KyuExercise40/Attempts

Black to live and keep all territory.  

Is this even possible?

Option "i"  

3 liberties vs 2 liberties!

If White is greedy and tries to kill the entire group by playing at above, Black would be able to achieve the original goal of saving the entire group. The following is one possible sequence:

Black to play and live. No seki.  

Note that this is NOT a double ko seki that gives white an infinite number of ko threats. Even if White had a stone at S, Black can play either ko for endgame points; so this is not seki. In addition, A White approach at 'a' to attempt to kill Black results in self-atari. So Black doesn't need to force a win in the ko battle. This prevents White from using this situation as an infinite ko threat for a Ko elsewhere on the board.

Black to live and keep all territory.  

The possible sequence splits into three different methods:

Method #1 continued  

White's is forced (can't let Black make that other eye)!

Method #1 subset "b" Kofest variation  

or

End result (Ko fest)  

impu1se: I think this is right. White must play to keep black from making an eye. Black will now live due to the double ko. However, white has a nice source of ko threats.

IlyaM: Yep, this is the correct solution. Fortunaly in my game where this position appeared it appeared very late in the game so there were no ko-fights.

End result (Ko fest)  

EricBackus: I'm missing something. At any given move, black will hold either the 'square' ko or the 'circle' ko, and white will hold the other.

If White is allowed to take away Black's outside libery at 'c' and fill the inside liberty at 'd'; then this reduces to Double Ko Seki (right?) which we're told is a failure. To prevent this, black must take 'd'. But to do that requires winning a ko fight. It seems to me that black gets to choose between double-ko seki and a single-ko fight, and we're told that seki isn't good enough so this must be a single-ko fight. Is this really the best solution available to black?

Bill: Black can still live in double ko.

Double ko life  

lives. To escape atari on her four stones White can take the ko on the right with . Then Black takes the ko on the left with . When White plays Black takes the second ko on the left with , yielding a double ko life. :)

Method #2 continued  

White has a choice here...

White prevents a trick  

Bill: Through the result is seki.

Method #2 subset 'h'  

White direct eye attack.

Method #2 subset 'h' Low Road variation  

The Black move of 7 aims to be able to play at square next. The extra liberty on the outside at circle should put Black ahead in the ko fight.

continuation trap!  

EricBackus: Isn't this seki, and therefore a failure for black? (Assuming Black plays 'square' next -- Then circle for White)

White mistake  

White is a mistake. This leads to a ko fight for life. Hence Black still has a chance to win the game.

tragedy continues  

Some possible sequences:

Black makes KO.  

Black can take the KO first here. White needs to find the first threat.

if White b... still the same  

EricBackus: Putting black in atari reduces this to a ko for life in the corner. So it's not life, it's ko, and thus a failure if unconditional life was possible?

Black to play and live.  

This looks like a seki to me.

Bill: If you are using GoTools, try marking as the aim. :)