A strategic concept? "Base limit"?

Tami · #1

Before we start, I am using circled W and circled B to represent moves past 9 in variations.

Click Here To Show Diagram Code: [go]$$c Setting the scene $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . b . . . . . . O . . | $$ | . . . X . . . . . B W 8 6 4 2 , . . . | $$ | . . . . . . . . . . 9 7 5 a 3 1 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Black has played at 9, presumably because he does not like the forcing moves beginning with a that are usual in this joseki.

I wonder if White's last move (circled W) should have been at b, to stay ahead in the race.

However, my big question about this position is how far should White extend from her wall, if she wished to do so. In exploring this, I wonder if I have stumbled upon a strategic principle.

First, if White goes as far as possible from the wall:

Click Here To Show Diagram Code: [go]$$c Maximum extension $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 2 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . O . . . . . . O . . | $$ | . . . X . . . . 1 . . O O O O , . . . | $$ | . . . . . . . . . . X X X a X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Then Black can invade and pincer like this:

Click Here To Show Diagram Code: [go]$$c Maximum extension $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . 3 . X . 9 . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . 8 . 2 6 O W . | $$ | . . . . . . . . . . . . . . . 5 7 . . | $$ | . . . . . . . . . . . . . B . . . . . | $$ | . . . . . . . . . . . . . . . 1 . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . 4 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . O . . . . . . O . . | $$ | . . . X . . . . X . . O O O O , . . . | $$ | . . . . . . . . . . X X X a X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

And it is not clear to me that White is doing better - I have had positions like this where Black makes sabaki with his invading group and counter-attacks. In the meantime, Black has taken quite a few points on the bottom, so White would really like to make the wall accomplish something.

But, if White extends a little closer to the wall, Black can still invade and leave her without a clear plan:

Click Here To Show Diagram Code: [go]$$c More conservative $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 2 . . . | $$ | . . . . . . . . . . . . . 6 . . 4 . . | $$ | . . . , . . . . . , . . . . . 5 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 7 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . O . . . . . . O . . | $$ | . . . X . . . . 1 . . O O O O , . . . | $$ | . . . . . . . . . . X X X a X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If White, cuts off the path away from the wall, say by attaching at 4 or using an iron pillar, Black can still make a base, and will probably live, leaving White with a territorial problem.

If White extends too close, the she will be unhappy too:

Click Here To Show Diagram Code: [go]$$c Black erases the thickness from afar $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . 2 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . O . . . . . . O . . | $$ | . . . X . . . . 1 . . O O O O , . . . | $$ | . . . . . . . . . . X X X a X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

So the only remaining option is to play like this:

Click Here To Show Diagram Code: [go]$$c The "Base Limit" (?) $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 2 . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . O . . . . . . O . . | $$ | . . . X . . . . 1 . . O O O O , . . . | $$ | . . . . . . . . . . X X X a X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

And here is the thing I happened upon: this seems to be a kind of limit, because Black does not have space behind him to make a base if he invades:

Click Here To Show Diagram Code: [go]$$c Black erases the thickness from afar $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 2 4 . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . a . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . O . . . . . . O . . | $$ | . . . X . . . . 1 . . O O O O , . . . | $$ | . . . . . . . . . . X X X a X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The point a is not enough - White can attack severely.

So, my idea is that this move, 2, is a kind of "base limit". If White goes past it, then Black can invade and make a base if White cuts off the escape away from the wall. If White plays up to it, then Black cannot get a base after White cuts off the escape route with a move such as 4.

Possibly my examples have been clumsily chosen and provided with dodgy tactics, but apart from receiving corrections to those faults, I would very much like to know if there is such a concept as a "base limit" for these situations - namely, the point the where running away and making a base are no longer miai.

NOTES

I think this is separate from the idea of playing where you have space on either side for a base (as in a wariuchi, for instance).

Also, I know that White could extend on the third line, but then a shoulder hit would look far too inviting for Black.

Also, after publishing the first time, it occurred to me that White could play a high one-space approach...but, for now, it's the extension that I am most concerned with.

coderboy · #2

I was always told NOT to make a wall like that unless I have a good extension already in place..? Black gets a lot of territory so your wall had better be useful.

Just my 0.02..

gogameguru · #3

Nice discovery Tami

Yes, five spaces is one of those rules of thumb for the maximum 'extension' (even between just two stones). It's something I didn't learn about for quite a long time either and I think it doesn't get enough explicit coverage in Western Go resources.

You're right again that the reason is that it stops an invader making a two space extension. Under certain circumstances (usually when you have even greater thickness than in your example) you can extend six spaces or maybe even more, but it relies on you being able to get a good result even if your partner invades (e.g. a counterattack).

In fact, that's the case with all extensions - you need a plan to deal with an invasion. Usually that means the extension is still close enough that you can get in front of the invading stones and seal them in (probably with a knight's move or diagonal move, sometimes a long knight's move) by connecting to your wall around the outside. Even if the invader lives on the inside you have thickness and your wall is connected.

This is where the N+1 rule of thumb for walls comes from (I think this one is more well known?). i.e. 2 stone wall = 3 space extension, 3 stone wall = 4 space extension... and so on. It's the maximum length that (usually) still allows you to enclose and connect.

If your 'wall' isn't strong enough to enclose and connect (if they can break through and attack one side or the other), you usually need to play a capping play instead to take the high ground while also developing the pseudo wall group into the center.

Those cases are both for an eyeless wall - a 'wall' that has good eye potential lets you do basically whatever you want, because you don't have to worry that it will be attacked later.

But all of these heuristics break down under certain conditions, so the best approach is to use them to assist your intuition and then ask yourself 'what if they invade?' and 'what if they force from the outside?' and do a little bit of reading to see how you'll deal with it.

As an aside - in your second diagram above, if white's plan is to approach the top right corner with 2, it would be better to probe there first before starting that flow with the press in the lower left. That's because white would then have a more flexible position if black still pincers.

EDIT: @coderboy, it depends a bit on whether you can make the wall in sente. Walls are often made in gote and in those cases it's usually a good idea to have the 'extension' in place already.

Bill Spight · #4

I was taught, soon after I learned to play, that 5 points was the limit for an extension, because a longer extension left room for the opponent to invade and threaten a two space extension.

I remember that we had quite a discussion on Sensei's Library some years ago about how far to extend, but I couldn't find it quickly now. This is all that I found in a brief search. http://senseis.xmp.net/?SixSpaceExtensionTest

Bill Spight · #5

coderboy wrote:

I was always told NOT to make a wall like that unless I have a good extension already in place..? Black gets a lot of territory so your wall had better be useful.

Just my 0.02..

That is only true in certain situations. As I have mentioned before, one thing that surprised me about playing over ancient games was how, in a time when top players were more territorial than they are now, they were often content to make walls that did not seem to do much.

You do have to be concerned about making a wall work, but that is not an easy question.

Bill Spight · #6

BTW, Black's low nobi (that kind of extension) still leaves weaknesses. White need have no fear of pushing once more.

Click Here To Show Diagram Code: [go]$$B $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . a . . . . . . O . . | $$ | . . . X . . . . . 3 2 O O O O , . . . | $$ | . . . . . . . . . 8 1 X X 4 X X . . . | $$ | . . . . . . . . . . . . 6 5 7 . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Not that White should play :w4:

instead of "a" (or even play :w2:

now), but this variation illustrates Black's weakness.

Bill Spight · #7

Here is an illustrative game from 1960.

Click Here To Show Diagram Code: [go]$$Bm11 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . 0 . . . . . . . . | $$ | . . . X . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , 9 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 8 . . . . . . . . . 6 . . . . . | $$ | . . . . . . . . . . . . 1 O . . . . . | $$ | . . . O . . . . . , . . X 4 X , O . . | $$ | . . . . . 7 . . . . . . 5 X O O . . . | $$ | . . . . . . . . . . . . 3 2 . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The Black wall does not need an extension, because it has eye potential. It threatens to capture :w12:

. So

is better thought of as an approach, rather than as a 6 space extension. Note that after :w18:

neither player is anxious to play on the bottom side.

The full game follows.

Note how the bottom side evolves.

Tami · #8

Bill Spight wrote:

As I have mentioned before, one thing that surprised me about playing over ancient games was how, in a time when top players were more territorial than they are now, they were often content to make walls that did not seem to do much.

This reminds me of another idea that I had, a long time ago, about how thickness can generate points over the course of a game, even if you do not make straightforward efforts to do so (e.g., by making extensions or attacks). I called it the Deadweight Value of Thickness, meaning that thickness has a value simply for being there.

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

The example in this thread was made up by me, but I had a similar game recently, and I attacked very clumsily and was outread in all the local fighting - yet still gained an easily winning position. It was as though the thickness was determined to yield a harvest, even though I had rusty tools and lazy labourers!

Anyway, I'm not surprised that there was already a well known principle concerning maximum extensions, but I feel rather pleased to have worked it out for myself

A strategic concept? "Base limit"?

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