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Subject: Re: Mathematical How!!!

Author: KarinsDad

Date: 09:49:59 05/21/99

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On May 20, 1999 at 15:24:36, Dann Corbit wrote:

>On May 20, 1999 at 14:13:34, Dann Corbit wrote:
>[snip]
>>>The thread about representing positions in the minimum number of bits is also
>>>about setting an upper bound on the maximum number of chess positions. 160 bits
>>>is 2^160 or  ~= 10^48.
>>Yes, what a fascinating rejoinder!  In this case, if 10^52 is correct, then 173
>>bits should be the minimum, since 2^173 = 1.197e52
>>If we can encode in less, then the number of board positions is less than we
>>thought (or we have an error in our thinking and the scheme won't work).
>Which brings up another fascinating idea.  If we can come up with a minimal
>encoding, we can bound the maximum possible number of chess positions.  If the
>claim that all positions can be encoded in 100 bits is true, then there are
>"only" about 1e30 board positions!!  Several orders of magnitude below any limit
>claimed that I know of.  After all, if the mapping really is invertible, we will
>have a one to one and onto map from a 100 bit binary number to all possible
>board positions!

Dann,

Where did you come up with this 100 bit possibility?

It seems extremely unlikely that this is true for 2 reasons. One, is that the
10^30 board positions is many many magnitudes lower than even the most
aggressive minimum number of positions estimate that I have ever read.

Secondly, after spending many hours on attempting to decrease the minimum even
to 160 bits, I cannot even fathom a paradigm shift (such as a compression scheme
after getting to the 170+ bit range) that would enable someone to decrease the
documented minimum (of approximately 173 bits) by over 40%. This seems absurd to
me.

Is this just a computer chess urban myth?

KarinsDad :)




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