Thickness vs. Walls

dwest · #1

Hey everyone,

I've got a couple questions.

1. I'm wondering if someone could explain the difference between a wall with few defects (protected cuts, like the white wall on the left) and thickness. My main concern is with the proverbs that say, "Don't play close to thickness," and "Don't make territory with thickness." At some level you want to extend from a wall, but is there a point at which your wall is so strong that to extend from it would be bad?

2. The following position came up in a game of mine and I was unsure where to move next. I was very tempted to solidify my framework with a move around K7, but that leaves a lot of viable points of invasion and seems overly ambitious. Playing on lines closer to the bottom edge, however, feels like the white stones are overconcentrated. Is my inclination that K4 or K5 are overconcentrated and slow correct? Where should I be looking on this board if I'm concerned about using my two walls well?

Thanks!

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . X . O . O O . . | $$ | . . . X . . . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Numsgil · #2

Some theory:

The most efficient way to enclose territory is with a square (not unique to go, just a general principle about square grids). If you try to enclose territory with a rectangle (particularly a tall rectangle coming off the edge vs. a fat rectangle running along the edge), you're being inefficient.

So you can build territory with a wall/thickness (really it's more of of a moyo than territory, though), so long as you can get fully extend from the wall. How far is fully extended? The goal is to make a square territory, so that means you want to find the height of the wall above the edge, and move that far along the side. You subtract height for defects in the wall, because if (when) your opponent invades you want to be able to effectively attack them, and if they get forcing moves in against your wall you'll need your extension to be closer to help the attack. You might also subtract some points if you're approaching your opponents own thickness, but there's less math and more art to that. If it's not far enough, you're building a tall rectangle of territory, which is inefficient.

Examples:

A single 3rd line stone has a height of 3, so you move 3 over along the 3rd line and plonk a stone down for a 2 point extension (an n-stone extension counts the number of open spaces, so the stone is actually n+1 spaces over).

A single 4th line stone has a height of 4, but it has a defect at the 3rd line, so you still move over just 3 lines and make a two point extension on the 3rd line.

A 3rd line stone and a 5th line stone have a height of 5, but have a 4th line defect. So you can extend 5-1=4 spaces, so you make a 3 point extension on the 3rd line.

Your game has a wall with height 7 (up to C7). So you count 7 over from the C7 stone which puts you at K3 or K4. Your other wall has a height of 7 too, but it has one defect. So you count over from R7 by 6, which puts you at L3 or L4. (You could also ignore the top stones and just count your wall as a height of 3 from the O3 stone, and you'd arrive at the same answer in this case).

Which suggests, if you want this bottom area to become moyo/territory, you can do it pretty efficiently by playing a stone at K/L 3/4. I'd favor L since your left wall is stronger than your right wall. And I'd favor a 4th line stone to form a meatier moyo, but that's less precise and more just gut feel. Any of K/L 3/4 would probably be okay.

That doesn't necessarily mean that you should do that right now, though. There might be bigger moves on the board. In this case, I would probably play it right now because the right wall looks a little fragile (it doesn't have very compelling shape). Or maybe something like O6 instead to more directly help that wall be 2 dimensional/ have some shape (though that doesn't discourage invasions nearly as much).

If you're comfortable with the health of both walls, I'd leave this bottom area completely and play on the top somewhere, and then come back to this area later.

...

Caveat:
This principle is for when you're trying to make a moyo/base/territory. Not when you're playing lightly. So often a 4th line stone gets a 3 point extension on the 3rd line because it forms a really flexible shape. But you can't say it's making territory effectively.

pwaldron · #3

dwest wrote:

Hey everyone,
1. I'm wondering if someone could explain the difference between a wall with few defects (protected cuts, like the white wall on the left) and thickness. My main concern is with the proverbs that say, "Don't play close to thickness," and "Don't make territory with thickness." At some level you want to extend from a wall, but is there a point at which your wall is so strong that to extend from it would be bad?

John Fairbairn has devoted a number of posts to this topic. I won't claim I understand it, but I think the basic idea is that thickness is "power". It represents a strong (i.e., powerful) position that you can use to do, ahem, stuff. What that stuff is seems to be the essence of being able to make use of thickness, and consequently takes some strength.

Usually the advice is to use the thickness to attack, but you could do this in a few different ways. You might build a territorial framework that gets so large that your opponent is forced to invade, giving you a target to attack. You might also use that thickness to support an invasion into your opponent's territory or framework. You might also be able to tenuki away from your own weak group, saved by the fact that there's no effective attack thanks to your thickness. It all depends on the game, which I know is a bit of a cop-out.

Switching to your positional question. Your opponent has taken two corner territories, the first stone in the top left and a formation on the right. You have one corner territory, a formation on the bottom and sente. If you just try and enclose the bottom, I would be worried that it would be on too small a scale. I think there's a real danger that your opponent will also go building his own formations and you'll find yourself behind.

I would consider playing at 'a'. I haven't read it out so I don't know if it works, but that's the first move that I want to play. The basic response would be one of the 'b' moves, but it seems like that will be building your position on a larger scale than his. If he tries something else, you have the chance to start a fight and put your walls (thickness?) to work for a better purpose than territory.

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . X . O . O O . . | $$ | . . . X . . . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . b X . . . | $$ | . . . , . . . . . , . . . . a b . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

[/quote]

Shaddy · #4

A thick group is a group against which there are not so many forcing plays. Basically, it's a group that you don't have to worry about, and which will not become a liability to you in a fight (which is why you should pick a fight when you're thick). A wall may be thin and a non-wall may be thick: thickness only has to do with how strong the group is.

Uberdude · #5

k4/5 are indeed slow and overconcentrated. I'd probably just approach the top left corner and play some normal go. Which side to approach? Here are my ideas

Approach on left side and might go like this. Pro: wide open space, no danger, can build something. Con: open at a. W top side is nothing special as you have invasions or easy yose at b.

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Top side might go like this. Pro: aims at cut at a. Con: narrower space so could be weak.

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You could do something like the suggested shoulder hit at p10, but another idea is simply to say "thickness, meh" and let your opponent worry about reducing your potential while you just go and take points round the corners/sides whilst he plays reducing dame. Of course if his reduction also grows his own moyo such a strategy is not such a good plan.

mitsun · #6

In cases like this, estimating the score can help guide your play. On the upper half of the board, B has played 3 more stones than W, and they all look reasonably well placed and efficient, so B leads by around 30 points there. In addition, B has two corners worth 10 points each on the bottom half of the board. So to maintain equality, the W moyo needs to be worth 50 points. It does not look like a conservative move like K3 or K4 will achieve that goal. Even if W plays K5, B can simply cap at K7. If W manages to enclose all the territory below this, it will barely add up to 50 points, but while W is enclosing this territory, B will gain enough outside influence to maintain a solid lead. So in this position, I think W must dispense with a simple and safe extension and try something on a grander scale.

K7 might be worth a try; this would at least produce enough territory if B invaded deeply and died

PWaldron's suggestion to expand the moyo by pressing at P10 is also a good idea.

Finally, you could switch to the upper left corner for awhile and see how things develop. Uberdude gave two possibilities there; I prefer the first, as it seems to work better with the W moyo. After that sequence, a W move at P10 would be superb, so B will probably have to start some sort of reduction or invasion.

Bill Spight · #7

dwest wrote:

Hey everyone,

I've got a couple questions.

1. I'm wondering if someone could explain the difference between a wall with few defects (protected cuts, like the white wall on the left) and thickness. My main concern is with the proverbs that say, "Don't play close to thickness," and "Don't make territory with thickness." At some level you want to extend from a wall, but is there a point at which your wall is so strong that to extend from it would be bad?

Takagawa explained a major difference in types of walls, those that have eye potential and those that need an extension. Obviously, your wall on the left has eye potential. It is less obvious, but so does your wall on the right. It is big enough, and it can extend in two directions.

Quote:

2. The following position came up in a game of mine and I was unsure where to move next. I was very tempted to solidify my framework with a move around K7, but that leaves a lot of viable points of invasion and seems overly ambitious.

No, it would be too unambitious.

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . X . O . O O . . | $$ | . . . X . . . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . 1 , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If you want to make a good framework using your walls, :w1:

or thereabouts looks pretty good.

It also reduces Black's potential on the top. Black's play has been inefficient, too low in the bottom right corner, with a close extension on the right side. I would not choose :w1:

myself, but from this position I think that I would have good chances of winning, even without receiving komi.

Quote:

Playing on lines closer to the bottom edge, however, feels like the white stones are overconcentrated. Is my inclination that K4 or K5 are overconcentrated and slow correct? Where should I be looking on this board if I'm concerned about using my two walls well?

Like Uberdude, I like approaching the top left corner.

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . X . O . O O . . | $$ | . . . X . 2 . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . 1 . . . . . . . . . . . . . . . . | $$ | . . . . . 3 . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Here is one possibility. :w3:

is a situational move. It aims to reduce Black's potential and is supported by White's wall on the left. IMO, White has a winning advantage.

Loons · #8

I have a question. Lots of very strong players have endorsed the knights approach at C14.

My own first thought was rather a high approach instead; I guess I was worried about :b2:

or 'a' because black also has a vested interest in the centre.

Why was this not expected? x/y aji? A secondary concern might be black tenuki to start the centre reduction.

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . y . O . . . . . | $$ | . . . . . . . . . x . X . O . O O . . | $$ | . . . X . . . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . 1 a 2 . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

I may just be pointing out that a game of go is happening.

mitsun · #9

Loons wrote:

I have a question. Lots of very strong players have endorsed the knights approach at C14. My own first thought was rather a high approach instead; I guess I was worried about :b2:

or 'a' because black also has a vested interest in the centre.

That would be a great answer by B, in keeping with the whole board position. By the way, I prefer B in this game.

Bill Spight · **#10**

Loons wrote:

I have a question. Lots of very strong players have endorsed the knights approach at C14.

My own first thought was rather a high approach instead; I guess I was worried about :b2:

or 'a' because black also has a vested interest in the centre.

Why was this not expected? x/y aji? A secondary concern might be black tenuki to start the centre reduction.

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . y . O . . . . . | $$ | . . . . . . . . . x . X . O . O O . . | $$ | . . . X . . . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . 1 a 2 . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

I may just be pointing out that a game of go is happening.

Based upon his previous play, I would not expect :b2:

.

Besides, in this situation, :b2:

leaves the top side wide open to invasion. There is a seven point gap and Black is not thick.

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . 1 1 . . . . X . O . O O . . | $$ | . . . X . 1 1 . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . 1 1 . . . . . . . . . . . . . . . | $$ | . . . 1 . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

I think that any of these approaches is eminently playable.

Magicwand · **#11**

i dont know what correct move is but..
below is missing natural flow...i would never play that.

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . X . O . O O . . | $$ | . . . X . . . . . , . . . . X X X . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . 1 . . . . . . O . . | $$ | . X O . . . . . . . . . . . . . O X . | $$ | . X O . . . . . . . . . . . . O . X . | $$ | . . X O . . . . . , . . . . . , . . . | $$ | . . X O . O . . . . . . . O O . X . . | $$ | . . X X O . . . . . . . . O X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

jts · **#12**

Chime in if I've got it wrong.

(i) Some walls need extensions to get a base (i.e., potential eyespace). That's pretty much what people mean when they say to extend n+1 spaces from a wall of length n.

(ii) Walls that don't need an extension for eyespace want a really, really long extension for the sake of marking out an area in which to attack the opponent. If he comes in, you drive him into your wall; if he doesn't come in, you have huge potential.

(iii) If you don't need the n+1 extension for eyes, and you don't have enough room for an extension across the board because your opponent's stones are too close, he may have played close to your thickness. Invade, and push him towards your wall.

(iv) If you don't need the safety extension, can't make a super-long extension, and can't invade in a way that forces weak stones against your wall, tenuki.

RobertJasiek · **#13**

Bill Spight wrote:

Takagawa explained a major difference in types of walls, those that have eye potential and those that need an extension.

Right but it is only one aspect of what degrees of thickness mean. More see below.

jts wrote:

to extend n+1 spaces from a wall of length n.

As viewtopic.php?p=41038#p41038 explains, this proverb is too weak knowledge.

dwest wrote:

1. I'm wondering if someone could explain the difference between a wall with few defects (protected cuts, like the white wall on the left) and thickness.

The difference is explained precisely in the thickness chapter of Joseki Vol. 2 Strategy by means of defining thickness. On an informal level, see http://senseis.xmp.net/?Thickness On the formal level, it amounts to assessing the degrees of connection and alive, see http://senseis.xmp.net/?NConnection, and estimating the amount of territory protected by the thickness using an iterative territory model (100% for the already safe territory, 50% for the additional territory gained after 1 extra move etc.). In particular the defects aji of a wall is identified by the n of n-connected of the wall's (or the wall's and its extension's) stones. Ordinary thickness should be 0-connected; -1-connected is worse; 1-connected indicates great thickness (if also the alive degree and territory potential are reasonable).

Thickness vs. Walls

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