When it is said that the 4-4 corner is for influence, does this just mean that it is one point nearer the centre?

That does not seem that significant, and not worth the much greater security of the corner that the 3-4 point gives you.

Or am I missing something?

_________________
Regards,

Peter

I'd say the real point of the phrase is that it's specifically not for territory. It's a common thing to see a 3-3 invasion and be dismayed because you thought you'd already claimed that corner. Of course, it might claim territory (another move can take the corner inefficiently, or two moves can make a very efficient enclosure or framework, or you could use a single move to do both a little bit). On the other hand, if the opponent invades underneath it you normally can't kill and might even take gote, but the point is the opponent can't do so without giving you a great deal of thickness.



Well...it is significant, and it is in general terms worth it. In the end this is a pretty subtle thing, it's easy to say that it's true but one of many things you can't really justify with a few paragraphs and diagrams - it's just too big a topic. Overall, it turns out that the ability of the 4-4 to participate in large scale frameworks and general skirmishing makes up for its not immediately claiming the corner territory.

I suggest playing some more games, where you play 3-4 points. Your opponents will often play 4-4 points. When they still win a fair fraction of them, review them focusing on how the 4-4 point didn't damage their game even with its clear territorial weakness.

In the opposite direction, you might try playing the 3-3 point. This avoids even the 4-3 point's weakness (the opponent can still play 3-3 if they really want) to take practically definite territory. But I think you'll quickly find that your opponent makes big moyos almost without trying because even though the 3-3 point is another just one space into the corner, that turns out to be a big difference.

Well, this is about the time someone whips out that cheesy diagram of one side with a wall around the board on the third line, and the other the same on the fourth.

The real answer is that it's not about the stone itself, but the thinking behind it. Third line stones are not easily undermined, so it is relatively simple to take territory with them, but it is a modest amount of territory that the opponent doesn't need to be frightened by, and can easily hold down to the 3rd line. Fourth line stones get 50% more territory, IF they get it, but they are much more easily undermined, so you can't count on it, and that extra territory makes it more worrisome even if the opponent holds it to the 4th line. This means that when you play stones on the 4th line, you can't count on that as territory and need to play to develop them to make points in some other way. Generally, that other way is influence, which you then use as an anvil to beat the opponent's groups against.

A 4-4 stone is on the fourth line in both directions, so it's particularly bad at being territorial without a few third line follow ups. This means that it is less efficient at taking territory directly. A 3-4 stone, by contrast, is on the 3rd line in one direction, and the 4th line in another, and can be easily balanced to make a strong corner enclosure with 1 move instead of 2. This makes it easier to hold territory in the one direction where it is on the 3rd line, but it can also be used for a strategy of influence in the 4th line direction, so in this way, it is more flexible than the 4-4 point. It is less flexible, however, in that the direction in which you play for a particular goal is already fixed, meaning that you can choose a direction, or a goal, but not both. Usually, the opponent selects a low or high approach to the 3-4 stone based on this consideration of whether they want to limit the territory direction or the influence direction.

If you want to go for territory only without regard to direction, it may be better to play a 3-3 point, but your opponent can cap it to limit its effect on the rest of the board without needing to worry that you will make too much territory for them to deal with through that stone.

Looking back at this, and the 3rd/4th line stone difference, I think you could say that the natural way to limit a 3rd line stone is to cap it and hold it down to the third line, and the natural way to limit a fourth line stone is to go under it and ruin any potential territory there. Because the stones in the corner are on 3rd and 4th lines, this follows in how they tend to be dealt with.

Yes, one point can make a great difference, even in the opening.

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

Visualize whirled peas.

Everything with love. Stay safe.

Let's hope not.

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

Visualize whirled peas.

Everything with love. Stay safe.

I can understand the big difference between being 3 or 4 lines away from the edge. It is less intuitive to me that the difference between being 6 or 7 lines away from tengen is just as significant, but it must be right for so many people to play it.

_________________
Regards,

Peter

I think the significance in being either 6 or 7 lines away from tengen is that you are either 3 or 4 lines from the edge.

I don't even know how many lines away from tengen the 4-4 point is!

Here's a thought about why the one line difference between 3-3 (or 3-4) and 4-4 is more significant than the one line difference between 4-4 and 5-5, or 5-5 and 6-6. I think I'm saying roughly what skydyr said above, but with different words, or at least a different permutation on some of the same words.

Plays on the third line are just high enough to be able to live locally, even if there are (not too many) opposing stones above. The second line is generally too low. Thus, if you play at 3-3 (or 3-4), you can expect to make territory locally.

For that very reason, a play on the fourth line cannot expect to make territory: if you play at 4-4, I can play at 3-3 and expect to live underneath you.

And for that reason, a play at 4-4 is influential. It's not because the fourth line is particularly high all by itself, but because my playing at 4-4 gives you something like two options:

1. You leave me alone and I get to play in the corner again (and again and again?) until my 4-4 stone is alive locally. This means I get a big corner. Yay for me! Sad for you.*

*[of course, this ignores all the not-sad things you might be doing on the rest of the board while I'm playing in one corner.]

2. Since option 1 was sad for you, you instead invade the corner and live locally. Yay for you! However, unless I make a real botch of things, I can make you work to live locally by pushing on you from above. I wind up with a wall facing the centre, or one of the sides. Yay for both of us!

So as I see it, the 4-4 stone doesn't represent one stone, one line closer to the centre, it represents either a big(ger) corner (than 3-3 or 3-4) or a wall. Walls are obviously influential.

4-4 represents a potential wall precisely because it's only one line above the third. A play at 5-5 is going to have a harder time putting pressure on a 3-3 invasion, and so can expect to wind up with a higher but shorter (or thinner or otherwise less complete) wall.** In other words, it's not distance from tengen that matters, it's distance from the side/corner. It's about being juuuuuust high enough that the opponent can invade and live locally.

**that said, crazy people do play at 5-5 and win, and it's presumably a more influential place to play than 4-4. I'm not strong enough to understand those crazy people, though, so I'll pretend they never happened.

That's enough to explain it. You're generally fine with giving up 3rd line territory in exchange for influence but not 4th line territory. So if you play 3-4, there's a good chance you'll be on the territory side of any exchanges, and if you play 4-4, there's a good chance you'll be on the influence side. It's not that influence is better at the 4th line, it's just that your opponent isn't going to offer you influence for territory trades when you're on the 3rd line.

The 4-4 has also been viewed as faster. With the 3-4, I'm hoping I get to complete the shimari and an extension from it. With the 4-4, I'm kind of ambivalent as to whether I play twice in that corner or the opponent approaches. That sort of ambivalence about which option you get to play is usually a good thing, because once you prefer one future move over another too much, the opponent is going to take the other choice.

I get it. The measurable closeness to tengen is incidental. Even on a 100x100 board, players would still often open on 4-4. The key measurement is 3 from the edge, which is the smallest invasion/enclosure that can live, and line 4 happens to be the best place to build a wall after such an invasion. The 4-4 point gives you the most flexibility in which way that wall faces.

_________________
Regards,

Peter

One point that I don't think has been mentioned yet is that a stone on the 3-4 point basically needs another stone to fulfill it's main purpose in life - to make a shimari, whereas the 4-4 stone, while it tends to like an extention to the next available hoshi point, can be left to it's own devices. Thus the 4-4 stones are helpful in letting you stake out other claims on other parts of the board.

_________________
Patience, grasshopper.

Well...

There's a point at which the sheer size of the centre overwhelms the value of claiming 3rd line territory, so that it's a bum deal, much like 2nd line territory on a 19x19 board. Technically you can claim it, but it's generally seen as bad to give the wall in exchange for it, specific circumstances excepted. At that point, for that size, people will tell you that crawling on the 3rd line is the way to lose and you need to crawl on the 4th to get an even exchange, etc. You may have noticed that a 3-3 invasion on a 13x13 board right off the bat is much better than the same on a 19x19 board, and this is kind of a counter-example. Of course, the farther you get from the edge, the less its special properties affect the fighting to come, so it may not be as extreme.

That said, no one really plays on boards much larger than 19x19 with any seriousness, so the point is kind of moot.

Regarding the rest of your statement, the 4-4 is more flexible in that you can leave it after the one move and be okay, but it also doesn't have as great a follow-up move as a 3-4 stone does. The 3-4 stone, by contrast, has a specific followup area that wants to be played sooner. However, if an opponent approaches a 3-4 stone, it is less urgent than an approach to a 4-4 stone, generally speaking, because the 3-4 stone is more grounded to form a base. The standard approaches to a 3-4 stone, at the 5-3 and 5-4 points, are valid opening moves in their own right, and playing at 3-4 is a standard approach to them, leading to very normal (though sometimes complicated) joseki. With the 4-4 stone, if the opponent gets a double approach, it can live and fight, but a lot of its effect is lost, and the joseki are more clearly tenuki joseki, where one side got two moves in a row and will get a better result locally because of that.

Some people will try and tell you that 4-4 is better because of X, or that 3-4 is better because of Y, but it's a tradeoff either way. It's better to experiment with both and pick openings knowing what both can do and trying to exploit that to its fullest.

Yes, I think I'd say something like this too. A 4-4 stone is stable, but does not claim the corner; instead, it threatens to claim the corner, but if your opponent denies you the corner, the 4-4 stone will turn into a lot of thickness.

Influence and thickness can happen on the second line as well as on the eighth, but in some sense, it seems to me that the fourth line is the line of influence because the third line is the line of territory - in any sensible line of play, one person will steal some territory, and the other will fight back to claim influence in return.

Except if the centre is so big then it's easier to live inside it. I have no idea if 4th line influence is better or worse on a 100x100 versus 19x19. Maybe we should ask beerslayer*.

* KGS user who plays 38x38 a lot.

I tried to underline the mis-understanding in the quote - the main idea in the opening is not claiming territory as fast as possible. If you stick on territory too soon, your game may become too slow. It is also important to get influence and be prepared for fighting at the relevant places all over the board. A strong player in my club once told me that Go is a game on connecting your own groups and separating your opponent's groups. If your opponent is busy with settling his weak and split groups you will get many sente plays, which can be used e. g. to attack while growing your territory.

It is an interesting exercise to focuse mainly on separating opponent's groups while playing games instead of securing territory - this usually leads to games with enhanced stress level and very clear results at the end (in both ways). Playing on WBADUK (despite the dreadful Windows client...) can give you an idea about that . On the other hand, a territory-oriented calm style - if played well - could also achieve the goal. But that's how the difference in 3-3 and 4-4 may be expressed (all above IMHO of course, please correct any misjudgements).