Two-Eye-Formation

    Keywords: Theory

Definition

A two-eye-formation is a set of one or several strings of the same player and exactly two empty intersections so that each of the strings is adjacent to each of the two intersections, none of the strings is adjacent to another empty intersection, and each of the two intersections is adjacent only to the strings.

Example 1

[Diagram]

Two-eye-formation


Example 2

[Diagram]

This is not a two-eye-formation. It is independently-alive though. Also Black can force a two-eye-formation:

[Diagram]

Black forces a two-eye-formation


[Diagram]

Result: Black has got a two-eye-formation


Example 3

[Diagram]

Two-eye-formation

Here is an example of a two-eye formation with two strings of black stones.

A possibly silly question: is it possible to construct a two-eye formation involving three strings?

RobertJasiek: On a regular board, up to four strings are possible. Construction should be obvious but is left as an exercise for the dear reader :)

Herman: See [1]

unkx80: Make it example 6?


Example 4

[Diagram]

This is not a two-eye formation, because the empty intersection a, being next to a white stone, violates the condition each of the two intersections is adjacent only to the strings. Black can force a two-eye formation as in example 2.


Example 5

[Diagram]

Before B1, we have a two-eye-formation. After B1, we no longer have a two-eye-formation.


Links to original places of definition

Remarks

In most cases, the informal "a group with two eyes", which is also known as independently alive, is not a two-eye-formation. However, the alive player can force a two-eye-formation.

History

  • 1990ies: Informal language spoke of "group with two eyes" or some similar expression while mostly meaning a group with bigger eyespaces and possibly more than two eyes and only scarcely meaning exactly a group with two 1-point eyes.
  • 1994: In Mathematical Go Endgames, Berlekamp defined a related but different term in a different way for greedy ancient rules.
  • 2002-2003[?]: Robert Pauli used the term in his [ext] Logical Japanese Rules of Go but defined it in a somewhat complicated manner integrated in his rules.
  • 2003-08-24: The currently earliest found rec.games.go [ext] article.
  • 2006-04-14: Robert Jasiek used the current form of definition for a [ext] Model for the World Amateur Go Championship Rules. It is possible though that he might have formulated it some days, weeks, or months earlier in a different study.

See also

Reader exercise solution

[1]:

[Diagram]

Two-eye-formation with 4 black strings


This is a copy of the living page "Two-Eye-Formation" at Sensei's Library.
(OC) 2009 the Authors, published under the OpenContent License V1.0.
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