Kirby wrote:
Maybe a couple of years ago, I ran across a go blog, which stated that in life and death problems, if you capture any shape consisting of 3-stones, it's enough space to make an eye. I remember being quite interested in this, because I hadn't realized it before. I thought, "Wow, I guess that's right", and couldn't think of an exception.
I'll come back to that below.
Quote:
As a result, when I do life and death problems, my mind stops reading when I see a 3-stone group that will be captured, and I assume that it implies that the opponent will get an eye there. So basically, seeing 3-stones that would be captured was equivalent to an eye in my mind.
However, this problem proves that this heuristic that I've been using is wrong! Indeed, I assumed that the three black stones on top were definitely an eye for white:
- Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . O O W b B B B . |
$$ | . . . . . . . . . X . O X . W O O O X |
$$ | . . . . . . . . . . X X . . . a O X . |
$$ | . . . , . . . . . , . . X . O O X . O |
$$ | . . . . . . . . . . . . . X X X . X X |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]
Furthermore, since I could not take away the eye at 'a', and because I couldn't create a shortage of liberties to prevent white from capturing the three black stones... I was at a loss.
(White markings and "b" added by me.)
Wow! That's three heuristics violated by this problem.
1) Capturing a three stone string produces an eye.
2) White has an eye at "a".
3) The
stones are connected.
Oops! Sorry. The first heuristic is not violated. If White captures the marked three stone string White indeed has an eye there. What is violated is this heuristic:
Capturing a four stone string produces an eye.
If White captures
only the three marked stones he has an eye there. So that heuristic is not violated.
BTW, I never learned that capture three heuristic. I figured out something better for myself, which says that in this position
if White plays at "b" he can capture the three
stones for an eye.
I never learned the heuristic about White having an eye at "a", because it is simply false.
And everybody knows that the diagonal connection can sometimes be cut.
Now to return to the theme of thinking of an exception to the capture three heuristic. It is no secret that I do not belong to the reading über alles persuasion.
I think that both knowledge and heuristics are important. (And, OC, knowledge trumps heuristics.
) Now, thinking of an exception to a heuristic is not a reading problem per se; it is more difficult, as you have to imagine a position and then read it out. There is no shame in not thinking of an exception. IMO, when you are learning, thinking is not enough. Do what children do and play with stones on the board.
Let's play around a bit.
Remember that bit of go knowledge that eight stones in a row on the second line are alive?
- Click Here To Show Diagram Code
[go]$$B Eight lives
$$ ------------------------------
$$ . . . . 1 2 C C C C 4 3 . . . .
$$ . X . X O O O O O O O O X . X .
$$ . . . X X X X X X X X X X . . .
$$ . . . . . . . . . . . . . . . .[/go]
Even when Black plays first, White has a four point linear eye, which is enough to live.
- Click Here To Show Diagram Code
[go]$$B Eight lives, variation
$$ ------------------------------
$$ . . . . 1 3 4 C C C C 2 . . . .
$$ . X . X O O O O O O O O X . X .
$$ . . . X X X X X X X X X X . . .
$$ . . . . . . . . . . . . . . . .[/go]
- Click Here To Show Diagram Code
[go]$$B Eight lives with hanes
$$ ------------------------------
$$ . . . O 1 3 . . . . . 2 O . . .
$$ . X . X O O O O O O O O X . X .
$$ . . . X X X X X X X X X X . . .
$$ . . . . . . . . . . . . . . . .[/go]
Hmmm. With the hanes White does not have to answer
. I have learned something today by playing around.
- Click Here To Show Diagram Code
[go]$$B Eight lives with hanes, continued
$$ ------------------------------
$$ . . . O B X 2 . 4 1 . O O . . .
$$ . X . X O O O O O O O O X . X .
$$ . . . X X X X X X X X X X . . .
$$ . . . . . . . . . . . . . . . .[/go]
throws in at
does not work, since capturing the two stones gives White a half eye. With one and a half eyes in the four point eye, White is alive.
If
at 4,
at
, OC.
Does that mean that seven lives with hanes? Let's play around and see.
- Click Here To Show Diagram Code
[go]$$B Does seven live with hanes?
$$ ------------------------------
$$ . . . O 1 a . . 3 . 2 O . . .
$$ . X . X O O O O O O O X . X .
$$ . . . X X X X X X X X X . . .
$$ . . . . . . . . . . . . . . .[/go]
Nope.
kills.
at "a" would be a mistake, OC.
Isn't go fun?
Back to eight lives.
- Click Here To Show Diagram Code
[go]$$W Capture eight and live
$$ ------------------------------
$$ . . . 1 X X X X X X X X O . . .
$$ . X . X O O O O O O O O X . X .
$$ . . . X X X X . X X X X X . . .
$$ . . . . . . . . . . . . . . . .[/go]
Playing around a bit, we find that capturing eight stones lives. And it lives by making a four point eye. (We have just seen that capturing seven does not live.)
Well, 8 - 4 = 4. Does that mean that capturing five stones makes a one point eye? 'Deed it does.
- Click Here To Show Diagram Code
[go]$$W Capture 5 for an eye
$$ ------------------------
$$ . . . 1 X X X X X O . . .
$$ . X . X O O O O O X . X .
$$ . . . X O . O X X X . . .
$$ . . . X X O O X . . . . .
$$ . . . . . X X X . . . . .
$$ . . . . . . . . . . . . .[/go]
- Click Here To Show Diagram Code
[go]$$W Capture 5 for an eye, continued
$$ ------------------------
$$ . . . O 2 3 . 5 4 O . . .
$$ . X . X O O O O O X . X .
$$ . . . X O . O X X X . . .
$$ . . . X X O O X . . . . .
$$ . . . . . X X X . . . . .
$$ . . . . . . . . . . . . .[/go]
- Click Here To Show Diagram Code
[go]$$W Capture 5 for an eye, variation
$$ ------------------------
$$ . . . O 2 4 . . 3 O . . .
$$ . X . X O O O O O X . X .
$$ . . . X O . O X X X . . .
$$ . . . X X O O X . . . . .
$$ . . . . . X X X . . . . .
$$ . . . . . . . . . . . . .[/go]
White can ignore
.
Well, if you have to capture five in a row to make an eye, where did the capture three heuristic come from?
- Click Here To Show Diagram Code
[go]$$W Capture 3 for an eye
$$ ------------------------
$$ . . . 1 X X X O . . . .
$$ . X . X O O O W X . X .
$$ . . . X O . O X X . . .
$$ . . . X X O O X . . . .
$$ . . . . . X X X . . . .
$$ . . . . . . . . . . . .[/go]
The heuristic came from ignoring the go knowledge that the corner of the eye has to be occupied or controlled, as indicated by the
stone. Away from the edge there are other corners to consider, as the SL page (
http://senseis.xmp.net/?CaptureThreeToMakeAnEye ) discusses.
BTW, I am annoyed at the SL page, which talks about the heuristic as a proverb and mentions exceptions to it. The correct go knowledge is no more esoteric than the knowledge that eight in a row on the second line lives. Knowledge trumps heuristics.