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Extending On Third Or Fourth Line
This is often the most difficult decision to make, and the answer depends on both what you are extending from and what you are extending towards. Furthermore, it also depends on your overall strategy. This is intended just as a couple of guidelines.
See also Know Your Lines.
White has 11 * 11 = 121 points. Black has (18+11+1) * 4 = 120 points. Be happy to live with the third line! JamesA: Just a couple of points... In the diagram above black has played 4 moves more than white, which may explain the higher score! Also, I don't think it is a good general rule to use the 3rd line when invading - very often this will lead to a heavy group. Third, I don't agree that when extending between positions you should play on the third line as a general rule - think about the sanrensei fuseki. Last point, if you are worried that your group may come under attack, it's often worth playing on the fourth line to get out into the centre and avoid being sealed in. Gorobei: Black has actually played the same number of stones as white. Giving the corners to black is a little unfair, tho. My diagram was only an illustration of the surprising strength of the 3-line (thanks to BigNose for pointing out the break-even line as a concept.) Goran: I still think b played more stones :) 13*4 > 12*4 JamesA: Urm, sorry Gorobei but black definitely has 4 more stones on the board than white - just count them! The diagram is therefore invalid... that's why I'm pressing the point. Gorobei: Ok, so I was never good at counting :) HolIgor: Moreover, you can take away 4 more white stones without changing the score while all black stones work hard. But that is not the point. A third line move really helps to get a basis for a group. Too low but solid. StormCrow: I've updated the diagram so both sides have made an equal number of moves. I've seen this diagram done this way in books. Done this way, black has 120 points (one less than white's 121, but it demonstrates the balance of the third line). BillSpight: What it illustrates is the inefficiency of the White layout. White has 16 inefficient stones! The original diagram, with White stone on the 4th line and Black stones on the 3d line, appeared in textbooks to show how central territory is not as big as it looks. Fujisawa Hideyuki pointed out, many years ago, that Black had 8 more stones than White. IMO, that diagram, and its derivatives, should have disappeared from textbooks by now. ;-) JamesA: In the diagram below, would anyone be happy taking black? I wouldn't!
Bill: Suppose that you use 12 stones to surround territory with a single wall.
You can surround 4 points in the center, 30 points in the corner, and 12 points on the side. Building a wall up to the 4th line on the side makes the same amount of territory as going up to the 3d line. What if we use 16 stones to surround territory on the side?
Now the wall on the 4th line surrounds 24 points, while the wall on the 3d line surrounds only 20 points. Going up to the 4th line is more efficient. :-) Years ago I read something by Ishida referring to an article in Kido magazine by a mathematician about territory on the side. The most efficient shape for territory on the side is a rectangle with a 2:1 ratio of length to height. If you make a wall on the 4th line, your opponent may still have room to play underneath on the second line. But with a wall on the 3d line, you may reasonable estimate the territory by dropping perpendicular lines at the edges.
That leads to this diagram as the basic efficient shape for a 3d line wall to make territory. A wall of 6 stones forms a 4 by 2 territory (a 6 by 3 area). The rule of thumb, then, is not to form a longer wall on the 3d line, or to force your opponent to do so. It also means that it is OK, as a rule, to extend (nobi) along the 3d line up to 5 points from the opposite end of your 3d line territory.
I don't completely buy that argument, but it's good enough for Ishida. ;-) This is a copy of the living page "Extending On Third Or Fourth Line" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |