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Warn moderators| Author : | Topic: Endgame-Theory: Theoretical endgames | Bottom |
| Abalone-Theory-Forum admin Posts : 153  |
Theoretical endgames According to the Endgame-Theory-Introduction (click here ) this is the "Theoretical endgames-Topic". Here you can present results, tasks, problems - and so on - for theoretical problems. Greetings, Funky-AbaloneTheory-JazzClub --Last edited by Funky-AbaloneTheory-JazzClub on 2005-11-08 01:16:52 -- |
| nacre Posts : 54  |
The program that did the computation above contained a bug (thanks to Eobllor for verifying the computation). I have not yet found a full solution. After fixing the bug the program claims that there are no solution to the position below. I cannot find the solution, but perhaps somebody else can? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . 1 1 . . . . . . 2 . . . . . . . --Last edited by nacre on 2005-11-10 21:59:18 -- |
| nacre Posts : 54 |
After fixing a few bugs, I was able to get a solution again. This sequence should be more accurate than the first (and also longer) Abalone 4-1 endgame database generator Board: . . . . . . . . . . . . . 1 1 . . . . . . 1 . . . . . . . 1 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: E3-1, ply=44 Board: . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . 1 1 . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: @0-0, ply=43 Board: . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . 1 1 . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: F3-1, ply=42 Board: . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . 1 1 . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: @0-0, ply=41 Board: . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . 1 1 . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: E4-1, ply=40 Board: . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 1 . . . . . . . . 1 . . . . . . . 2 . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: @0-0, ply=39 Board: . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 1 . . . . . . . . 1 . . . . . . . 2 . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: F4-1, ply=38 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . . . . . . . 1 . . . . . . . 2 . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: E7-5, ply=37 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . . . . . . . 1 2 . . . . . . . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: D5-1, ply=36 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . 1 1 2 . . . . . . . . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: F6-5, ply=35 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 . . . . . 1 1 . . . . . . . . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: D6-5, ply=34 Board: . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 1 2 . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: G5-2, ply=33 Board: . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 1 . . . . . . . 1 2 . . . . . . . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: F4-1, ply=32 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . 1 1 . . . . . . . 2 . . . . . . . . . . . . 2 1-0 2-0 Optimal move: F7-2, ply=31 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . 1 1 . . . . . . . . . . . . . 2 . . . . . . 1 1-0 2-0 Optimal move: F5-2, ply=30 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 1 . . . . . 1 . . . . . . . 2 . . . . . . 2 1-0 2-0 Optimal move: E8-3, ply=29 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 1 . . . . . 1 . . . . . . 2 . . . . . . . 1 1-0 2-0 Optimal move: F6-2, ply=28 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 1 1 . . . . . 2 . . . . . . . 2 1-0 2-0 Optimal move: D8-3, ply=27 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 1 1 . . . . 2 . . . . . . . . 1 1-0 2-0 Optimal move: E7-3, ply=26 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . 1 1 . . . . . 2 . . . . . . . . 2 1-0 2-0 Optimal move: C8-3, ply=25 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . 1 1 . . . . 2 . . . . . . . . . 1 1-0 2-0 Optimal move: E5E6-3, ply=24 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 1 1 . . . . 2 . . . . . . . . . 2 1-0 2-0 Optimal move: B8-4, ply=23 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . 2 1 1 . . . . . . . . . . . . . . 1 1-0 2-0 Optimal move: D5D6-3, ply=22 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 2 1 1 . . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: B7-1, ply=21 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . . 1 1 . . . . 2 . . . . . . . . . 1 1-0 2-0 Optimal move: D7-2, ply=20 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . . 1 . . . . . 2 1 . . . . . . . . 2 1-0 2-0 Optimal move: B8-4, ply=19 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 2 1 . . . . . . 1 . . . . . . . . 1 1-0 2-0 Optimal move: C5-2, ply=18 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . 2 1 . . . . . . 1 . . . . . . . . 2 1-0 2-0 Optimal move: @0-0, ply=17 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . 2 1 . . . . . . 1 . . . . . . . . 1 1-0 2-0 Optimal move: C8-5, ply=16 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . 2 1 1 . . . . . . . . . . . . . . 2 1-0 2-0 Optimal move: B7-1, ply=15 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . 1 1 . . . . 2 . . . . . . . . . 1 1-0 2-0 Optimal move: C6-1, ply=14 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 1 . . . . 2 1 . . . . . . . . 2 1-0 2-0 Optimal move: B8-4, ply=13 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 2 1 1 . . . . . 1 . . . . . . . . 1 1-0 2-0 Optimal move: D7-3, ply=12 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 2 1 1 . . . . . . 1 . . . . . . . . 2 1-0 2-0 Optimal move: A7-4, ply=11 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 . . . . . . . 1 1 . . . . . . 1 . . . . . . . . 1 1-0 2-0 Optimal move: B7-4, ply=10 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 2 1 . . . . . . . . 1 . . . . . . 1 . . . . . . . . 2 1-0 2-0 Optimal move: A6-1, ply=9 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 2 . 1 . . . . . . 1 . . . . . . . . 1 1-0 2-0 Optimal move: C7C8-3, ply=8 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 2 1 . . . . . . 1 . . . . . . . . . 2 1-0 2-0 Optimal move: @0-0, ply=7 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 2 1 . . . . . . 1 . . . . . . . . . 1 1-0 2-0 Optimal move: B5-0, ply=6 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 . . . . . . 2 1 . . . . . . 1 . . . . . . . . . 2 1-0 2-0 Optimal move: A7-1, ply=5 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 . . . . . . . 1 . . . . . 2 1 . . . . . . . . . 1 1-0 2-0 Optimal move: B6-0, ply=4 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 1 . . . . . 2 1 . . . . . . . . . 2 1-0 2-0 Optimal move: A8-1, ply=3 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 1 . . . . . . 1 . . . . 2 . . . . 1 1-0 2-0 Optimal move: C5-1, ply=2 Board: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 1 . . . . . 1 . . . . 2 . . . . 2 1-0 2-0 Optimal move: @0-0, ply=1 |
| SilverSurfer moderator Posts : 347  |
Hello nacre, I have some questions to you and one proposal. 1. completeness: boards, criterion, typology, reduction These board-results are sorted by ply. But probably there are some different positions for one identical ply. What is your argument to neglect the other positions? What is the criterion for the one selected board? There is certainly a necessity to reduce the variation-complexity of all possible variations into a typology. In which manner you would speak of a complete analysis ? What kind of typology is the background of your variation-complexity-reduction? 2. completeness: conditions and reduction, proposal Maybe there is a lack of the possibility to connect only 3 black marbles during the moves? My proposal to reduce the variations are: First, to explore only the 4th ring. Then we only have to analyse these two white marbles. And then there has to be variations of the black-groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . My propositions for the conditions would be: 1. In the starting-position the black marbles are connected 2. During the moves at least 3 black marbles are connected. 3. The White marble is on the 4th ring (2 possible spots) 4. Black has to move. --Last edited by SilverSurfer on 2005-11-15 23:33:11 -- |
| nacre Posts : 54 |
1. completeness The argument for the given sequence, is that it starts with a defender-marble in the center and a configuration of the attacker that should be easy to achieve. From this position the sequence is the shortest path to victory. There are other sequences but none are shorter. One example was given to me by Eob, where the attacker moves are more intuitive. The complexity was reduced by only considering attacker configurations where at most one marble where not connected to any other attacker marble. This significantly reduces the number of positions. Of couse symmetry was also used, but this has no impact on the sequence found. 2. at-least-3-connected condition If my result is correct, it is not possible in general to force a win if the attacker at all times must have at least 3 connected marbles. It *is* possible to always win if at most 1 marble must be non-connected, but note that this includes a 2+2 configuration. For the special case where the defender starts 1 step away from the edge (ring 4 in my old terminology), you can win if the defender is in the corner and the attacker has surrounded him with 3 marbles. The final attacker marble is drawn in, then you win. . . . . . . 2 1 . . . . 1 1 . . . . . . . . . . 1 . . . . . . . . . . Another special case where it is possible: . . . . . . . . . . . . . . . 1 2 . . . . . . 1 . . . . . . . 1 . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . 1 to move. 13 ply to go. The situations have in common that the defender is either pushed to the edge immediately, or cannot move. A case where it is not possible: . . . . . . 2 . . . . . . 1 . . . . . . 1 . . . . . . . 1 . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . 1 to move Another case where it is also not possible: . . . . . . . . . . . . 2 1 . . . . . . 1 . . . . . . . 1 . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . 1 to move |
| SilverSurfer moderator Posts : 347 |
Hello nacre, ok, there was a misunderstanding, lets drop the second condition, but what do you think of this proposal? My proposal to reduce the variations is: First, to explore only the 4th ring: we only have to analyse these two white marbles. And then there has to be variations of the black-groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . My propositions for the conditions would be: 1. In the starting-position the black marbles are connected 2. The White marble is on the 4th ring (2 possible spots) 3. Black has to move |
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