four-headed dragon

Reinhold Burger

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Mar 9, 2012, 10:05:12 PM3/9/12

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This is surely nothing new, but I have not seen it before.

A rule of thumb sometimes proposed to determine if a one-point eye
is false, is to check the corner points around the eye. If at least
three of the four corner points are controlled by the player "owning"
the eye, then the eye is real. Two corners or less, however, imply
that the eye is false.

(This is for an eye in the middle of the board. The rule must be
modified for one-point eyes along the side or in the corner.)

This usually gives the correct result, though exceptions are known,
such as a two-headed dragon. Here, only two corner points of each
eye are controlled by the player, yet the group is unconditionally
alive:

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

I wondered how far such a counter-example could be taken. It looks
like all four corner points of each eye can be controlled by the
opponent, yet the group can still be unconditionally alive.

To try to make it clearer, first we give the shape with just the
black stones (x) on the board:

19 . . . . . . . . . . . . . . . . . . .
18 . . . . . . . . . . . . . . . . . . .
17 . . . . . . . . . . . . . . . . . . .
16 . . . . . . x x x x x x x . . . . .
15 . . . . . . x . . . . . x . . . . . .
14 . . . . . . x . . . . . x . . . . . .
13 . . . . . . x . . . . . x . . . . . .
12 . . . . x x . x x x x x . x x . . . .
11 . . . . x . x . . . . . x . x . . . .
10 . . . . x . x . . . . . x . x . . . .
9 . . . . x . x . . . . . x . x . . . .
8 . . . . x . x x x x x x x . x . . . .
7 . . . . x . . . . . . . . . x . . . .
6 . . . . x x x . . . . . x x x . . . .
5 . . . . . . x . . . . . x . . . . . .
4 . . . . . . x x x x x x x . . . . . .
3 . . . . . . . . . . . . . . . . . . .
2 . . . . . . . . . . . . . . . . . . .
1 . . . . . . . . . . . . . . . . . . .
A B C D E F G H J K L M N O P Q R S T

There are four chains of black stones. The two eyes will be at
G12 and N12.

Enough space has been left between the chains for living white
groups. Adding these white stones (o), along with a surrounding
ring of living white stones gives the final position:

19 . . . . . . . . . . . . . . . . . . .
18 . . . . . . . . . . . . . . . . . . .
17 . . . . . o o o o o o o o o . . . . .
16 . . . . . o x x x x x x x o . . . .
15 . . . . . o x o o o o o x o . . . . .
14 . . . . . o x o . o . o x o . . . . .
13 . . . o o o x o o o o o x o o o . . .
12 . . . o x x . x x x x x . x x o . . .
11 . . . o x o x o o o o o x o x o . . .
10 . . . o x o x o . o . o x o x o . . .
9 . . . o x o x o o o o o x o x o . . .
8 . . . o x o x x x x x x x o x o . . .
7 . . . o x o o o o o o o o o x o . . .
6 . . . o x x x o . o . o x x x o . . .
5 . . . o o o x o o o o o x o o o . . .
4 . . . . . o x x x x x x x o . . . . .
3 . . . . . o o o o o o o o o . . . . .
2 . . . . . . . . . . . . . . . . . . .
1 . . . . . . . . . . . . . . . . . . .
A B C D E F G H J K L M N O P Q R S T

All black and white stones on the board are unconditionally alive.
In particular, black has two two eyes at G12 and N12. But at each
of these eyes, all four corner points are occupied by the opponent,
white.

So the rule of thumb can be quite far off the mark at times.

I am not sure whether this should be called a four-headed dragon,
or two two-headed dragons, or something else. In any case, it
appears unlikely that it would ever appear in a serious game between
strong players. Though of course, I would be happy to be proven
wrong, especially if someone knows of a professional game record
where such a thing occurred.

Reinhold

Robert Jasiek

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Mar 10, 2012, 2:01:22 AM3/10/12

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

Example 4.

Reinhold Burger

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Mar 10, 2012, 2:21:39 PM3/10/12

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On Sat, 10 Mar 2012, Robert Jasiek wrote:

> http://senseis.xmp.net/?TwoEyeFormation
>
> Example 4.

Ah, I have been anticipated. Though in a game this old, that is
not so surprising.

I must admit, the example on senesis is more artistic than mine.

Thanks for the reference.

Reinhold

Bill Taylor

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Mar 21, 2012, 12:22:37 AM3/21/12

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On Mar 10, 8:01 pm, Robert Jasiek <jas...@snafu.de> wrote:
> http://senseis.xmp.net/?TwoEyeFormation
>
> Example 4.

Yes, nice one! Very elegant, as Reinhold said.

This kind of example shows the danger and futility
of any mention of eyes, false eyes, or even life and death,
in any official rules. They should speak only of placement,
capture, ko, game end and scoring.

It amazes me that the Japanese Go culture still cannot see this!

-- Blustering Bill

Robert Jasiek

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Mar 21, 2012, 6:52:02 AM3/21/12

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Hello Bill, it is nice to see you must have survived both major
earthquakes during the recent years!:)

>It amazes me that the Japanese Go culture still cannot see this!

They see and understand but they value their, what they consider to
be, culture higher than reasoning. What astonishes me more though is
the modern Korean culture, which esteems the culture introduced during
the former Japanese invasion (about when Japanese rules replaced
Korean rules) and later changed for the worse within Korea higher than
reasoning. They accept some input though: Now the Korean insei league
uses Swiss with the very good pairing program MacMahon by Gerlach.
Compared to previously typical adjacency pairing, that is a huge
improvement.