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 Post subject: On "About Capturing Races"
Post #1 Posted: Sun Jun 21, 2020 4:06 am 
Tengen

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Quotation reference: https://www.lifein19x19.com/viewtopic.p ... 64#p257664

jumapari wrote:
In his book Richard Hunter speaks about "weak eyes". [...]
Is there any theory about this?


The theory is my definition of "weak eye" in the book Capturing Races 1 - Two Basic Groups. First, it provides definitions of

- "eye" of a capturing race
- "stable" vs. "unstable eye"
- "hot eye", which depends on unstable eye

Citation from the definition:

"An eye is 'strong' if
- only one string surrounds it,
- the eye is not hot,
- the number of approach liberties is not altered due to a position of the eye at an edge or in the corner of the board and
- supposing [1..., 2...,] 3. either player tries to prevent the other's new independent life, neither player can force occurrence of a seki or ko ban.

An eye is 'weak' unless it is strong."

Needless to say, I have provided definitions of "independent life", "(can) force", "prevent" and "ko ban" on my webpages about rules theory. The only ambiguity is in the definition of "eye" of a capturing race, which depends on the still undefined "essential string" so that one has to perceive strings as essential, which is possible in almost all practical examples. When "eye" is defined for different purposes, such as rules or 'life and death', I could provide unequivocal definitions. However, for capturing races, essential strings are a useful concept.

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