I have seen a lot of comment here about 3rd line vs 4th line but very few examples where players seem to play anything like the best moves. Obviously this is a theoretical exercise - but why not develop it in to a "real-world" real-game? exercise - then comments about the value of 4th lines plays can be properly qualified.
I will try to post some diagrams soon, but to open this up, lets start with the unconventional but not ridiculous? idea that black plays 4-3, white follows with 4-4 and black extends to 3-3. White then plays 3-4 and then instead of black hane? they make 3rd and 4th line walls across to the opposite 3-3 and 3-4 points.
There is now a black line along the third row and white along 4th line on the top side. What's black's best move here? Tengen? The 10-4 on the bottom side? 10-4 on either the left or right sides? A 4-4 or 5-4? on the bottom side?
It seems to me that white has no way to threaten the 35 points of territory that black has made on the top, but black has a number of options for countering the potential and the influence of the white wall.
If Black decides they need influence, and the above sequence were repeated in opposite with white following Black 4-4 with 4-3 or 3-3, then both players continuing a wall on the third and fourth lines?, then we end up with a situation where the value of black's sente is reduced, but we are essentially 60 moves in to a game of mirror go.
Perhaps Black takes tengen here, and things look from a 10k perspective? pretty tough for white.
As I said, I will come back to this idea, but my basic point is that White can't successfully invade Black's territory on the third line - but it seems that there are ample opportunities for Black to reduce the benefits that White gets from a 4th line wall.
Thoughts?