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Title: Recursive evluation of material Post by pago on Nov 17th, 2011, 11:53am Hello, I would like to suggest a new way to evaluate Arimaa material evaluator. It has some connections with the thread "Global Algebric Material Evaluator". The explaination are given in the following file : http://sd-2.archive-host.com/membres/up/208912627824851423/REM.pdf I doubt that it could have a practical interest for bot development. I am even not sure that it doesn't give silly results when applied on all material setups. However, I feel that this "formal" way to study Arimaa material balance seems to give "not so bad" results (probably due to the fact that the Arimaa major pieces are identical excepted for the hierarchy) I couldn't try the calculations for a large number of setups because it should be performed by a recursive soft. However I would be curious to see the results if someone would perform them. |
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Title: Re: Recursive evaluation of material Post by pago on Nov 21st, 2011, 11:12am I made some further experiment with Excel. As it is REM seems to overvalue rabbits. However, when I remove goal threats (only keeping trapping threats) from the transition graph, the results seem to be quite closed from the results got in its "cat tournament". Then rabbits seem to be slightly undervalued). |
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Title: Re: Recursive evluation of material Post by clyring on Nov 21st, 2011, 6:55pm Be aware that without allowing for goal threats in this evaluator, any material arrangement featuring only rabbits yields an undefined result. |
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Title: Re: Recursive evluation of material Post by pago on Nov 22nd, 2011, 10:35am on 11/21/11 at 18:55:00, clyring wrote:
Yes I agree with you. The evaluator would not be totally consistent and would give awefull results such as a 100% victory of Gold ER against silver 8r. What I am really testing is a graph where I keep all the threats (including goal threats) but with only 2 daughter nodes in all cases : a) The node that maximizes REM when a Gold piece is trapped b) The node that minimizes REM when a silver piece is trapped. The idea would be to draw a kind of Min-Max tree : Against a threat the weaker side has always the choice to sacrifice the piece that minimises the consequences. For example a side with only one rabbit would prefer to lose a major piece instead of losing his last rabbit or let an adverse rabbit reach the last rank. For instance with EDCR versus ecr we would get the following graph : EDCR/er <--6--- EDCR/ecr ---5--> ECR/ecr 6 = 3 for "E,D or C trapping r" threat + 2 for "E od D trapping c" threat + 1 for the "gold goal" threat 5 = 2 for "e or c trapping R" threat + é for "e trapping C or D" threat +1 for the "silver goal" threat The first calculations seem to show a very good behaviour in "cat tournament". I will try to make some calculations with dogs... |
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Title: Re: Recursive evluation of material Post by pago on Dec 1st, 2011, 12:40pm After some tests I have come back to the initial idea with some ajustments to get correct rabbit values. I have now a version of a recursive evaluator that seems to give correct results : The link are : Explainations : http://sd-2.archive-host.com/membres/up/208912627824851423/REM/REM_v2.pdf Calculation sheet (be carefull the .zip file size is 21,4 Mo and the uncompressed Excel file size is 105,4 Mo) : http://sd-2.archive-host.com/membres/up/208912627824851423/REM/REM_v2.zip As I have already said I don’t know whether REM may have an interest for bot development. However, I do find surprising that an interesting game such as Arimaa allows this kind of formal approach with very simple hypothesis to derive a material evaluation. As far as I know, it would not be possible with game like chess. However, seeing the number of reactions to this thread I shall admit that I am the lone person to share these interests :P I also wonder whether it would be possible to develop this approach by graphic model to include some positional parameters, in particular frozen pieces. The nodes would include setup with frozen pieces : A frozen piece could no more trap an adverse piece (it would affect the arrow weights) until it has been unfrozed. To weight the unfreezing arrows, we could consider that all friendly pieces could help it. The resulting graph would have some feedback loops, so the calculation would not be so simple. I imagine that we could use a kind of ranking on the model of the one used by Google. I am aware that all this idea is highly speculative but it might worth to try a new approach… |
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Title: Re: Recursive evluation of material Post by Boo on Dec 1st, 2011, 12:54pm Quote:
Quote:
Well.... this is more like a philosophical question, but why bother researching something that does not have a practical interest? Why bother looking so deeply into something with no practical application? :) |
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Title: Re: Recursive evluation of material Post by 99of9 on Dec 1st, 2011, 4:28pm on 12/01/11 at 12:54:32, Boo wrote:
Because it's beautiful. Or because it has a practical application that you don't know about. Or because it educates you. http://en.wikipedia.org/wiki/G._H._Hardy |
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Title: Re: Recursive evluation of material Post by pago on Dec 3rd, 2011, 2:49pm Quote:
and why bother playing Arimaa ? Why bother developing bots ? Why bother discussing in forum ? Quote:
Quote:
I am admiring of scientists such as Hardy. These guys are in an other galaxy compared to my own mathematic skills... |
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