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Almost Almost Fill
    Keywords: Life & Death

KarlKnechtel: To "almost-almost fill" (and a better term really is needed) an eyespace is to fill all but two liberties inside.

Life and Death Implications

Consider a group with a single eyespace (the "large group"), which is almost-almost-filled with some enemy stones (the "small group"). Assume the large group cannot escape or connect out anywhere. What happens next depends on two basic variables:

  • The number of outside liberties of the large group. Possibilities:
    • None (case L0)
    • One (case L1)
    • More than that. (case L2)
  • The shape of the small group, and the shape formed by adding a stone to the small group in either position. Possibilities:
    • The shape is a killing shape, and at least one of the extensions makes a killing shape. (case S0)
    • The shape is a killing shape, but neither extension makes a killing shape (case S1)
    • The shape is not a killing shape, but at least one of the extensions will make a killing shape (case S2)
    • The shape is not a killing shape, and neither is either extension (case S3)
  • Whose turn it is.

See almost fill for more discussion of killing shapes.

The results are:

  • With owner of large group moving first
     L0  L1  L2
 S0  R1  R1  R1
 S1  R3  R3  R3
 S2  R1  R2  R2
 S3  R3  R2  R2
  • With owner of small group moving first
     L0  L1  L2
 S0  R1  R1  R1
 S1  R3  R3  R3
 S2  R1  R1  R1
 S3  R3  R3  R2

Here, the results are:

  • R1: Large group dead, small group alive.
  • R2: Large group alive, small group dead.
  • R3: Both groups alive in seki.

Then again, all of this ignores the possibility of various ko situations. ^^;

Practical example

[Diagram]
Seki with threats

This configuration is seki. The lack of outside liberties actually doesn't matter in any case here. The points a and b are miai in a sense:

  • Either a or b by White threatens to kill.
  • Either a or b by Black threatens to make Black alive with two eyes (not in seki any more) and kill the white stones.

Black's threat is worth 6 points: 4 points for eye space, plus 2 for white prisoners, minus the 0 existing value of the seki. White's threat is worth 34 points: 16 for black prisoners, plus 18 for resulting territory. (Not 36 points, as one might normally count, since the circled points aren't Black's territory to begin with.)


[Diagram]
White's threat

Proof that White threatens to kill: playing at both a and b results in this situation. We have S0 (the white stones make a squared four and a play at either marked point makes a bulky five) and thus R1 - Black dies.


[Diagram]
Black's threat

Proof that Black threatens to kill and make eyes - obvious.


[Diagram]
Responses to White's threats

When Black responds to White's threat, we have case S1 - the white stones make a triangle (a killing shape) but any extension makes a bent four (in case a) or a twisted four (in case b) - not killing shapes. S1 implies R3 - Black restores the seki. The indicated black plays are the only sufficient answer to the white threat.


[Diagram]
Responses to Black's threats

When White responds to Black's threat, we again have S1, with identical analysis. Thus White restores the seki. The indicated white plays are the only sufficient answer to the black threat.



Conclusion

The original diagram is indeed seki; with alternating play, it reduces to an obvious seki no matter who starts. However, the position gives either player a ko threat. It is certainly in Black's interest to use this threat if a ko comes up, since doing so also denies a large ko threat to White. White should only use the threat if the ko is important enough, but it's still preferable to using some other 34-point ko threat. (I think.) Because of the huge difference in the threat value, it may be in Black's interest to play the threat immediately, so that White does not get the big threat later.

Of course, White does have a big threat regardless, since any seki offers an unremovable ko threat. However, while the first threat costs nothing and removes a small threat from Black, the second threat costs 8 points outright if Black answers. See LosingKoThreat.



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