moha wrote:
I think on your first board the added empty points are basically points that can still be contested. That's why the behaviour changes.
That behavior change reveals that the top left is a ko position.
That's why I say that White's play there is not a protective play. Locally it gains ⅓ pt. or 1⅓ pt., depending on the rules.
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The second board seems identical to the original, but you say "not jigo". I guess because W not yet made the first connection, which you consider a competitive play?
Well, that depends upon the exact definition of competitive play, but there is a ko fight in this position, even if we can predict who wins it. Chinese/AGA and Korean/Japanese rules treat the ko fight differently, because when White takes the ko back Black must pass (or play inside territory). Chinese/AGA rules treat the pass as the same as filling one's own territory (as long as it does not make it dead); Korean/Japanese rules treat the pass as the same as filling a dame, which is one point better than filling territory.
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It would be ko if it would be B's turn (or if W passes). But if W's turn it seems jigo both in Chinese and Japanese.
The result, with best play, would be jigo. Traditional baduk evaluation and characterization of positions does not depend upon who has the move. Unlike one form of game theory. (Combinatorial game theory, OTOH, agrees with baduk tradition.)
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And still, I'm not sure the button behaviour here is desirable. Or if resolving a jigo by threats is ok, the button seems redundant and unnecessary.
The basic idea of button go is to unite area and territory scoring by being a hybrid of the two. It adds a play that gains ½ pt. by area scoring or loses ½ pt. by territory scoring. (Button go uses area style scoring.) Under normal circumstances who gets the last dame matters to the area score, despite the fact that correct play by territory scoring is also correct play by area scoring. Adding the button in such circumstances makes who gets the last dame irrelevant. If Black gets it, she gains 1 pt., but then White gets the button, so the net gain to Black is only ½ pt. If White gets the last dame, Black gets the button, also for a gain of ½ pt. Under ordinary circumstances in button go, who gets the last dame does not matter, as with Korean/Japanese rules, but life and death questions can be resolved by play, as with Chinese/AGA rules. Button go has the best of both worlds.
Button go normally produces scores ½ pt. better for Black than Korean/Japanese scoring would, but there are some exceptions. In some very rare cases there are plays that, like the button, gain less than filling a dame. They have been constructed on the board, but none is know to have occurred in actual play. In rare cases there are one-way dame which are worth a point by Chinese/AGA scoring and button go, but not by Korean/Japanese scoring. And occasionally there are ko fights which are not resolved while there are dame left, which is the case in your example.
Black is an odd number of points ahead on the board by both area and territory rules, so normally Black would take the button. But because White can win the ko fight, White can take the button and then fight and win the ko. The result is then ½ pt. less for Black instead of ½ pt. more. One may consider this an undesirable side effect of Button go, but it is an exceptional case, not a common one.
Suppose, instead, that there was also a dame on the board besides the ko. If White had no ko threat, then White would resolve the ko and Black would take the dame. The area score would be 1 pt. better for Black than the territory score, and the button score would be ½ pt. better. The hybrid score lies in between the two other scores. If White had a ko threat, then White would take the dame and later win the ko fight. In button go Black would get the button. The area score would be 1 pt. worse for Black than the territory score, and the button score would be ½ pt. worse. The button score is not better for Black than the territory score but it would still lie in between the area score and territory score. One might regard the fact that the score by button go lies in between the area and territory scores as a desirable side effect, but such kos are still uncommon.
Anyway, button go is a hybrid of area and territory scoring, and there are pluses and minuses to that.
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moha
shocked but not surprised 
}
takes the button, 
takes ko, 
fills ko 
leaves a ko fight which White can win by connecting at 40. However, White is komonster, which means that White can delay winning the ko, so 
could be a pass, OC. 
. Playing