At Maximum Number Of Live Groups, the question arose if there can be a position that is globally stable although locally being instable.
rubilia-- What about a board filled with this pattern?
If one player moves, is there any safe way to the opponent to win the game? Or, on the contrary, is there any safe way the first moving player wins the game? Perhaps it is something you could call a "global seki"? - Although I´ve been trying to analyse it for quite a while, I still don't know anything about it. So, if you're sure that it's not stable at all, just remove it. :)
(Sebastian:) Well, that's what it's a game for - let's play it:
- Odd Dots Go Ongoing Game (first try, unbalanced)
- Dots Go Ongoing Game (improved, balanced version)
- Dots Go Ongoing Game2 (Let's have another one)
blubb: There are positions which, all in all, are stable, but nevertheless "locally instable": see e. g. Double ko seki or Quadruple ko seki. However, the degree of local instability (however exactly one could define that) seems to be much lower there.
PurpleHaze: This is a silly position. A seki is by definition stable. All these cut/connections are very urgent. Many stones will die rapidly. I suspect that black wins by about 40 points regardless of whose move it is. (Note: In the original suggestion, there were 100 black and 81 white stones, with all stones at borders being black.) --blubb)
Tas: Well that turned out not to be true, after fifty moves have we yet a kill in the ongoing game?
rubilia-- Maybe I shouldn't use the word "seki" to refer to what I'm thinking about: a whole board position the score of which is better for both players than what each of them could expect to gain from additional moves. This kind of position can be locally stable (like usual sekis), but it does not have to. In both cases there's a negative global temperature, that's why I used the expression "global seki". Don't stick to that single word, please.
Concerning this particular position: how to get the 40 points estimation? I am curious about details. :) --2003-11-17
PurpleHaze: You still don't get it. In this position playing is better than passing and will be for a long time. There is no sense in which this position could be called stable, either locally or globally.
There are 100 black stones versus 81 white stones. If we make the assumption that black can kill white stones at the same rate that white can kill black stones, which seems reasonable to do, then the extra stones will provide an advantage. I guesstimate this as being in the same ratio as the number of stones, though the rule set used makes a big difference.
rubilia-- As mentioned above, I am not sure a bit about this position. So, if you are, I'd like you to share a little more of your knowledge. Wich moves are the best ones to start? How to continue?
To be a globally unstable position, any "perfect play" sequence must favour the first moving player. Perhaps we should try to find it (first, on a smaller board?) to understand what can happen.
Appropriate komi might be 100 - 81 = 19, but it also could be much less because of the weakness of stones at the edges. (Anyway, that doesn't affect the stable/unstable question. About some small so-called "unstable seki" you may want to have a look at http://harryfearnley.com/go/bestiary/rule_challenge.html. The label "unstable" seems mistakable, since those positions are globally stable, of course - otherwise they wouldn't be called "seki" at all.).--2003-11-18
Heres another 181-stringy monster. I don't really think it's stable. Who knows? (According to the ruleset, chose komi so that, if considered to be a "global seki", it's a tie: 0 in japanese, 3 in chinese counting.) -- rubilia
I think on this one, White has the best chance to get some life. The first black ring (from the center) is dead, and White can salvage it. At least I have no idea how black could prevent that. -- (Sebastian)----
Tas: I tried this as an atempt on an actual seki, but it is clearly very unstable.