It's my understanding that many times the third line is considered low. I've heard that crawling along the third line isn't a bad result for either the outside or inside. I wanted to see how high black would have to be to beat white (with 6.5 komi) if black took only the sides, and white took the rest of the center. The results surprised me, so I thought I'd share it with other beginners and see what they get from it.

So the question is: supposing black built a perfect wall facing towards the edge, while right next to black is a white wall facing the center, on what line would the black wall have to be in order for black to have more territory than white plus komi? The answer was less than I expected.

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Done? The answer is 3. A black wall on the third line, and a white wall on the fourth, results in B+8.5. This may make you think twice about giving up a "low" piece of side territory in order to gain influence in the center (something I used to do, but do less now). Honestly I did this just out of curiosity (how much is the center worth REALLY?), but now I'm going to be thinking about this result for weeks to come. I even opened up CGoban to see how this looked, and I thought white was going to win. Shows how much I know. =P

What insights, if any, does this give you?

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??/10,000

Don't know! Haven't been counting. Will count eventually...

But in your hypothetical setup, black played 8 more stones than white... you should calculate area divided by stones (IOW, efficiency-- how many points, on average, did each stone get you?) to be fair.

3rd line is not necessarily considered to be low. 3rd line is the line of territory, 4th is the line of power. Sometimes 3rd line is too low, sometimes 4th line is too high.

2nd line is, of course, the line of victory (sarcasm).

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But then where would the other 7-8 white stones be? They would die in black's territory, so they can only be placed inside white's. You can also assume those 7-8 were sacrifices to gain outside influence when white was originally low. Also, sorry, I didn't mean low as in ghastly low (2nd line == win, yes?), but low as in secure territory. I think of low as territory and high as invadeable territory. There's too high (highly invadeable territory) and too low (not enough secure territory), but no "kinda sort middleish."

But none of that is important. Notice that black took the "territory line" while white opted for the "power line." That's the result that interests me. The way I imagine it, white opted to play outside in exchange for black getting secure territory, which happens in my games. Of course I don't let black get ALL the side, but all I'm wondering is if there's a lesson to be learned here.

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??/10,000

Don't know! Haven't been counting. Will count eventually...

This result completely ignores the order of the moves, which is vital.

Lets say, for instance, the players start by giving white fourth line stones and black third line stones across one side of the board. Now, white can smash black about all over the rest of the board because his influence is overwhelming - but in your situation, he refuses to do so and plays suboptimally to end up with 4 walls which don't work together. Whilst there is some truth in saying that the centre isn't that big, in a real game it comes with a host of other considerations that you can't ignore.

All in all, the situation you describe is interesting (I think there's a SL page about it), and I've seen it put forward as a reason that 19x19 go is the best size. However, I think it is a very dangerous idea to draw the conclusions that you seem to be taking from it. You cannot just look at when 'black has more territory than white', because white's wall comes with a hefty dose of influence which isn't counted when you construct an artificial end-of-game position.

From my experience, a 4th line wall is worth more than 3rd line territory.

To add a bit, I'd say third line group stability is bigger than fourth-line wall, which is bigger than third-line territory. But I don't actually know how to use influence. =)

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Someday I want to be strong enough to earn KGS[-].

This kind of setup has a long history. In old textbooks it was used to show that the center territory is less than the territory on the sides and corners. However, some pro (Fujisawa Hideyuki, I believe) pointed out that Black had played eight more stones than White.

For more discussion, see http://senseis.xmp.net/?ClassicalExampl ... eTerritory

and

http://senseis.xmp.net/?FourthLineVsThirdLine

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

If you assume bad play by one player, then you will get a bad result for that player.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Where do the extra stones go when B has the 4-4 and W invades on the third line?

This. If there's a black/white boundary across one side of the board, with black on the third line and white on the fourth, I'll take white every time.

The third line is the line of territory. The fourth line is the line of influence. Counting the territory alone omits influence (which is only valuable while the game is still in progress - before the four walls get built) from the equation.

Click Here To Show Diagram Code

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$$[/go]

This is a won game for White.

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A good system naturally covers all corner cases without further effort.