O . O X . | $$ | . . . , . . . 8 6 X X X X X O O X X . | $$ | . . . . . . . 5 O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X 3 . | $$ | . . . . . . O O X X X O X O . O X 2 . | $$ | . O O . O O X O O . . . . . . X O X 0 | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O X O . O X . . . O 1 O . | $$ | . . . . . X . . . . . . . . . X 4 X . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$B Moves 178 to 187, 8 at 2 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . 0 . X . X O X O . O X . | $$ | . . . , 4 . 9 O O X X X X X O O X X . | $$ | . . . . . . 3 X O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X X . | $$ | . . . . . . O O X X X O X O 7 O X O . | $$ | . O O . O O X O O . . . 6 . 1 X O . O | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O X O . O X . . . O 5 O . | $$ | . . . . . X . . . . . . . . . X 2 X . | $$ ---------------------------------------[/go]

I will post some variations next.

hiyayang · Post by **hiyayang** » Fri Dec 31, 2010 8:16 pm

Assessment of the situation:

Click Here To Show Diagram Code: [go]$$Bc Moves 158 and 159 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . f . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X b . | $$ | . O O . O O X . O . . . a . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . e . X O O c d . O X . . . . 1 2 . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

It has already been hinted that W 'a' is sente, forcing B 'b'. In addition, W 'c' or 'd' is sente, forcing B 'e'. OTOH, B 'c' is also sente, forcing W 'd' (and then H6 when B puts the two white stones in atari). And B has to watch out for the cut at 'f'.

With these in mind, you will see that B's options to live the LR group without getting his other groups killed are really limited, hence :b1:

.

hiyayang · Post by **hiyayang** » Fri Dec 31, 2010 9:39 pm

Black failure #1:

Trying to live without ko, B ends up getting his group killed --

Click Here To Show Diagram Code: [go]$$Bc Black group dies $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X 3 . | $$ | . O O . O O X . O . . . 2 . . X O X . | $$ | . O X . . X X . O X X O d O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X c X X X O . . | $$ | . . . . X O O . b . O X . . 9 6 X O . | $$ | . . . . . . . . . . a 0 e 8 5 7 1 4 . | $$ ---------------------------------------[/go]

Note:

1. B 'a' is not sente (because W 'b' is), otherwise W :w8:

would be unable to go home.

2. It is important that B 'c' does not force W 'd', otherwise B could throw in at 'e' to live. Therefore, W has to be careful with :w2:

, as he would get an inferior result by playing this way:

Click Here To Show Diagram Code: [go]$$Bc White fails $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X 3 . | $$ | . . . . . . O O X X X O X O . O X 2 . | $$ | . O O . O O X . O . . . 6 7 5 X O X 4 | $$ | . O X . . X X . O X X O b O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X a X X X O . . | $$ | . . . . X O O . . . O X . . . . X O . | $$ | . . . . . . . . . . . . c . 9 . 1 8 . | $$ ---------------------------------------[/go]

Later B 'a' would enable a ko at 'b' or a throw-in at 'c' as described above.

hiyayang · Post by **hiyayang** » Sat Jan 01, 2011 3:42 pm

Variation #1:

So double hane to live with ko is the best result B can hope for in this situation.

Now W has a choice. If W avoids the ko, B lives:

Click Here To Show Diagram Code: [go]$$Bc White backs off; Black lives $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . f . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X 5 . | $$ | . O O . O O X . O . . . 4 . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X 9 X X X O 2 . | $$ | . . . . X O O . . . O X 8 a . . X O . | $$ | . . . . . . . . . . . 6 7 0 3 . . 1 . | $$ ---------------------------------------[/go]

Then B 'a' lives.

But why should W be afraid of the ko fight? He has virtually nothing to lose here -- even if B won the ko fight, the W group in the LR corner is still alive:

Click Here To Show Diagram Code: [go]$$B Moves 190 to 191 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . 2 . . . . | $$ | . X X . X X . X O . O . X . . . O O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . O . X . X O X O . O X . | $$ | . . . , O . X O O X X X X X O O X X . | $$ | . . . . . . X X O b X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X X . | $$ | . . . . . . O O X X X O . O a O X O . | $$ | . O O . O O X O O . . . O B X X O . O | $$ | . O X . . X X . O X X O . O O . O O c | $$ | O X X X . . . X O O X X O X O , O . d | $$ | . O O X . X X . O . O X . X X X O 3 4 | $$ | . . . . X O O X O . O X . . 1 O X O . | $$ | . . . . . X . . . . . . . . . X . X . | $$ ---------------------------------------[/go]

That is, even if W got cut at 'b' and B played the circled stone (to destroy W's eye) instead of the actual game move 'a' (to give W fewer ko threats). Then, whether B plays :b3:

or 'd',

secures the eye at 'c'.

W just has to make sure he gets compensated elsewhere for the loss of the ko fight.

hiyayang · Post by **hiyayang** » Sat Jan 01, 2011 4:12 pm

Black failure #2:

Point wise, fighting the ko in the center is less advantageous for B than in the corner:

Click Here To Show Diagram Code: [go]$$Bc After move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X 7 . | $$ | . O O . O O X . O 9 8 1 2 . . X O X . | $$ | . O X . . X X . O X X 6 3 O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . 5 . X O O . 4 . O X . . . 0 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

hiyayang · Post by **hiyayang** » Sat Jan 01, 2011 4:30 pm

Variation #2:

In previous diagram, W has to be careful with the ko threat :w4:

. For example, I don't think :w4:

in the following diagram would work out for W:

Click Here To Show Diagram Code: [go]$$Bc After move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . W 5 X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O 6 O 4 O X 7 . | $$ | . O O . O O X . O . . 1 2 . . X O X . | $$ | . O X . . X X . O X X O 3 O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O . . . O X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The problem with this :w4:

is that it allows B to cut in sente ( :b5:

). As a result, the marked white stone would have to run in gote.

Life In 19x19

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