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Subject: Re: The depth of the chess tree, the size of the game of chess...

Author: Angrim

Date: 22:20:59 05/11/01

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On May 11, 2001 at 17:16:26, Dann Corbit wrote:

>On May 11, 2001 at 15:49:19, Angrim wrote:
>
>>On May 11, 2001 at 03:29:43, Dann Corbit wrote:
>>>Which brings up another thought.  What percentage of moves are so horrible that
>>>they are not even worth considering.  Is it 99.99999999999999999999999999%?
>>
>>not of moves, but of the set of all possible games, the percentage that contain
>>an error of that magnitude is roughly 99.999<insert 2 pages of 9s>99%
>>Even if you define such an error as "any move which can be shown to lose
>>with a 1 second search" rather than the possibly unsound "any move which
>>crafty would score as 10 points lower than the favorite after a 1 second
>>search".
>
>I don't think that such a percentage can really be quite so high.  I notice in
>the middle game that there are usually about 35 choices that can be made.  Super
>GM's will usually pick about 3 different options in such an example.  So that's
>about ten percent from a given node.  Now, it is interesting that it is a sort
>of exponential trimming, since (.10)^k grows towards zero quickly.  But then,
>that's just another way of saying that the average branching factor is about 3,
>which means we are right back in exponential-ville.
>

a 90% prune rate is much more optimistic than I was thinking.
Even allowing for the fact that "random" positions will generally have
much less king defenses than positions reached by solid play, I doubt that
more than 50% of the legal moves would lose trivially.
However, if you estimate that most of the legal games are at least 5000
moves long, and 50% of the moves at each ply are errors, then the fraction
of those games which include an error would be 1-(0.5^5000) which has a
lot of 9s in it :)

<big snip of factoring stuff>
wow, you really are bored.  Whats the address for the
factoring message board? :)

Angrim



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