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Notcher

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Referenced by
TableOfNotchers
KanazawaSolution57
KanazawaSolution58
GoTerms
ThreeSpaceNotchers
HitachiNumber314I...
TwoSpaceNotchers
OneSpaceNotchers
CriticalNotchers
MetaDiscussion2001

 

Notchers
Path: LifeAndDeath   · Prev: FourDieButSixLive   · Next: CombFormation
    Keywords: Life & Death, Shape, Go term

"Notcher" is terminology borrowed from James Davies' excellent book on life and death, which is called, well, "Life and Death".

There are now separate pages on one-space notchers, two-space notchers and three-space notchers. One day, my son, this will all be ... WikiMasterEdited

--Dieter

One space notchers

The following is a one space notcher that is six spaces long (meaning: from end to end the black group is six points wide).

[Diagram]
One-space notcher

The rule for one space notchers is: "Four die, Seven live". You may also remember this as: "Five and Six are unsettled".


[Diagram]
Four die

Here's the proof that "Four die". Even if Black plays first, White always has an answer to keep his group dead. Black 1 is answered by White 2 and vice versa.


[Diagram]
Seven live

Here's proof that "Seven live". Even if White plays first, Black always has an answer to keep his group alive. The diagram shows one white attack that fails. You can verify for yourself that it doesn't matter where the notch is located. You can also verify that five- and six-space notchers are unsettled, i.e. that the black group is alive if Black plays first and dead if White plays first. If you don't know how to verify unsettled cases, look below in the discussion of two space notchers.



Two-space notchers

[Diagram]
Two-space notcher

The rule for two space notchers is, depending on how you want to formulate it, either "Five die, Seven live" or "Six is unsettled". This time we'll leave proof of the two extremes to you and demonstrate the unsettled case.


[Diagram]
Black goes first and lives

If Black goes first, he can live. White is again rather stubborn to keep trying with 2 and 4, but after 5 Black has completely constructed the two eyes he needs to live.


[Diagram]
White goes first and kills

White can start her attack with a hane at 1.

(Reducing your opponent's eye space like this should always be the very first option you consider when examining the status of one of his groups, by the way. See also the article on approaching a life and death problem the right way.).

Even if Black were to resist, White can keep his group dead.

unkx80: See also Two Space Notchers Not Fully Connected. I am expanding this topic in response of Stefan's note below.



Three-space notchers

[Diagram]
Three-space notcher

The rule for a three space notcher is either "Four die, Six live" or "Five is unsettled". Verify for yourself that Black can live and White can kill by playing at a in the diagram. For this reason a is called the vital point of this formation.



--Stefan

Note: expand later with some examples of connecting points missing in the group under investigation.


A systematic approach to notchers

Suppose the notcher is black and the surrounding group white.

[Diagram]
Notchers

Marked points: possible weaknesses
Circled stones: legs
Squared stones: notch



  1. The notcher has a notch of n spaces
  2. The notcher has a degree of weakness, depending on the color of the top corners of the notch. The letter W means that the stone is white (weak), N means that it's absent (neutral) while S means that it is black (strong).
  3. The notcher has a left leg of length k and a right leg of length l. The legs are the stones on the second line not belonging to the notch (not adjacent to the empty points that constitute the notch).

We put this information into a code nklxx where n, k, l take numerical values and the x-es can be either W, N or S.

Status abbreviations

Let's define the following abbreviations:

L: alive even if attacker plays first
D: dead even if defender plays first
LD: defender can make life - attacker can kill
LK: defender can make life - attacker can make a ko
KD: defender can make ko - attacker can kill

These do not cover all possible statuses such as approach kos, and do not provide details such as seki either.

Tables

See OneSpaceNotchers, TwoSpaceNotchers and ThreeSpaceNotchers

Critical notchers are notchers that represent a critical point in the notcher space. An example is the weak flying saucer shape 222WW, which is dead. Anything weaker is obviously also dead. Anything stronger, however, is either unsettled or alive.

Here is the Table of Notchers.



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This is a copy of the living page "Notchers" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.