Net versus ladder
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[problem- can't this net be defeated by the sequence c-d-e-f-g? sorry for poor notation.]
No, see here "White can't cut...". Black plays at g instead of f. White has no choice but to capture at f; B at h forces white to fill in at and a couple more black moves capture the whole thing.
The net is better, because the ladder variation allows white to play a ladder block somewhere along the path of the ladder
Tapir: Even if there is no ladder breaker played by White, Black needs to capture at a time just in case. That is what I took from Kageyama: to capture with a ladder you need two moves, to capture with a net only one.
In this variation of the taisha joseki. What the books say is that is only playable when the ladder at a is good for White, capturing the stone with the net White b and c isn't enough.
If the net continuation were good, White could play at in the setup diagram independent of the ladder, thereby avoiding the most difficult variations.
After these plays, however, Black has a good result, and the possibility of a black peep at d remains. Also forces . Both of these effects are there because the marked black stone is still on the board.
For comparison, see the usual result from the ladder variation. White's capture in the ladder forces .
There is also an interesting tidbit in "Lessons in the Fundamentals of Go" by Kageyama. He states that when there are two ways to capture with one move, then the firmer is correct (choose the firmer capture).
In this example the two white stones can be captured with a geta by playing at a. However, according to Kageyama, the correct move is b, which has a firmer grip on the two stones.
Alex Weldon: There's something about this proverb that bothers me. Unless he also gives an objective definition of what "firmer" means (less liberties? That can't be it, or else a ladder would be "firmer" than a geta), I would read "firmer" to mean "with least aji." But since aji is bad potential, this just boils down to "Given a choice between two methods of capturing, the one that leaves the least bad potential is better," which is starting to sound an awful lot like a circular argument.
Alex Weldon: The circularity is not in defining "firmness" as "with good aji." The circularity is in stating that out of two ways of capturing a stone (or stones), the firmer way is better. On the surface, it sounds like wisdom, but it boils down to "out of two ways to capture a stone (or stones), the one with better aji is better," which is a tautology.
Gregory Wonderwheel: Unless "firmer" has a special meaning in Japanese Go jargon, at face value of the proverb, I take "firmer" to mean "with less cutting points" because that would reduce the number of possibilities for peeps before the capture, thus reducing the options for the opponent. Thus a short ladder could be firmer than a large net, and vice versa, a small net is more likely to be firmer than a long ladder.
Dieter: I believe there is this trade-off with ladders and nets.
- Ladders have long-range aji, nets have short-range aji.
- A ladder breaker (being the ladder aji put to use) can be answered once and the aji is gone. After a peep (the aji of a net put to use) is answered, the aji of another peep still exists.
I believe Kageyama's statement is that the long-range effect of a ladder in general is a heavier burden than the multiple short range aji of a net. As always with heuristics there are quite a few exceptions imaginable. In particular when the range of the ladder is rather short, it will most often be preferred over the net.
BTW, I would not call "the one with better aji is better" a circular statement, but I agree it just shifts the problem to the definition of good aji.
Notochord: Only if you consider aji to be the only characteristic of a position, which is stretching the definition a mite too far, I think. The point is essentially that the issue of aji, of giving those (most usually cutting) stones as little room to maneuver as possible, is often by far the most pressing concern. You should as a general rule play as tightly as possible, and avoid thinking that any move that succesfully makes a capture is just as good for the purpose of capturing as is any other move which does the same. As something of a corellary, I think that a main idea of the statement (Proverb?) is that we should not try to stretch our shape too much in capturing vital stones, in order to (for instance) reach towards some other position, and thus make our move 'less gote', since this usually creates a great deal of bad aji for the opponent to exploit which overwhelms the minor gains made from making a looser, weakly double-purpose capture.