Forum for Rectangular six in the corner
one outside liberty: Black tenuki after White connects at 4 [#4965]
(I'm the person who made the Feb 17 2018 edit, but I think what I'm saying would apply even to the version before that.)
I'm more interested in the programming and mathematics of Go than actually playing Go, so I may be underestimating the significance of needing to find the first ko threat, but anyway:
I notice that after White connects at 
, White is _still_ not threatening to kill outright. Rather, _regardless_ of who plays the next local move (Black at a or White filling the outside liberty), that local move yields a direct ko in which Black needs to find the first ko threat. If White fills the outside liberty instead of connecting at , then although Black responding will make White need to find the first ko threat, White _is_ threatening to kill outright (Black is in atari).
Accordingly, I will wait between one and two weeks, at which point if no one has indicated otherwise then I will edit again to give filling the outside liberty as the main line and move connecting at into a sideline.
Readers are advised to study the bent four in the corner ;)
They should also notice that the position I'm describing is one in which the attacker has _already_ formed a bent four in the corner, rather than one in which the defender can't stop the attacker from _reducing_ to a bent four in the corner whenever the attacker wants to. As a result, even if the defender has no non-removable ko threats, the defender can get something by starting the ko while the defender still has ko threats that can be used. (If necessary, that may be before "the determination of life and death at the end of the game, after play has stopped".)
It's unclear what the what here. If this is about "Black's throw in at is necessary: if White gets to play there she makes it a bent four in the corner." White playing there kills outright. Only if White's outside group were in trouble would she need to think about playing the ko to capture. (In principle, if Black disputed the result, White could remove all ko threats during scoring then initiate the ko, taking first). The defender in this position is Black.
This is about the "one outside liberty" position just "after White connects at 4":
![[Diagram]](diagrams/36/ebddd00da94c8e13fe3bbd86aa498d77.png)
The point is, _each_ player has the ability to start the at-least-mostly-inevitable ko, and those are the only relevant local moves.
In particular, even if Black would be declared dead if this were still on the board during "the determination of life and death at the end of the game, after play has stopped", Black can start the ko before then, while Black still has ko threats that can be used.
When White connects, the result is White-takes-first ko.
When White fills the liberty instead, the result is Black-takes-first ko.
The significance can be said to be 1/3 of Black's life.
There can be reasons to fill the liberty first, but not when White's outside is secure. It would be an extremely unlikely setup that Black would be ko-master for the rest of the game, but not at the moment.
That much of Black's life would indeed justify the structural inferiority.
However, since you mention "ko-master":
After White connects at 4, if one ignores the issue of how large Black would live if Black does live, then unless one's opponent is ko-master, one should only start the final ko when the ko threat situation would otherwise change in ones opponent's favor. For example, if the eventual winner won't change but the amount of compensation the loser will get will decrease by x points _due to normal play_ rather than the eventual winner spending a move for that purpose, then the eventual loser starting the ko is an x-point reverse sente.
If the eventual winner will instead have to _spend a move_ to do that, then the eventual winner spending that move and the eventual loser starting the ko will both be gotes with miai value x/2.
That's really cool. The value of threats may tend to decrease as normal play goes to endgame...(in a sense inconvenient to specify). There is also a lot of variability and creation of threats. Some simply wouldn't have cause to be removed once present, until scoring dispute phase.
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