Hi cherryhill,
I actually understand your uneasiness about not capturing the stone firmly. I think it stems from several factors, among those:
1. You play games against (much) stronger players who punish you for leaving the door open like that, and
2. You still lack the experience to know what you can do when White starts funky business with the single stone, and
3. Because of the above, you tend to exaggerate the weakness of your groups while often overlooking the weakness of opponent's groups.
Having said the above, there is some potential left in the White cutting stone, and there are situations in which capturing it firmly is preferable. So, the issue is that of recognizing when the White stone is dangerous and needs to get captured, and when it can be left alone for now.
To be able to make this decision you have to imagine your opponent will move the stone out, and then compare the potential weaknesses of all stones. Who will be in more trouble? I know, I know - you always think it will be *you* in trouble, but you have to get past this idea to get stronger, even if it will lose you games initially. Maybe try to think of the position as one you are observing rather than one you are playing...
The bottom line, and what other people are saying here, is that in a vast majority of the cases the White cutting stone, if activated, will be much weaker than either of the surrounding Black groups, so most likely it will be in much bigger trouble. For this reason, it might be actually to your advantage to have it move, so instead of one half-dead stone, you will have a more substantial target for your attack. Even if you never kill this stone in the end, attacking a running group like that might have game-changing advantages for you if played right.
So, we have two important concepts in the above:
Concept #1. Comparative strength of stones - if you have several weak groups fighting, the important thing is often not that they are all weak, but which ones are the weakest.
Concept #2. Look at opponent stones also as targets for attack, not only as nasty little things that try to do you harm.
To glue it together, and make the decision possible, there is also a third concept necessary here:
Concept #3. Look at the overall whole-board position. In particular - if there are any stones already on the board which can substantially affect the evaluation of who is weak and who is strong. For example: are there already White stones nearby which will make White cutting stone stronger or your weak groups weaker, and stuff like that.
To reiterate Concept #3: As one of my teachers told me when I was a beginner, you can never become strong if your nose is too close to the board.
PS>
A few final comments.
- Thinking of the Concept #1, a situation like that can be looked at in two ways, generally. When faced with a potential of a cut or activation of cutting stone like that, you can either capture the stone which removes the problem, or make your surrounding stones stronger. The latter makes it less lucrative for the opponent to cut and in addition, it usually gives you more strength globally rather than just locally capturing a stone. I think this exactly is what the move you asked about does. It tells the opponent: see how strong I am around here, you ould just be asking for trouble to try anything funny.
- I have often seen weak(er) players worrying too much about things like cutting and connecting. It seems like a funny thing to say, but I think it is actually a stepping stone to understand a few things here. Cuts should only be executed when they make sense - when they actually cause or can cause trouble. So, cutting two strong or even already alive groups is often a waste of a move. Also a waste of move is to try to connect two living groups. Why bother? A cutting or connecting move should aim at changing the situation in your favor, not at giving the opponent another free move elsewhere.
- Same goes for capturing or saving stones. Are the stones to capture/save important enough to invest a move in order to capture/save them?
- And finally, lets compare the two possible ways of playing visually:
$$B1
$$ . . . . . . . . . . . |
$$ . . 3 . . . . . . . . |
$$ . 2 . X 1 . . . . . . |
$$ . . O X O . . X . . . |
$$ . X X O O . . . . . . |
$$ . X O . . O . X . . . |
$$ . X O . . O X . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$B1
$$ . . . . . . . . . . . |
$$ . . 3 . . . . . . . . |
$$ . 2 . X 1 . . . . . . |
$$ . . O X O . . X . . . |
$$ . X X O O . . . . . . |
$$ . X O . . O . X . . . |
$$ . X O . . O X . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ -----------------------[/go]
$$B1
$$ . . . . . . . . . . . |
$$ . . . . 4 . . . . . . |
$$ . 1 3 X 2 . . . . . . |
$$ . . O X O . . X . . . |
$$ . X X O O . . . . . . |
$$ . X O . . O . X . . . |
$$ . X O . . O X . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$B1
$$ . . . . . . . . . . . |
$$ . . . . 4 . . . . . . |
$$ . 1 3 X 2 . . . . . . |
$$ . . O X O . . X . . . |
$$ . X X O O . . . . . . |
$$ . X O . . O . X . . . |
$$ . X O . . O X . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ -----------------------[/go]
By far the majority of strong(er) player would prefer the second position as white to the first, unless there is some substantial White support nearby on the board. If you imagine yourself as White in this situation - which looks better for you? If it is the first position, rest assured that you are not correct.
) to the effect that "If there's no blood, you're not cut". Similarly a couple of years ago Rob van Zeijst explained to me a taxonomy of cuts that he was working on for one of his books. He went progressively from the best cuts (dividing your opponent into two weak groups) to the worst cuts (dividing your opponent into two strong groups = no cut at all). In the original example as long as Black can ensure strong stones on either side, there is no cutting stone, only a target.