Seki unambiguous definition discussion
Presume the Japanese 2003 Rules / version 35a. Then use the following citation:
Subject: Group, Seki, Eyespace: Definitions
Date: Tue, 18 Nov 2003 18:37:42 +0100
From: Robert Jasiek
"Definition: A black-group is the union of all black-strings of a black-region.
Definition: A white-group is the union of all white-strings of a white-region.
Definition: A group is either a black-group or a white-group.
Note: For other purposes one might want to define group differently.
Definition: An in-seki-space is a dame and, recursively, any adjacent dame or any adjacent intersection of an in-seki region.
Definition: A seki is the union of all strings of an in-seki-space."
Note: One can argue that there are Matti Siivola's other non-independently-alive groups without a dame that are seki-like. The definition above does not include them.
All simple sekis are some subset of all sekis.
- A mutual liberty is an empty point that reaches two chains of different color.
- Two chains of different color live in simple seki if they reach no empty points but the same two mutual liberties.
- A group of stones is alive in simple seki, if for any sequence of moves by the opponent, there is a sequence of answers that turns the group into a chain which is part of a pair of chains, complying with definition 2.
(TapaniRaiko: The proposal is not enough, as these two examples show. I have seen an example where a 35x35 board was filled with small groups all living in a single seki.)
How about something along the lines of:
"A local position with at least one mutual liberty or single point ko which cannot be filled by either side without incurring a loss." We still have to read out the consequences of moves, but I think this captures what we mean by Seki and applies to all the examples there.
jvt: This is still ambiguous: how to define which chains belong to the 'local position'? Some chains may be in seki even if they are not adjacent to any dame.
RobertJasiek: Needless to say, the Japanese 2003 Rules will provide an unequivocal definition of "seki" under those rules. For other rules, minor modifications would be necessary then.
KjeldPetersen: If a group (with max 1 eye) is moving out (not filling the eye) and thereby get into a position of atari, then this group is posible part of a seki? Look at the example at the top. All three groups will go into atari if they move out.
Chris: The definitions given here are a bit naive. For all of them it is not very difficult to come up with couter-examples. I don't think an attempt to define seki by the possible shapes that are seki will succeed. A position is a seki because of the possible sequences in the position, not because it has a particular shape. Hence, it is probably impossible to define seki without referring to a search. For computer-go it is important to know what is seki. I wrote a seki-recognizer that I hope is not too inaccurare. Here is more info.
Michael?: A definition based on game theory. A seki is any position which locally has a value of *. http://en.wikipedia.org/wiki/Star_%28game_theory%29
Superdave: No, star means unsettled--whoever moves first wins the local position. 0 is the CGT value that means whoever goes first loses, which would be a better analogy for a seki, except that CGT models games where you are not allowed to pass.
Michael?: Ah, you're right, it's been a while since I read winning ways.