I recently came across an interesting game in one of the online tournaments:
$$B
$$ ----------------------
$$ X . X X O . . . . . . |
$$ . X . X O . X X W . . |
$$ X X X O O . . O X . . |
$$ . . . . O . . O X . . |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . . . . . . |
$$ . X . X O . X X W . . |
$$ X X X O O . . O X . . |
$$ . . . . O . . O X . . |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
The question is, after white's move, can black defend the corner without a ko?
$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X X X 3 |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X O 1 |
$$ X X . O X X . O X O 4 |
$$ . X O . . . O O O X 2 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X X X 3 |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X O 1 |
$$ X X . O X X . O X O 4 |
$$ . X O . . . O O O X 2 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X X X 3 |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X O 1 |
$$ X X . O X X . O X O 4 |
$$ . X O . . . O O O X 2 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X X X 3 |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X O 1 |
$$ X X . O X X . O X O 4 |
$$ . X O . . . O O O X 2 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
$$W
$$ ----------------------
$$ X . X X O . . . . . . |
$$ . X . X O . X X 1 2 . |
$$ X X X O O . . O X . . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . . . . |
$$ . X . X O . X X 1 2 . |
$$ X X X O O . . O X . . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
Ko. I don't see any way for Black to keep the whole corner, at least the 2 stones on top are going to get ko'd.
$$B
$$ ----------------------
$$ X . X X O . . . 3 . . |
$$ . X . X O . X X W 1 . |
$$ X X X O O . . O X 2 . |
$$ . . . . O . . O X . 4 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . . . 3 . . |
$$ . X . X O . X X W 1 . |
$$ X X X O O . . O X 2 . |
$$ . . . . O . . O X . 4 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
The empty triangle looks good to me at first, but...
$$B
$$ ----------------------
$$ X . X X O . . . . . . |
$$ . X . X O . X X W 2 3 |
$$ X X X O O . . O X 1 6 |
$$ . . . . O . . O X . 4 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X 5 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . . . . . . |
$$ . X . X O . X X W 2 3 |
$$ X X X O O . . O X 1 6 |
$$ . . . . O . . O X . 4 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X 5 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
However, does black need to play :b3?
$$B
$$ ----------------------
$$ X . X X O . 8 6 9 7 0 |
$$ . X . X O . X X W 2 4 |
$$ X X X O O . . O X 1 . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O 5 |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . 8 6 9 7 0 |
$$ . X . X O . X X W 2 4 |
$$ X X X O O . . O X 1 . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O 5 |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
This seems to work:
$$B
$$ ----------------------
$$ X . X X O . O O 1 . O |
$$ . X . X O . X X O O O |
$$ X X X O O . . O X X . |
$$ . . . . O . . O X . X |
$$ X X . O X X . O X O X |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . O O 1 . O |
$$ . X . X O . X X O O O |
$$ X X X O O . . O X X . |
$$ . . . . O . . O X . X |
$$ X X . O X X . O X O X |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
However:
$$B
$$ ----------------------
$$ X . X X O . . 7 . 6 . |
$$ . X . X O . X X W 2 4 |
$$ X X X O O . 8 O X 1 . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O 5 |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . . 7 . 6 . |
$$ . X . X O . X X W 2 4 |
$$ X X X O O . 8 O X 1 . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O 5 |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
So perhaps:
$$B
$$ ----------------------
$$ X . X X O . . 9 . 6 . |
$$ . X . X O . X X W 2 4 |
$$ X X X O O . 7 O X 1 . |
$$ . . . . O . 8 O X . 3 |
$$ X X . O X X . O X O 5 |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . . 9 . 6 . |
$$ . X . X O . X X W 2 4 |
$$ X X X O O . 7 O X 1 . |
$$ . . . . O . 8 O X . 3 |
$$ X X . O X X . O X O 5 |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
$$W
$$ ----------------------
$$ X . X X O . . . 6 . . |
$$ . X . X O . X X 1 2 . |
$$ X X X O O . . O X 5 . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X 4 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . 6 . . |
$$ . X . X O . X X 1 2 . |
$$ X X X O O . . O X 5 . |
$$ . . . . O . . O X . 3 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X 4 |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X 2 X 1 |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X . O |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X X |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X 2 X 1 |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X . O |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X X |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O . O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X . X . |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X a O |
$$ X X . O X X . O X O b |
$$ . X O . . . O O O X X |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O 1 O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X . X . |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X a O |
$$ X X . O X X . O X O b |
$$ . X O . . . O O O X X |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O 1 O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
Black is captured, because he cant approach a, so white b next captures.
$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X . X . |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X a O |
$$ X X . O X X . O X O b |
$$ . X O . . . O O O X X |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O 1 O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$W
$$ ----------------------
$$ X . X X O . . . X . . |
$$ . X . X O . X X . X . |
$$ X X X O O . . O X O . |
$$ . . . . O . . O X a O |
$$ X X . O X X . O X O b |
$$ . X O . . . O O O X X |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O 1 O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]
Black is captured, because he cant approach a, so white b next captures.
I still don't get why black dies. Wouldn't 5 below save black if white played as expected above?
$$B
$$ ----------------------
$$ X . X X O . . . 3 . . |
$$ . X . X O . X X . 1 5 |
$$ X X X O O . . O X 2 . |
$$ . . . . O . . O X . 4 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O 6 O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$
[go]$$B
$$ ----------------------
$$ X . X X O . . . 3 . . |
$$ . X . X O . X X . 1 5 |
$$ X X X O O . . O X 2 . |
$$ . . . . O . . O X . 4 |
$$ X X . O X X . O X O . |
$$ . X O . . . O O O X . |
$$ O O O X X X O X X . X |
$$ . O X X . O . O X X X |
$$ . . . . X O . O 6 O X |
$$ . . . . X O O . O . O |
$$ . . . . X X X O . O . |
$$[/go]