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BeginnerExercise9

 

Beginner Exercise 9 Solution
  Difficulty: Beginner   Keywords: Problem

[Diagram]
Diag.: Solution.

unkx80: In case people get lost in the large number of diagrams in the discussions below, I have reproduced the solution diagram.

First throw-in at 1, then atari at 3. Subsequently, when Black plays at a, White will be the player to take the ko first. So White saves one ko threat. (See try to get first capture in a ko.)

Actually when I set this problem I wasn't intending to test how many local ko threats one can find, but it's an interesting discussion nonetheless. =)

Good work splice!



[Diagram]
Diag.: White may try this...

AGiss : Well, it looks like "Black is definitely alive", but, well, I've finally found a way to kill Black using the ko rule!


Now, the goban looks like:

[Diagram]
Diag.: 'a', 'b' and 'c' are important points


But, if White plays a now, then Black can either connect at b and White will take away the eye with c, or Black can play at c and White will separate the two eyes with b.

KarlKnechtel: Very good. Ordinarily I think Black would be said to "live in ko" after Black 4, especially since White had to throw-in to make the ko and Black captures first. But the cut at a-b offers an internal ko threat. Now Black needs a ko threat elsewhere on the board to recapture the ko and connect to make a true eye - but given the size of the black group it would have to be a HUGE threat!

[Diagram]
Diag.: White kills Black


[Diagram]
Diag.: White also kills Black, wakaiso Black !


[Diagram]
Diag.: Hmm...

splice: How about this? I can see two continuations from here... (Addendum: Just realized this is exactly the answer given above, but in a different order.. Well, it can lead to Black killing himself if he doesn't pay attention, saving White ko threats for later... any better? :)


KarlKnechtel: This is even better, definitely, and I scold myself for not realizing it would work. This makes White 3 a dual-purpose move, at once putting the two black stones into atari and completing the ko setup. Now Black needs two "HUGE ko threats". :)

... Wait! Actually, this sequence is necessary, because Black does have one of those threats - any internal threat is by definition big enough, and Black has one:

[Diagram]
Diag.: Black resists!

Quick note from AGiss: I would have played a. Why is the red circle better than a?

KarlKnechtel: Oh, it's not. That empty a point really spoils my analysis here, it turns out :( If White plays there, Black can threaten a connect-and-die by playing the circled point (with b as a follow-up), but either making one of the connections or (probably better) playing at c spoils Black's last plan.


White cannot win the ko by White 7 at 2, because Black 8 at the circled point would trap in and capture all eight white stones! So White must connect, and then plays her own internal ko threat:

[Diagram]
Diag.: Black resists! (2)

White 11 retakes the ko at 5, finishing the job unless Black has a "HUGE" threat elsewhere. :)


[Diagram]
Diag.: Ko Threat?

splice: Is Black 6 a real ko threat? Even if White connects the ko and Black takes the circled point...


[Diagram]
Diag.: Safe?

White should be safe since she can take the lone black stone. Unless I am missing something?



Why does White fill??

[Diagram]
Diag.: No need to fill

ikkentobi : There is no need for White to fear the ko threat at 6. Just capture at 7.


[Diagram]
Diag.: Black is dead

Black is dead since he has only one true eye, and the marked eye is a false eye



[Diagram]
Diag.: The squared point spoils my first idea, but what about the circled points?

KarlKnechtel: True - Black can connect, but White can too, and is safe while Black's eye is still falsified. A curse on that empty point! ;) Though, it occurs to me that Black may have two ko threats at the circled points - threats to escape. Hmmm.

(The rest of splice's analysis follows.)



[Diagram]
Diag.: First variation (5 at 1)

Either Black saves his two stones at the left by taking the white stone, and White takes the ko again, most likely connecting right after (probably nothing else as big on the board)...


[Diagram]
Diag.: Second variation (4 at 1)

Or Black connects the ko and White takes the two stones, killing the group. So it ends either in a ko or in death for Black.

fhayashi: Is this really Beginner-level anymore??





This is a copy of the living page "Beginner Exercise 9 Solution" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.