Double ko variation ?

[clemi]

Hi all, here's a variation on a problem coming from the book Tesuji :

$$W
$$ ---------------
$$ . . . . . . . -
$$ . . . O O O 5 -
$$ . . O X O X 4 -
$$ . . O X X X 1 -
$$ . . O X . O 2 -
$$ . . O X O . 3 -
$$ . . . O Y O B -
$$ . . . . Y Y . -
$$ . . . . . . . -

Click Here To Show Diagram Code

[go]$$W
$$ ---------------
$$ . . . . . . . -
$$ . . . O O O 5 -
$$ . . O X O X 4 -
$$ . . O X X X 1 -
$$ . . O X . O 2 -
$$ . . O X O . 3 -
$$ . . . O Y O B -
$$ . . . . Y Y . -
$$ . . . . . . . -[/go]

Can we say that the double ko after black takes at 2 and white takes the circle black stone forms a seki ? The triangle black stones must of course live for this to work and this seems to me to be the best defense for black for his group to not be captured.

What do you think ?

[Sverre]

Black is dead. Black can't fill the ko and White play atari at a every time Black takes at b

$$W
$$ ---------------
$$ . . . . . . . -
$$ . . . O O O O -
$$ . . O X O X X -
$$ . . O X X X a -
$$ . . O X . O X -
$$ . . O X O . O -
$$ . . . O X O b -
$$ . . . . X X 1 -
$$ . . . . . . 2 -

Click Here To Show Diagram Code

[go]$$W
$$ ---------------
$$ . . . . . . . -
$$ . . . O O O O -
$$ . . O X O X X -
$$ . . O X X X a -
$$ . . O X . O X -
$$ . . O X O . O -
$$ . . . O X O b -
$$ . . . . X X 1 -
$$ . . . . . . 2 -[/go]

[clemi]

Your point is right, I now see that it is a ko that black will never win locally. So the best yose for black is to capture 1 at b and connect whereas white will eat the black group.

[Sverre]

Your point is right, I now see that it is a ko that black will never win locally. So the best yose for black is to capture 1 at b and connect whereas white will eat the black group.

Note that every time Black takes the a ko White must take the b ko, and every time Black takes the b ko Whtie must take the a ko. Black should not be in any hurry to resolve this situation as either White must spend an extra move locally or Black has an inexhaustible supply of ko threats.