Smallest Group with Two Eyes

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Table of contents Table of diagrams
First corner group
Second corner group
Third corner group
Fourth corner group
First side group
Second side group
Third side group
Fourth side group
First center group
Second center group
Third center group
Fourth center group
Smallest groups with [two eyes]

Introduction

This is a list of the smallest groups with two eyes. They do not need a single further stone to defend them, no matter how many stones may be played to attack them.

Note by aLegendWai: Some have arguments relating to the smallest groups with two eyes.
- These special (though maybe arguable, you decide!) smallest groups are somewhat alive by means of special conditions like seki (mutual life) {some of them occur in rare situations (or theoretically)}.
- The 12 smallest groups (See [1] for all 12 groups) in the following are alive as normal.

See also: Basic Living Eye Shapes, Unconditional Life.


Smallest groups in the corner

In the corner, six stones are the minimum needed to complete a group with two eyes.

[Diagram]

First corner group

[Diagram]

Second corner group

[Diagram]

Third corner group

[Diagram]

Fourth corner group

  • This is similar to the second corner group. The eyes are the same, the stones are slightly different.

Smallest groups on the side

On the side, the smallest groups with two eyes have eight stones.

[Diagram]

First side group

[Diagram]

Second side group

[Diagram]

Third side group

  • This looks like the second side group. Different stones, but the same eyes.
[Diagram]

Fourth side group

  • Again the same as the second group

Smallest groups in the center

In the center, 10 stones are required to make a group with two eyes.

[Diagram]

First center group

[Diagram]

Second center group

[Diagram]

Third center group

[Diagram]

Fourth center group

  • These all have the same internal eye space: 10 stones, but only one eye shape.

[1]

All Smallest Groups in One Sight

Here's a board containing all of the above groups:

aLegendWai: Excellent!! The best summary by a go-board I have ever seen!!

[Diagram]

Smallest groups with two eyes


On a side note, this diagram also illustrates a drawback of living small: very few points are gained, but relatively many stones are used up.

Here, the comparison isn't quite fair because, in this artificial setup, the move count is not balanced: 119 white vs. 96 black stones. Nevertheless, White's wider formation (241 zi) is far more efficient than Black's cramped groups (120 zi). White owns two thirds of the whole board, whilst Black's area is barely half that size.


The no. of stones of smallest groups should be...

aLegendWai (Contest Sponsor & Organizer): Good news! There are a lot of submissions relating to the contest of "Unbelievable! The super-smallest group that lives!)". The final result is released, arranging from the lowest to highest ranking. Although this contest is of little (not to say no) help with your Go skills, it is surely interesting to read. :P Enjoy!!

For the final result, please read The no. of stones of smallest groups should be....


Related Links


Some Authors in this page

  • FCS
  • Arno Hollosi
  • WME by Dieter on 26/12/2002
  • List and big diagram by saccade
  • Previous fixes on numbering in captions etc. JG
  • Headings-adding/-modifying, Re-numbering, Page regrouped/reorganized/resorting etc. by aLegendWai
  • Messy discussions reorganized by aLegendWai

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