A fundamental task of the middle-game-Theory

I think there is one important task for the middle-game-theory, with a fundamental relevancy:  



There are variations of this problem with 1,2,3,5 ejected White - and maybe 1,2,3 black - marbles and in the pattern (edge, ring, ect.)

Are there strategies for Black to come back into the battle or is the game already lost?
And if there are some strategies for black: can we figure out the typology of the strategies and which is the best?
And complenentary: which is the best strategy for White to keep the dominance?

This fundamental middle-game-problem is important for some reasons, I think so.  

--Last edited by Funky-AbaloneTheory-JazzClub on 2005-11-08 00:41:36 --

I call this a "witch-ring" since it is a pretty damned situation to be in for the defender.

The name was derived from the Danish name for Fairy rings (hag tracks in Britain): Circles or inedible mushrooms that grow in grassy areas. According to folklore, fairy rings are magical circles in which witches and faeries meet to sing and dance at night.

This is the optimal situation for the strongest evaluation functions known today. The problem with this is that programs tend to get stuck in this situation, unable to make the killing move. Werner describes a small modification to his evaluation function that makes it less likely to get stuck.

With respect to theory, I believe the critical component is that the defender has no 3-line that attacks ring 2. Since it is easy for the attacker to make 3-lines that attack ring 3, 4 or 5, the game is pretty easy to win.

My knowledge of Abalone is pretty small, but I think that the strategy for the defender must be to establish a 3-line that attacks ring 2. Otherwise, the attacker can play a block-strategy that never opens any weakness.

I think in this Situation, black is leading. My impression is that the position of White has the value of about 3 marbles.
What do you think ? How much is nacres score in this situation?

Aba-Pro Level 8 its -7,1 White / 7,0 Black  (very long thinking-time)  

--Last edited by SilverSurfer on 2005-11-12 23:38:00 --

With careful play I believe that white can force a win, even if he has lost 5 marbles. The reason is that the black defense has no 3-lines and even no 2-lines, thus white can push the black marbles as he likes.

Nacre gives a positive score to black - but there are several situations that Nacre does not play very well.

During the 2003 olympics AbaPro played an unofficial match against a third program, much weaker than Nacre. This situation quickly occurred (with 0 lost marbles for white), but it took AbaPro several hundred moves to win. The defender kept all his marbles at the edge, evenly distributed. AbaPro was unable to see a win, even through humans can easily do it. The winning sequence is probably some 10-15 ply or more, which was beyond the search horizont of AbaPro.

There were four messages to this subject in a different topic:

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Abalekon said (Posted 13/11/2005 09:28:38 AM)

I agree with the name too   but I have to remarks :

1) this situation of game is purely theoretical, you can find real situations approaching that, but I doubt you will ever see such a perfect ring.

2) in this situation, who is the defender ? The position of white is pretty good, but 4 white marbles are already ejected. Black has still all his 14 marbles, but his position is weak.  

--Last edited by Funky-AbaloneTheory-JazzClub on 2005-11-22 18:03:34 --

nacre said (Posted 13/11/2005 03:47:35 PM):

I think this situation can be won by white, who has the center. Thus, black is the defender.  

--Last edited by Funky-AbaloneTheory-JazzClub on 2005-11-23 01:05:57 --

chriscool said (Posted 14/11/2005 12:14:26 AM):

I would feel more comfortable in the white position. However, whites may not be able to eat blacks without compromising their structure and position. So, i wouldn't be surprised if blacks could win either.  

--Last edited by Funky-AbaloneTheory-JazzClub on 2005-11-23 01:06:17 --

SilverSurfer said (  Posted 15/11/2005 10:46:31 PM)

Nobody declines the term “witch-ring”, because its a difficult situation anyway - independent of the question: "Who is the defender?"

But there is still a discussion about the "real score".

Of my point of view, White can force a draw for sore - maybe even in the case of 0 – 5.
Thus the only question is, if there are "winning-chances"  for White. I think that White has not a winning-chance in the case of 0-5, because black will attack White sufficient, if White tries to eject marbles. (chriscools argument, too - I think so). If White tries to eject a marble in this case, than Black will conquer space in the first rings. Its not necessary to build a 3-row in this case, I think so, too.
The question to me is still, which is the best strategy for White to win in the case of 0-4 ? Is there really a possibility to eject one single marble after the next single marble without losing the position?
A second question would be: is this certainly a draw for White? Probably yes. But in the case of 0-5, too ?  

--Last edited by AbaloneTheory-Forum on 2005-12-08 23:37:18 --