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TFG9BlackUpperLeft
TFG9PlayingHane

 

TFG9 White At The Top
   

Remember, here we are concentrating on the situation of the W group in the center top, ignoring for the moment the state of the B stones to the left.

[Diagram]
Diag.: Black plays first

(W 2,4,6 elsewhere)

As noted elsewhere, if B plays first, W has four liberties. This means that if B could make four liberties on the left in sente he could start here and capture W - in theory.
What it really means is that if B makes five liberties on the left, W can't afford to continue there and is forced to come back to the center top and play there. What happens if she does?

[Diagram]
Diag.: White plays first 1a


  • W 1 creates 5 liberties
  • B 2 reduces W back to 4. If W continues along the top, so does B. So...
  • W 3 tries to cut B off, but...
  • B cuts in turn with 4 and at the same time reduces W to 3 liberties.
  • If W 5, then B 6. W still has only 4 liberties (the sequence a, b, c, d captures W). W can also play next at 'b' (B captures at 'a') to make a ko. B needs only three plays to capture W, ignoring her ko threat).


[Diagram]
Diag.: White plays first 1b

If W tries 5 here, extending the liberties of the cutting stone, B stops W cold with 6, reducing her to 2 liberties (either of the points 'a' next put W in atari).

From this it is clear that W 1 above does not help W. What next?

[Diagram]
Diag.: White plays first 2a


  • W tries this 1 next
  • B tries this 2
  • W 3 threatens to live, so...
  • B is forced to answer at 4 to prevent W playing here.
  • W lives with 5. (Note that of course if this situation arose B would not choose to play 4 but would instead attach on the outside of 1 to force W to live smaller.)

Note that this case raises the important question of what happens if both sides live. Assuming that W came back to the center after not being able to capture B on the left, who wins the game if B lives on the left while W lives in the center?

But is this the best that B can do?

[Diagram]
Diag.: White plays first 2b

  • W plays 1
  • B plays 2 to prevent W expanding to the right. W's shape is too small to live so the question becomes how many liberties does W have?
  • W connects at 3, threatening to live.
  • B plays 4 to stop W
  • W plays 5 and has 2 outside liberties and 6 inside for a total of 8!

[Diagram]
Diag.: W's internal liberties 1

(2 elsewhere) The count is B + 2, W - 1 = Net +1


[Diagram]
Diag.: W's internal liberties 2

(2, 4 elsewhere) The count is B + 3, W -1 = Net +2 with +1 in the previous diagram so total Net +3


[Diagram]
Diag.: W's internal liberties 3

(2, 4 elsewhere) Final count is +3 here with +3 in the previous diagrams for a total of 6 internal plays required for B to capture W.


[Diagram]
Diag.: White plays first 2c

Note that B can't switch 4 in diagram 2b to here. Because W has an outside liberty at 'a', she can throw in at 5 and after B captures at 6, trap two B stones with 7.

Oops!!!! This is not correct. When B plays 5, W will not capture at 6 but instead will extend at 7. After W 'b', B 'c' it is ko but W has less liberties than in 2b (total of 5?). This changes the conclusions below. I'll have to revise them later. Dave


So at this point W has only one eye at the top but has extended from 4 liberties to 8 liberties in gote (i.e. if B plays next on the left or 7 in sente (if B plays next at the top and lets W play next on the left). What does this mean for the status of the B stones on the left? Remember that W played tenuki on the left in order to play at the top.

  • If B has two eyes on the left then W is dead.
  • If B can extend to more than 8 liberties on the left then W is dead.
  • If B can not make more than 7 liberties on the left then W wins the fight and captures B.


This is a copy of the living page "TFG9 White At The Top" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.