mgoetze: After , a and b are miai - If black plays a, b destroys the second eye and black is left with a killing square four; if black plays b, white a makes a killing bulky five.
demetria: What I really want to know about this problem is : What is the value for white in destroying the eye?^{[1]} Doesn't it cost too much to kill it?
mgoetze: Uhm, the value is that all the black stones are dead afterwards, when they could have lived otherwise. If you look at it in terms of area scoring (which doesn't produce a different result than territory scoring, it's just easier), there are 9 black stones enclosing another 7 or so intersections... white gains this area, black loses it, so playing 1 puts white ahead about 30 points... (I suck at counting though, so if anyone cares to correct me...)
Demetria: I can't say if your answer about the points is correct - estimating the score makes no sense to me. Oh, thanks for clearing up the part where if black a then white must take b, there were some people who didn't see that a dead shape is only dead in the absence of another eye.
[1]
Bill: lives. Later, on the standard assumption that the area to the right is White territory, - is sente, and we assume that Black can play it. Black gets 9 points of territory.
If kills, White gets 18 points for the captured stones, plus 6 more points of territory, including the CE points that are not territory if Black lives. That makes a total of 24 points.
In the original position the encircled region is worth (24-9)/2 = 7.5 points for White. A play by either player picks up 16.5 points.
As mgoetze says, area counting is a bit easier in such cases. In this diagram Black gets an area of 17 points, and there is one point, CE, in dispute. If White kills, White gets all 18 points. A play by either player picks up 17.5 points. (In nearly all cases the difference in play value between area counting and territory counting is 1 point.)