Life In 19x19

So it regularly happens that I have a nice large area of territory, and my opponent manages to break in. Take the following fictitious example :

Click Here To Show Diagram Code

[go]$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Normally I end up "squeezing toothpaste and end up losing most of my area..

Click Here To Show Diagram Code

[go]$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O 2 3 9 X .
$$ . . X . . . 1 4 6 8 X .
$$ . . X . . . . 5 7 . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

What would be a better way to play this? Or is it generally the case that if an opponent can get an attached stone into you area, it is largely lost?

In your example, the toothpaste had already been squeezed. Please show an example of an earlier situation!

mongus wrote:Or is it generally the case that if an opponent can get an attached stone into you area, it is largely lost?

If it's like your example, then yes. Trying to keep the territory there is now a small endgame move. Calculating the exact size is difficult, but it's in the ~5 points area and there are probably much more important moves elsewhere on the board until the late endgame (say around move 200). The other important thing to realise is if you do answer white may tenuki to such a more valuable place. This means white encroached into your area in sente. Avoiding your opponent making gains in sente is one of the most important ideas in Go, it's why we don't like weak groups, as the opponent can typically profit in sente by attacking them. To make this clear, let's rewind one move, and it's white to play:

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[go]$$W start position
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

If white extends and black plays your suggested 2 (which is probably the best move locally, so at least well done on that) then we end up with the below position. It's again white's move. Who gained from that exchange? White did. He reduced black's points in sente, it's still white's move and he can do something valuable elsewhere.

Click Here To Show Diagram Code

[go]$$W end position
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . 1 . . . X .
$$ . . X . . . 2 . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Even if black plays first next he can't get as good a result as if he played next in the first diagram, compare these 2:

Click Here To Show Diagram Code

[go]$$B start position, black first
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . 1 . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Click Here To Show Diagram Code

[go]$$B end position, black first
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O 1 . . X .
$$ . . X . . . X . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

mongus wrote:So it regularly happens that I have a nice large area of territory, and my opponent manages to break in. Take the following fictitious example :

$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .

Click Here To Show Diagram Code

[go]$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Normally I end up "squeezing toothpaste and end up losing most of my area..

$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O 2 3 9 X .
$$ . . X . . . 1 4 6 8 X .
$$ . . X . . . . 5 7 . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .

Click Here To Show Diagram Code

[go]$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O 2 3 9 X .
$$ . . X . . . 1 4 6 8 X .
$$ . . X . . . . 5 7 . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

What would be a better way to play this? Or is it generally the case that if an opponent can get an attached stone into you area, it is largely lost?

As Uberdude has indicated, a lot of the territory can go away when the opponent intrudes. As for how to play once that has happened, it could be worth your while to play around with this position and try to find out.

Also see viewtopic.php?f=12&t=12327&p=204861#p204861 where I have invited readers to evaluate a similar position.

Edit: Link corrected, thanks to Kirby. I hope that my analysis is better than my linking.

Cool idea to set this up as a problem, Bill.

I think the link you intended is this one:
viewtopic.php?p=204861#p204861

Sennahoj wrote:In your example, the toothpaste had already been squeezed. Please show an example of an earlier situation!

Good point. These situations normally occur because my opponent has exploited a weakness in my defences, or because I haven't been able to fully enclose the area and so technically the territory wasn't really mine at all..

Often the key to avoid these sort of incursions is to fall back a bit. For example in the below if white plays 1...

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[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X 1 X X X . .
$$ . . . X X . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

and you connect the stone in atari then white can march inwards (note the classic broken shape):

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[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X 1 X X X . .
$$ . . . X X 2 3 . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

but if you fall back and give up a stone white can't poke in so much. An analogy I've heard that might be useful is trying to stop a river, if you just plop a stone in the current it will flow round, but if you step back and build a dam you can contain it (there's probably a better way to phrase it, but hopefully you get the feeling).

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[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O . 1 X X X . .
$$ . . . X X 3 2 . . . X .
$$ . . X . . 4 . . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Note that the block of 2 does leave some cuts, which don't work in this case, but if they did you can consider falling back more:

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X 1 X X X . .
$$ . . . X X . . . . . X .
$$ . . X . . . 2 . . . X .
$$ . . X . . . . . . . X .
$$ . . X . . . . . . . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Hi, mongus.

With the corner invasion analysis going on on This 'n' That, it will probably be some time before we address your problem. So let me ask a question.

Click Here To Show Diagram Code

[go]$$B
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . . . O 2 3 9 X .
$$ . . X . . . 1 4 6 8 X .
$$ . . X . . . . 5 7 . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

I suppose you are illustrating pushing out the toothpaste, but after where does White play?

With the corner invasion analysis going on on This 'n' That, it will probably be some time before we address your problem.

No worries.

So white now has a nice atari to play which lets him take the rest of space..

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . 4 3 O O X X X .
$$ . . X . 5 1 X O O O X .
$$ . . X . 6 . 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

As far as I can see, black is doomed.

Thanks, mongus.

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O . . . X .
$$ . . X . 4 3 O O X X X .
$$ . . X . 5 1 X O O O X .
$$ . . X . 6 . 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

and are big (in this box).

A few more questions:

Does Black have a better play than ?

Does White have a better play than ?

Does Black have a better play than ?

Enjoy!

Ah, ok. It has occurred to me I haven't been thinking in terms of eye space.

Bearing this in mind, move is just a waste of a move. Where I played it was dead space anyway and would not get any player any points or eye space. Black needs to play here to get an eye followed by a or b. White can't stop this as if White plays a black plays b and vice versa.

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O a b . X .
$$ . . X . 4 3 O O X X X .
$$ . . X 6 5 1 X O O O X .
$$ . . X . . . 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Even without thinking about eyespace (in these sort of endgame problems you usually assume everything's alive unless there are obvious issues), your new is worth more points than your old choice (the intersection above it is Black territory for sure now).

And don't forget that Bill had another couple of questions

mongus wrote:Ah, ok. It has occurred to me I haven't been thinking in terms of eye space.

Well, this discussion was about hanging on to territory -- or not! As for the life of the Black group as a whole, on an empty board it is quite strong, even with no eyes inside. Besides, the White group is weaker.

Bearing this in mind, move is just a waste of a move. Where I played it was dead space anyway and would not get any player any points or eye space. Black needs to play here to get an eye followed by a or b. White can't stop this as if White plays a black plays b and vice versa.

$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O a b . X .
$$ . . X c 4 3 O O X X X .
$$ . . X 6 5 1 X O O O X .
$$ . . X . . . 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O a b . X .
$$ . . X c 4 3 O O X X X .
$$ . . X 6 5 1 X O O O X .
$$ . . X . . . 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

Yes, here is much better than the original . Well done!

In addition to making a likely eye and point of territory at "c", what else is good about ?

Bill Spight wrote:
In addition to making a likely eye and point of territory at "c", what else is good about ?

I'm not 100% sure. Is it something to do with connecting the two black groups? If 6 is not played the marked black stones could be quite vulnerable if the following was played instead.

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O Y O X X X . .
$$ . . a Y Y Y O . . . X .
$$ . . X 9 4 3 O O X X X .
$$ . . X 7 5 1 X O O O X .
$$ . . X 8 6 . 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

dfan wrote:And don't forget that Bill had another couple of questions

Yes.. I dodged those questions because I couldn't think of any better move for . I think that was the best move (locally).

If white played here instead, from what I can see the outcome would not look much different.

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O a b . X .
$$ . . X . 6 3 O O X X X .
$$ . . X . 4 1 X O O O X .
$$ . . X 8 7 5 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

For this I think is better.

Click Here To Show Diagram Code

[go]$$W
$$ . . . . O O O O O O . .
$$ . , . . O X O X X X . .
$$ . . . X X X O a b . X .
$$ . . X 6 5 3 O O X X X .
$$ . . X . 4 1 X O O O X .
$$ . . X . 8 7 2 X X . X .
$$ . . X X X X X X X X X .
$$ . , . . . . . , . . . .[/go]

It is still very painful for black.