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Topic: Generalizing Arimaa and variations (Read 1368 times) |
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clojure
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Generalizing Arimaa and variations
« on: Sep 17th, 2010, 7:05pm » |
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The Turing test topic brought to my mind that it would be interesting to explore different Arimaa variations with computer, at least by pruning out those that computer excels at.
It could be programmed to try out to find some kind of local patterns etc and give a value how well the dynamics change.
But aside from computers, if people someday realize that there is some problem with Arimaa that makes the top players' games uninteresting for them, we should still have a solid ground on building even better game.
Some quick ideas that has come to my mind but haven't thought about:
For puzzles, simply allow arbitrary boards that have traps wherever the designer of puzzle wants. Also any number of pieces (this is mostly useful for elephant and camel, since only one of them). I think this could yield into lots of fun puzzles.
* moving traps
** would affect dynamics a lot so must be careful how it is moved
** e.g. game doesn't end when rabbit is at the end flank. it could change into a moving trap; or, the player could put an existing home trap to anywhere he likes (only once for that trap)
* rat, i just noticed that someone suggested a variation where there's one piece that is less stronger than any piece else but elephant. i'm not sure i like intransitivity in general but it might fit here. maybe a rabbit could become a rat in the middle 4 squares so it wouldn't do any harm but block the center
* The much renowed attribute of arimaa is that it's hard for computers. and one of the reasons is that it's hard to calculate concrete goals. So how about making the goal different
** one's objective would be to go opponent's homerow and push back an opponent rabbit to make it harder. the amount of rabbits might have to be reduced. Since pushing/pulling takes more time, one might need to have more alternative threats than in normal Arimaa.
Well, I actually like the mix of struggling of position and very sharpness of rabbit goaling, so maybe that is too essential part of Arimaa to be get rid of.
Now, other thing that might be interesting: to generalize Arimaa. Is it possible to make a nice stackable piece game with rules similar to Arimaa? So that 3 pieces stacked would be stronger than 2. Also it could be that the amount of movement for that piece in one turn could be related how many pieces it has. Maybe this would fail miserably but it would be a bit more elegant in that there would be only one type of piece that can be interacted with others...
Oh well, maybe I should stop dreaming and just learn to play Arimaa in the first place.
edit: Also pushing and pulling could be chained: if there are two consecutive friendly pieces side by side, they could push or pull two opponent's consecutive pieces with 4 steps so that they move as a chain (e.g. in worm game). The strength limitation is that, for pusher's pieces x and y, and opponent's pieces a, and b, and for relation stronger(p1, p2), stronger(x, a) & stronger(y, b) is satisfiable. That allows for example that E and D pushes m and r since stronger(E, m) and stronger(D, r) even though stronger(m, D).
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| « Last Edit: Sep 17th, 2010, 8:26pm by clojure » |
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clojure
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Re: Generalizing Arimaa and variations
« Reply #2 on: Sep 17th, 2010, 10:19pm » |
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Thanks for the links. I'll look them up later. The general game playing engine could be fun and it's nice to see a LISP has been used for that purpose 
I was thinking in the stacking variant that one could steal opponent's pieces into one's own stack, and that the topmost piececolor would indicate how the freezing works. So if gold steals opponent's piece (temporarily) he can move faster and push/pull stronger opponents but is freezing own pieces 
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| « Last Edit: Sep 17th, 2010, 10:24pm by clojure » |
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clojure
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Re: Generalizing Arimaa and variations
« Reply #3 on: Sep 21st, 2010, 12:34pm » |
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I forgot this thread but now I will crawl the links.
But the thing what got me here was that the stackable pieces give another generalization for push/pull.
The pull/push is allowed if there exists a sequence of player's pieces whose total number is more than that of an opponent's piece sequence.
This would allow for example a 2-piece stack to be pushed with 3 stacks, each consisting of one piece. In Arimaa context this could be seen as weaker pieces combining their strength to push one otherwise-never-to-be-pushed piece.
With stacks that have more than one piece, one could even beat "elephant's" strength, e.g. if horse was a 4 and camel 7 pieces in a stack, their sum strength would be 11 which is more than, say elephant's 10.
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ocmiente
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Re: Generalizing Arimaa and variations
« Reply #4 on: Sep 21st, 2010, 2:42pm » |
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I'm not sure what you mean. Do you mean pieces stacked on top of each other, or pieces pulling as in a tug of war, or pushing as in a conga line?
So if you had, for instance three cats in a straight line and a cat in front of them, the rabbits could all push together to move the cat, costing 4 moves (1 to move the cat, then the rabbits would all have to move one space following the cat - as in a conga line)
Similarly, a cat and a rabbit could pull a cat, etc. rabbit strength=1, cat=2, etc.
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clojure
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Re: Generalizing Arimaa and variations
« Reply #5 on: Sep 21st, 2010, 2:51pm » |
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Quote:| So if you had, for instance three cats in a straight line and a cat in front of them, the rabbits could all push together to move the cat, costing 4 moves (1 to move the cat, then the rabbits would all have to move one space following the cat - as in a conga line) |
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Yep. Like this. I read the other threads and noticed that mostly people were worried about that elephant's invincibility shouldn't be changed. But I think if it was hard enough to affect elephant but still possible, it would prevent staling/congestion but wouldn't affect too much of the strategy: i.e. a many pieced stack is powerful in the center since it can with one move affect a lot compared to a sequence of pieces.
What I'm interested in is to find out what is the essential aspects of pushing/pulling game. It doesn't have to have same strategies as in Arimaa. Just finding an elegant ruleset that makes a positional game where you have to move your troops properly by distributing the strength across the board by having high level goals but still needing to tactically excel. I feel that the conductivity of strength could make the flow of the game smoother, so that high level strategy wouldn't fail because of too discretely proportioned strength variance.
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| « Last Edit: Sep 21st, 2010, 3:04pm by clojure » |
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clojure
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Re: Generalizing Arimaa and variations
« Reply #6 on: Sep 24th, 2010, 11:08am » |
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Arimaa has two important concepts, forced moving (push/pull) and freezing. I think they can be seen as separate functions, and thus would give possibility for variations.
A flying piece comes to my mind, say a parrot, who could not push nor pull anyone but could move over other pieces, and it's function would be to free other pieces from being frozen.
If it is in the air, it could also pass enemy pieces. If this is too powerful, then another way is that it couldn't move over other pieces but could move as wishes while his turn. Snake would be better animal mapping then, I guess.
The idea of flying piece made me think about two-leveled board, where some pieces could move between levels. Main intention being that one could by-pass blockades in the other level by changing temporarily level. There could be birds who would only move in 2nd level and elephant could only in first level.
To move between levels could take maybe from 2 to 4 steps to keep it discouraged.
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| « Last Edit: Sep 24th, 2010, 11:09am by clojure » |
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clojure
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Re: Generalizing Arimaa and variations
« Reply #7 on: Sep 28th, 2010, 10:13am » |
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To make Arimaa game playing style more balanced, or weird, I suggest two alternatives.
Players would make 4 steps as normally but would also choose 2 pieces (that didn't move in this move). On opponent's turn the opponent can move those 2 pieces in any way he wants. If two is too much, maybe one is enough. This could prevent some stagnation issues (or make them worse).
So if I chose C and D, then silver could (must?) move each 1 step to any available direction. (The pieces selected must have available step combination).
Another variation idea is to choose not 1 move as in regular Arimaa but two alternative moves. The opponent then chooses which one of the moves is played out. This could possible force to play in a style that isn't very narrow minded.
e.g. move 1 has only steps for E, and move 2 threatens to capture a small piece R. Now silver can choose which one he prefers to continue with. This could potentially make the game harder for computers, since they have to provide two moves...
Now the problem is what rules we set for the alternative moves. Clearly same steps in different temporal order is prohibited. There could be rule that at least one moved piece is different between the variations.
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| « Last Edit: Sep 29th, 2010, 11:24am by clojure » |
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