Protecting the cut - Example 2
It depends. Method a leaves no ko threat for White to exploit later; b has good potential for making eyes, if necessary; c might be good depending on the surrounding situation, but looks a little odd in isolation; d extends the group further, but later in the game you may need another stone to protect against a double atari.
Most of the time I vote for b (or a, if I'm wary of ko); but d is often good too, as long as you don't let White set up a double atari.
-- TakeNGive, 10kyu on KGS
The whole question makes more sense if there are the circled white stones preparing for the cut.
Otherwise also e and f are even preferable shape options (certainly over a or c; see also a. g, h, i below).
Option e can capture a cutting stone c with Black g (for geta) if one of the circled stones was not present.
Forget about a and c above: even fear of imaginable future ko fights cannot justify such immediate local losses (already a small number of them add up to a bigger value than many kos).
If c (in the first diagram) is peeped and answered, the a-shape's empty triangle has been filled to make the perfect dango.
Option b (in the diagram immediately above) has the big disadvantage of not making eye shape (just when you might need it). The squared white stone can create a false eye.
Why not also option f? In the middle of the board it radiates influence and a cutting stone is captured in geta with x to z.
f's disadvantage is that it can be attacked by White x and z or y.
The plays in d and f are both good general purpose moves (and much better than a or c); also b is often quite suitable (if eyes are not important). If I had to chose only one candidate, for a general rule of thumb, then d fits best (even over f) without any if's: it protects the cut and creates eye shape. Because these situations occur so often in games, even the smallest difference in efficiency adds up hugely in the result.
Does 1 in option g work? Which stones are important? What does 1 threaten elsewhere? Could I play Black m and o in sente against a white n if this were a corner? If I play o, do I then create a loose-ladder option r up to v (or r-x?) against a cutting stone (note, it depends where the edge in this diagram is)?
These are questions which are not so far of from the fundamental, underlying question: must the stones be 100% connected? Are they all that important, compared with sente? The tenuki option is h. Could I fight, if cut? Could I rely on a ladder? That implies some ladder breaker options i?.
I found this shape issue of such fundamental value, that I had to comment on the typical bad shape examples a and c.
-- Tderz, 3 dan European