I need a project... exploring carpenter's squares may well help my reading ability.
The carpenter's square is unsettled. is the vital point, making it unconditionally alive.
at
and
at
is seki.
If white loses the ko, black has 7 points (3 net captured stones, 4 territory) in the corner + a later one point sente reduction on the first line. (Note: all first line follow up values given here and later depend on the exact configuration of stones on the outside.)
This is the best play by white.
If Black wins the ko, he will resolve it by capturing and
, black ends with 9 points (3 net captured stones, 6 territory), Black can later reduce white left edge territory in sente by 4 points for a difference (and has reduced one point already) of 6 points to ko n°1. Thus this ko is worse for white.
A refutation (why can't be at
) - killing by nakade, the number of black's outside liberties doesn't matter
If Black wins the ko it has a 4 point sente endgame on the upper side (and has reduced one point already) and a bigger corner (5 net captured stones + 5 territory) than in original ko n°1. The difference is 8 points (16:8)
White needs two moves to almost fill the corner and in this process she can't make a dead 6-point-shape inside so this ends in seki. This seki usually is even worse for white than the above ko. (If white wants a seki, she can make a better one by deviating with from the normal ko n°1 line.)
If Black wins the ko, he'll resolve it by capturing and
. Black has 10 points in the corner (5 net captured stones + 5 territory), he can further reduce white along both sides in sente by 5 points. The difference to a lost ko n°1 is 12 points.
White can't answer with a because this ends in double ko life for Black. But if White hasn't enough threats left, she can still settle for a - with the double ko life giving an infinite amount of ko threats for White / later two moves in a row if Black is finally going to resolve it. Thus this is a lot better for White. (I'm not sure about the ko with
at b)
connecting is wrong, White wins the eye-vs-non-eye semeai
at
(changing move order) do not change the result.
If Black wins the ko, this should be as big as ko n°2 (9 points in the corner + 5 point sente reduction of white upper side territory).
After Black is dead (LeatherScrollProblem144/Solution)
If connects out, black is dead, if white can fill with dead shape + eye (so that it can not be seki) it is dead. So actually there is no way to live.
This is no dead shape, but white wins the eye vs. non-eye semeai with 3 vs. 2 effective liberties. This line is sensitive to outside liberties and doesn't work with black outside liberties.
While f and g are obvious failures - e.g. after a black answer at the vital 2-2 point - d and e merit some discussion. CarpentersSquareWrongAttack discusses e (against which Black stretches for at least seki) in detail.
This is pretty similar to a first move at e - with the additional (and bad) exchange of for
, which disables the seki lines.
The refutation of at
see above, doesn't work with outside liberties, the refutation of
at
as well... so everything changes. (below diagrams to be changed).
Black can't avoid ko, if he tries with this , he dies by nakade. If not, he has just another ko. But this ko may be worse for white in the endgame if she loses the ko since
is in place already.