I've been thinking a lot lately about the flexibility of a particular stone and I'm trying to better understand the dynamic value of a given position. For instance, in this diagram from a recent game I played, the two white stones at C7 have just been killed. Now it's an obvious example but it illustrates some important concepts: Though the white stones have quite a bit of room, they lack an opportunity create any sort of base. Now, its clear that the white stones are losing the liberty race with with southern black group by one liberty so we understand why that fight won't work. What I find peculiar is the relationship of the of the white stones to the black stone at C10. This stone likewise only has four liberties but is much stronger because of two things: it has an escape and and it can easily connect to the three black stones in the northwest corner. That's not to say that these stones are invincible by any means, however, an invasion into this area by white would be a poor choice at this point in the game (says me).

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[go]$$c Black to move.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O O . . . . . . . . . . O O X . . |
$$ | . . X X O . . . . , . . . O . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ | . . O O X . . . . . . . . . . . . . . |
$$ | . . . X O O . . . . . . . . . . . . . |
$$ | . . X X X O . . . . . . . . . . O X . |
$$ | . . X O O . . . . , . . . . . O X X . |
$$ | . . X X O . . . . . . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The idea I'm driving at is also present in the following move choice. The white approach at a is quite bit more popular than at b (disregarding the whole-board position). This is because the low approach permits more options to the player playing the approach. What do you guys think and what would be some productive ways of studying the flexibility of a given position?

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[go]$$W
$$ ---------------
$$ - . . . . . . .
$$ - . . . . . . .
$$ - . . . . . a .
$$ - . . . X . b .
$$ - . . . . . . .
$$ - . . . . . . .[/go]

_________________
Thinking like a go player during a game of chess is like bringing a knife to a gun-fight. Thinking like a chess player during a game of go feels like getting knifed while you're holding a gun...

The first thing that comes to mind is that black's shape has an obvious weakness, so if black does not reinforce, white can aim for sequences like this:

Click Here To Show Diagram Code

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

I was thinking the same thing but I don't see much profit for white there.

_________________
Thinking like a go player during a game of chess is like bringing a knife to a gun-fight. Thinking like a chess player during a game of go feels like getting knifed while you're holding a gun...

Determine development directions, neutral stones (their changes; doing so is easier than determining valuable stones, so derive the latter from the former), statuses, options, aji, local potential, influence, thickness, fights. Consider and imagine invasions, reductions, exploitations of aji, uses of influence, development of fights. To do all this well, learn the related theory and apply it together with reading. Note that "flexibility" is the name of a particular strategic concept, but when you ask for the flexibility of a given position, you ask for positional judgement of the non-territory, non-static, dynamic aspects listed above.

At the moment, there are much more important places to play on the board (the shapes look incomplete in three corners, plus both the top and the bottom is very wide). But the fact that this weakness exists in black's side means at the very least that black cannot consider the left side as territory, and that the C10 stone is not actually in a good place.

Flexibility is a difficult concept to quantify, but I think there are a few questions you can ask to determine if a stone is "flexible." (My list is meant to be representative rather than exhaustive.)

• Can this stone make life in its current position?
• Can this stone make life in more than one way / direction?
• Can this stone join with another group?
• Can this stone run to the center?
• Does this stone offer useful influence elsewhere on the board (e.g. ladder breaker)?
• Can this stone be usefully sacrificed?
• Does this stone threaten a big follow up?

If you can answer yes to several of these (or other similar) questions, then I would consider the stone flexible. A flexible move is not always the best move on the board, though it certainly is a strong consideration during the opening.

The move at C10 was made much earlier in the game whereas the move at E8 was made two moves ago. This being said, was there a stronger way to protect the E7 stone while also building up the left side?

_________________
Thinking like a go player during a game of chess is like bringing a knife to a gun-fight. Thinking like a chess player during a game of go feels like getting knifed while you're holding a gun...

Click Here To Show Diagram Code

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

The two W stones are very far from dead. Others have shown sequences if W tries the marked escape immediately. But suppose W prepares by playing the 1-2 exchange first? Then W escapes cleanly, having already defended against the B cut.

Thinking about flexibility is a double-edged sword though: it's easy to confuse yourself into playing bad moves because you think you are being clever and flexible, but in reality the move is bad and the simple "inflexible" move you didn't want to play was actually urgent and correct. For example in this game black seems to have suffered from this thinking and got himself into bad shape several times:
- not playing r18 which is a key point for base for both players
- not playing e16 key shape point and thus allowing white to get the excellent hane at the head (or did black do the ugly bump after white 3-3 attach?)
- I don't know what happened in the lower right corner but it's still urgent and something went wrong there.

On the first, black extended after white attached. A move that I've been told is too heavy but it seemed appropriate here. As for the south-east corner, I played tenuki there because I felt that my shape had the "flexibility" of either developing up the side or down into the corner.

_________________
Thinking like a go player during a game of chess is like bringing a knife to a gun-fight. Thinking like a chess player during a game of go feels like getting knifed while you're holding a gun...

But white has a good result there, so just the usual hane in the corner and white pulls back would be better. After that you could take sente and tenuki, or extend into the corner and then white should extend on the top side, or else you could attack there. If c10 was already in place you could also think about directly pincering after white pulls back as c10 helps a lot in the fights that follow. Perhaps you feared white would tenuki after hane in the corner? It is certainly true that is plausible for white and black's followup is not as crushingly severe as if white tenukis after the ugly bump; but that just means with the bump you are sure white will answer and you get a bad position. If you don't like the resulting positions then probably your knight's move to the 4th line answer to the high approach was wrong. What was going on at the top right at the time? Maybe simple attach under the approach to get a big corner was better.



Yes, your shape is flexible if that's what you call the state of it won't die if white plays first, but you will make a miserable life whilst white gets a much better outside. I would actually say those stones are more heavy than flexible, the atari/extend at c6 is urgent for both. Stopping your opponent from getting profit in sente is very important. The below shows one way black can live in gote with white making a magnificent outside.

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[go]$$Wc
$$ | . . X , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ | . . O O X . . . . . . . . . . . . . . |
$$ | . . . X O O . . . . . . . . . . 1 5 . |
$$ | . . X X X O . . . . . . . . . . O X . |
$$ | . . X O O . . . . , . . . . . O X X . |
$$ | . . X X O . . . . . . . . . . O 4 . . |
$$ | . . . O . . . . . . . . . . . 3 2 6 . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Now black could avoid having to take gote to live by crawling on the 2nd line a lot, but the wall white gets is amazing for white...

Click Here To Show Diagram Code

[go]$$Wc The line of defeat (8 example tenuki)
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . 7 . . |
$$ | . . . . X . . . . . . . . . . . 5 6 . |
$$ | . . O O X . . . . . . . . . . . 3 4 . |
$$ | . . . X O O . . . . . . . . . . 1 2 . |
$$ | . . X X X O . . . . . . . . . . O X . |
$$ | . . X O O . . . . , . . . . . O X X . |
$$ | . . X X O . . . . . . . . . . O . . . |
$$ | . . 8 O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Black can tenuki again for 14 and the turn at a isn't sente for white, but the cost of that white wall is huge. Black's upper right group is also dying now (due to not getting r18 key base point).

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[go]$$Wcm9 The line of defeat contd.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O O . . . . . . . . . . O O X . . |
$$ | . . X X O . . . . , . . . O . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 5 a . |
$$ | . . X , 6 . . . . , . . . . . , 3 4 . |
$$ | . . . . . . . . . . . . . . . . O 2 . |
$$ | . . . . X . . . . . . . . . . . O X . |
$$ | . . O O X . . . . . . . . . . . O X . |
$$ | . . . X O O . . . . . . . . . . O X . |
$$ | . . X X X O . . . . . . . . . . O X . |
$$ | . . X O O . . . . , . . . . . O X X . |
$$ | . . X X O . . . . . . . . . . O . . . |
$$ | . . X O . . . . . . . . . . . . . 1 . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]