Life In 19x19

I'm confused by this problem because I don't see any "win" for black. The program's stated answer is shown below as 1-3.

My objection is 4 & 6.

Click Here To Show Diagram Code

[go]$$B Corner
$$ ------------------
$$ | . O X 1 4 X 2 . .
$$ | . O X 6 X O . . .
$$ | 3 O X X O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Is the problem in error? Or am I missing something terribly obvious?

Yes you are missing
After the situation turns into a Ko. Living without Ko is usually better than Ko, but Ko is better than plain dying. So the answer is "Black can make Ko with 1 and 3".
Just for comparison, this is what happens when white can play first:

Click Here To Show Diagram Code

[go]$$B Corner
$$ ------------------
$$ | . O X 2 . X 4 . .
$$ | . O X 3 X O . . .
$$ | . O X X O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Now black can't connect because it is self-atari, so black is outright dead.

MagicMagor wrote: Just for comparison, this is what happens when white can play first:

Black 3 is Self-Atari, so White 4 should capture !

MagicMagor wrote:Yes you are missing
After the situation turns into a Ko. Living without Ko is usually better than Ko, but Ko is better than plain dying. So the answer is "Black can make Ko with 1 and 3".

I don't understand how this makes ko. What I see is elsewhere and killing all the group and taking the 6 stones. The reader is supposed to assume that is a sufficiently large ko threat played elsewhere on the board to make playing at the key point a bad decision? Couldn't you use that logic to solve every tsumego?!?

Drew wrote:I don't understand how this makes ko.

Hi Drew, it's B's turn to play, so:
Where can B play locally, and what are the different results, locally ?

Can you see, and do you agree, that if B does not play at the solution (x),
but anywhere else, then W can kill at least ?

Click Here To Show Diagram Code

[go]$$B :b1: not at (x)
$$ ------------------
$$ | . O Y x . X . . .
$$ | . O Y . X O . . .
$$ | . O Y Y O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .[/go]

Drew wrote:The program's stated answer is shown below as 1-3.

My objection is 4 & 6.

Sorry, what you said is a bit unclear:
does the program show the solution only up to ?
Or does it also include and ?

Drew wrote:What I see is elsewhere and killing all the group and taking the 6 stones.

Same question: does the program include , removing the 6 B stones, or is that your continuation ?

After hane, starts the ko.
Suppose is a ko threat elsewhere, and W replies with (also elsewhere).
Then B can re-take the local ko with , which gains an important liberty for B --
now the big B group momentarily has 2 liberties:

Click Here To Show Diagram Code

[go]$$B :b5:, :w6: elsewhere
$$ ------------------
$$ | . O X 1 4 7 2 . .
$$ | a O X . X O . . .
$$ | 3 O X X O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .[/go]

This means that if -- an important if --
B has the chance to play at (a) while the 6 B stones are not in atari,
then B kills W here, and B lives.

Which is better than simply dead for B.

This is why the solution is a ko.

Drew wrote:The reader is supposed to assume that ...

If your program includes removing the 6 B stones,
it's showing the local result when W wins the local ko.

Cassandra wrote:

MagicMagor wrote: Just for comparison, this is what happens when white can play first:

Black 3 is Self-Atari, so White 4 should capture !

White should not play 4. No need to. He should ignore it.

EdLee wrote:

Drew wrote:I don't understand how this makes ko.

Hi Drew, it's B's turn to play, so:
Where can B play locally, and what are the different results, locally ?

Can you see, and do you agree, that if B does not play at the solution (x),
but anywhere else, then W can kill at least ?

$$B :b1: not at (x)
$$ ------------------
$$ | . O Y x . X . . .
$$ | . O Y . X O . . .
$$ | . O Y Y O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B :b1: not at (x)
$$ ------------------
$$ | . O Y x . X . . .
$$ | . O Y . X O . . .
$$ | . O Y Y O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .[/go]

Drew wrote:The program's stated answer is shown below as 1-3.

My objection is 4 & 6.

Sorry, what you said is a bit unclear:
does the program show the solution only up to ?

Hi Ed,

It stops at and marks itself solved. I meant that was played elsewhere because I didn't see how it could possibly stave of locally, which is because I didn't consider the possibility of a ko threat outside the scope of the problem.

I can understand how the ko is possible now, thank you. Just too inexperienced with tsumego to understand what they were after.

Drew wrote:because I didn't consider the possibility of a ko threat

Hi Drew, you're welcome.

Yes, these are standard conventions: when a tsumego shows you only the local situation:
- if a ko develops, you have to look at all the local threats (if any), and we don't know about the global threats, because they depend on the rest of the board.
- usually you can assume all global ladders (not shown) are good for B, unless explicitly specified otherwise.