elbow

KarlKnechtel: This is my old term for an EyeSpace surrounded by two or more groups. (Sorry that it doesn't make much anatomical sense!) An elbow is "solid" if every liberty inside is shared by every bordering group. A solid elbow is as good as a one-space true eye for the purpose of determining life. If the elbow is not solid, repeated plays inside may allow the opponent to kill one of the groups (unless it has two other eyes). The simplest elbow is a diamond.

Thus, an elbow is often a source of ko threats, especially two-space elbows. A solid two-space elbow must have two surrounding groups (this is easy to show); if either group has no other eye, then playing inside the eye is a ko threat worth twice the size of that group (at least). Of course, if neither group has an eye besides the elbow, both are dead (the elbow is a 1x2 big eye which can only give one eye).

Elbows make "virtual connections"; it's generally not advantageous to play inside them. A three-space elbow, for example, will almost always give one eye and a connection. With sente it generally makes two eyes. So this is as good as a fully surrounded 1x3 big eye. Lesson learned: worry about how to divide the space first; and strengthen the corners later.

A solid elbow only offers a ko threat if one of the groups has no other eye - i.e., the elbow is being used mainly for its connection property. A non-solid elbow offers a ko threat unless the vulnerable group has two other eyes.

two-space elbows.  

Here, the elbow at left is "solid"; the one on the right is not. The circled space is not a liberty of the squared stone. Consequently, White at a or b provides a ko threat to capture and steal the eye at the circled point. Not a big one in this case assuming the large black group is alive without the eye; but still. The squared stone could instead be part of a large, surrounded group with one eye elsewhere, and then there would be a very big ko threat. The elbow at left provides no ko threat unless one of the groups somehow gets completely surrounded with no eye besides the elbow.