19x19 diagram  

After can White live here? It's a strange sort of game, I realize, but it's just theoretical. Maybe is misplaced. Maybe it should be at a.

Jan: Maybe at b, even. Sure White can probably (provably?) live small at the bottom, but White has only 76 points at the beginning, Black has 209, so White has a lot of catching up to do. There's also a diagram and discussion of this sort of situation on SL with White on the fourth line all around, but I can't find it right now.

Alex Weldon: I'm not sure this is necessarily the right way to look at it. Both this diagram, and the one Jan mentions sort of rely on proving that if one person takes edge territory and the other person takes center, one of them wins (depending on what line we're talking about). But the fourth line generally isn't *about* territory, it's about influence and the balance of power, which is a concept that's too abstract to really be seen from a diagram. Anyway, my understanding of the proverb that the fourth line is the line of victory is that taking territory on the third line doesn't usually give you enough points to compensate for the thickness that your opponent gets, while getting territory on the fourth line often does. I think the proverb is just generally there to discourage taking third-line territory and giving the opponent thickness, and discourage letting the opponent make fourth-line territory.

HolIgor: Black does not have to kill. Let us look at the territory. White has 4*19 + 6.5 komi = 82.5

19x19 diagram  

The marked 11x8 rectangle at the top has 88 points. Now Black's task is to secure that and take from the lower side at least as much as white. Black will win the game easily in my opinion. So, instead of 3 at the previous diagram I'd play boshi. In symmetrical situation make symmetrical moves. This allows white to choose on which side to extend. Then I'd continue to attack from the outside forcing White to find a way to live and reducing the living space for the next attempt.

A notion coined by me: a player that goes for influence takes the remainder, i.e. what remains after the territorial player builds eyes. In this situation the remainder is huge.

One more observation of mine: TheLargestAreaSamePerimeter

Let's take TheLargestAreaSamePerimeterTest