Example 2

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

Example 3

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

Example 4

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

Example 5

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 6

Before , we have a two-eye-formation. After , we no longer have a two-eye-formation. This may be quite counter-intuitive, but the definition of two-eye-formation is different from the typical meaning of "eye".

However, if the players continue playing, then Black will be able to force getting a two-eye-formation again.

Links to original places of definition

• Simplified Japanese Rules
• Model for the World Amateur Go Championship Rules
• Commentary on the Japanese 1989 Rules / Intermediate Step - Rules

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.
• The term two-eye-formation is relevant, e.g., for Chris Dam's theorem, which says that alive as defined by a good model of life as in the World Amateur Go Championship 1979 Rules is equivalent to alive as defined by the Japanese 2003 Rules.
• Two-eye-formation identifies a subset of chains that are pass-alive together with two empty intersections.

History

• 1990s: 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 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 article.
• 2006-04-14: Robert Jasiek used the current form of definition for a 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

• Topological Life
• Mathematical Ko Terms
• Two Eyes
• Attempts at formal definitions of eye
• Two Squares patterns