a is real because white cannot play at the corner point b. b is real because white cannot play at three out of four of the corner points around b (white only has one out of four). The solid connection definition gets this group wrong.

 

Once they understand this, I extend on it a little by give examples like this. a is real because white "cannot play" at b, because black will capture it. It's almost always a easy jump for beginners from "cannot play at all" to "cannot play without simply losing your stone", and while it fails occasionally with stuff like double snapback, it's correct for almost all basic situations. Beginners I have taught this way have also been quick to grasp that once white plays at c, black needs to play at b to defend the eye, because after c, now white *can* play b.

The solid connection definition does actually work here, because black can play b no matter what white does. But "black can play b no matter what white does" suggests to a beginner that he needs to check many possibilities and requires a reading depth of 2-4 (up to 4 when white plays at b himself). Also, beginners might iniitally not consider the possibility that they can get b no matter what, leading them to actually play b before white has threatened anything.

By constrast, the "white cannot play" definition suggests that black need only check a single thing - that white can play b successfully. I've found in practice that the "white cannot play" definition is actually conceptually easier to apply for beginners in these cases.

Thoughts?