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        Arimaa >> Off Topic Discussion >> Arimaa and Cellular Automta
        
(Message started by: NIC1138 on Mar 10^th, 2007, 1:24am)

Title: Arimaa and Cellular Automta
Post by NIC1138 on Mar 10^th, 2007, 1:24am

Hi... I believe all computer enthusiasts around here probably know cellular automata, like John Horton Conway's Game of Life...

I got myself thinking the other day: how complex would be a CA that implements basic arimaa tactics, like captures, protection, etc?...

Then I realized something: usually, when we compare games like chess and arimaa, for example, we always look from the perspective of moving a stone each time... But in CAs this is just a possibility!... There are some CAs like this, but usually it's a plane with parallel execution.

Can you imagine a biig arimaa board, with lots of stones, moving around at the same time, like in the Game of Life?... Wouldn't it be interesting?? ::) We can even do the same for chess, for example!... But then I think it won't be as much fun :P . But it might bring us some insights (not necessarily new) about the dynamics of those two games!...

Now it's the part I sleep before te delirium!!.. ;D

Title: Re: Arimaa and Cellular Automta
Post by IdahoEv on Mar 12^th, 2007, 1:22am

Sounds like fun! You'd need basic update rules for moving pieces around.

A few weeks ago I conceived of a massively-multiplayer version of arimaa, with many players at once having arimaa pieces on a giant board. You would be awarded new rabbits for capturing opponent pieces, and could exchange rabbits to upgrade your own pieces to higher value. i.e. trade in two rabbits to get a cat, trade in another rabbit to turn a cat into a dog, etc.

Title: Re: Arimaa and Cellular Automta
Post by NIC1138 on Mar 15^th, 2007, 9:22am

That sounds interesting too!...

One of the reasons I would like to try this is also because in chess, for example, many pieces can move infinite distances... In go too, you can put a stone anywhere. But in arimaa there is this limited "velocity", very akin to what happens in CAs... We don't feel it very much because the board is small. You only notice it when you stuck your elephant in a side of the board, and then it is too far to save a camel in the kill house at the other side! :D

This idea reminds me of perceptron networks... They are not a very good tool if you have to look at all variables at the same time... Not an astonishing performance. But they are quite good if you are looking for small parts of your domain!... So a neural network in a gigatic chess board would perhaps soon start to have performance issues... But for an arimaa gigantic board, what happens near a region is only influenced by a (Chebyshev distance) radius of fixed "N" houses.

Also, it would be interesting for example to have a bot playing arimaa in a gigantic board, and see the performance changing according to the number of moves per ply!... It's very usual to spend 4 moves to capture a certain stone. Maybe the function of the probability of capturing a stone according to the number of moves per ply would have some small spikes at multiples of 4! =)