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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 ImplicationsConsider 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:
See almost fill for more discussion of killing shapes. The results are:
L0 L1 L2 S0 R1 R1 R1 S1 R3 R3 R3 S2 R1 R2 R2 S3 R3 R2 R2
L0 L1 L2 S0 R1 R1 R1 S1 R3 R3 R3 S2 R1 R1 R1 S3 R3 R3 R2 Here, the results are:
Then again, all of this ignores the possibility of various ko situations. ^^; Practical example
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:
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.)
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.
Proof that Black threatens to kill and make eyes - obvious.
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.
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.
ConclusionThe 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. ![]() |