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Subject: Re: Mathematical limit forced by K. D. 's position vice. Any formal proofs?

Author: KarinsDad

Date: 10:43:47 10/22/99

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On October 22, 1999 at 13:14:47, Dann Corbit wrote:

[snip]
>Even with 161 bits, you have a sure numbering of every possible position if all
>of your positions can be encoded in that format (e.g. you may be able to squeeze
>them smaller, but if any board position can be encoded in 161 bits, then we can
>*clearly* number them from [1,..,2^161] and so there cannot possibly be more
>positions than that.  On the other hand, there might be a lot less, even by
>orders of magnitude.  But at least we would have a real, provable limit instead
>of just an educated guess.

Of course.

However, you already have real, provable limits which are no different than mine
with the exception of magnitude.

  1 side to move
 64 bitboard
128 4 bits per piece/state

= 193 bits

And, of course, there are other well known algorithms that can get you lower
(your 179 algorithm for example).

I think without some form of "super super" computer to calculate them all, we
will never know the exact number and if you read that AI article that was posted
last week, you may not want to have "super super" computers around.

KarinsDad :)



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