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Subject: Re: highschool math

Author: Vincent Diepeveen

Date: 05:37:07 01/30/02

Go up one level in this thread


On January 29, 2002 at 13:58:20, Dann Corbit wrote:

>On January 29, 2002 at 10:08:46, Robert Hyatt wrote:
>>First you are saying that you have proven that there are no more than 2^81
>>unique positions where neither side can castle...
>
>No.  His notion is that if you mirror using every symmetry, the total number of
>those positions (including ALL reflections) would be less than 2^81 in that
>category.

this is dead wrong, because then we can search that entire
search space without nullmove and with nullmove we do it in
a few seconds then, yet we do not search it within a few
seconds.

secondly mirroring reduces position by factor n.

Say n = 2 for pawns ==>  2^250 / 2  =  2^249

The whole problem is that you guys still haven't figured out highschool math!



>>Second, you simply store the index into the ordered list of positions.
>
>With all its associated data.
>
>>But you totally ignore how you are going to turn that "index" into a real
>>position?  Or how you are going to turn a real position into that index?
>
>You take the position you are interested, and create all of its reflections (it
>can be hundreds).  Then, you lexically sort them from smallest to largest using
>memcmp.  Then, you look in the database for the smallest of those positions.
>The same procedure will have been used to store the original entry into the
>database.  Let's revisit the set that Les posted:
>
>1R3K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>2R2K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>3R1K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>4RK1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>5K1k/8/8/8/8/8/8/R7 w - - ce 32762; pv Ra8;
>5K1k/8/8/8/8/8/R7/8 w - - ce 32762; pv Ra8;
>5K1k/8/8/8/8/R7/8/8 w - - ce 32762; pv Ra8;
>5K1k/8/8/8/R7/8/8/8 w - - ce 32762; pv Ra8;
>5K1k/8/8/R7/8/8/8/8 w - - ce 32762; pv Ra8;
>5K1k/8/R7/8/8/8/8/8 w - - ce 32762; pv Ra8;
>5K1k/R7/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>7r/8/8/8/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>8/7r/8/8/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>8/8/7r/8/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>8/8/8/7r/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>8/8/8/8/7r/8/8/K1k5 b - - ce 32762; pv Rh1;
>8/8/8/8/8/7r/8/K1k5 b - - ce 32762; pv Rh1;
>8/8/8/8/8/8/7r/K1k5 b - - ce 32762; pv Rh1;
>8/8/8/8/8/8/8/1r3k1K b - - ce 32762; pv Ra1;
>8/8/8/8/8/8/8/2r2k1K b - - ce 32762; pv Ra1;
>8/8/8/8/8/8/8/3r1k1K b - - ce 32762; pv Ra1;
>8/8/8/8/8/8/8/4rk1K b - - ce 32762; pv Ra1;
>8/8/8/8/8/8/8/K1k1r3 b - - ce 32762; pv Rh1;
>8/8/8/8/8/8/8/K1k2r2 b - - ce 32762; pv Rh1;
>8/8/8/8/8/8/8/K1k3r1 b - - ce 32762; pv Rh1;
>8/8/8/8/8/8/8/K1kr4 b - - ce 32762; pv Rh1;
>8/8/8/8/8/8/r7/5k1K b - - ce 32762; pv Ra1;
>8/8/8/8/8/r7/8/5k1K b - - ce 32762; pv Ra1;
>8/8/8/8/r7/8/8/5k1K b - - ce 32762; pv Ra1;
>8/8/8/r7/8/8/8/5k1K b - - ce 32762; pv Ra1;
>8/8/r7/8/8/8/8/5k1K b - - ce 32762; pv Ra1;
>8/r7/8/8/8/8/8/5k1K b - - ce 32762; pv Ra1;
>k1K1R3/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>k1K2R2/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>k1K3R1/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>k1K5/7R/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>k1K5/8/7R/8/8/8/8/8 w - - ce 32762; pv Rh8;
>k1K5/8/8/7R/8/8/8/8 w - - ce 32762; pv Rh8;
>k1K5/8/8/8/7R/8/8/8 w - - ce 32762; pv Rh8;
>k1K5/8/8/8/8/7R/8/8 w - - ce 32762; pv Rh8;
>k1K5/8/8/8/8/8/7R/8 w - - ce 32762; pv Rh8;
>k1K5/8/8/8/8/8/8/7R w - - ce 32762; pv Rh8;
>k1KR4/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>r7/8/8/8/8/8/8/5k1K b - - ce 32762; pv Ra1;
>
>All of these positions are exact equivalents -- created by rotations,
>reflections, etc.  (should be the pm instead of the pv, but that's neither here
>nor there).  Anyway, all we need to do is store the first position:
>1R3K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>And from that, we can generate all the others.  Using that position and its
>associated information, we can quickly look up the solution to any of the other
>problems.  We simply take the position we are given and perform the same
>rotations and reflections (they are very simple, and the code to do it is posted
>on my ftp site).  Then, pick the smallest one from that set and look into the
>database and see if it is there.  If it is present, then we have a solution
>move.
>
>>It is computationally intractable in either direction...
>
>Not only is it simple to calculate, he has a working version.
>
>>
>>>>
>>>>>
>>>>>k1K5/7R/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K5/8/7R/8/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K5/8/8/7R/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K5/8/8/8/7R/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K5/8/8/8/8/7R/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K5/8/8/8/8/8/7R/8 w - - ce 32762; pv Rh8;
>>>>>k1K5/8/8/8/8/8/8/7R w - - ce 32762; pv Rh8;
>>>>>k1K3R1/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K2R2/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1K1R3/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>k1KR4/8/8/8/8/8/8/8 w - - ce 32762; pv Rh8;
>>>>>5K1k/R7/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>5K1k/8/R7/8/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>5K1k/8/8/R7/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>5K1k/8/8/8/R7/8/8/8 w - - ce 32762; pv Ra8;
>>>>>5K1k/8/8/8/8/R7/8/8 w - - ce 32762; pv Ra8;
>>>>>5K1k/8/8/8/8/8/R7/8 w - - ce 32762; pv Ra8;
>>>>>5K1k/8/8/8/8/8/8/R7 w - - ce 32762; pv Ra8;
>>>>>1R3K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>2R2K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>3R1K1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>4RK1k/8/8/8/8/8/8/8 w - - ce 32762; pv Ra8;
>>>>>8/8/8/8/8/8/7r/K1k5 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/8/7r/8/K1k5 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/7r/8/8/K1k5 b - - ce 32762; pv Rh1;
>>>>>8/8/8/7r/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>>>>>8/8/7r/8/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>>>>>8/7r/8/8/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>>>>>7r/8/8/8/8/8/8/K1k5 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/8/8/8/K1k3r1 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/8/8/8/K1k2r2 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/8/8/8/K1k1r3 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/8/8/8/K1kr4 b - - ce 32762; pv Rh1;
>>>>>8/8/8/8/8/8/r7/5k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/8/8/r7/8/5k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/8/r7/8/8/5k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/r7/8/8/8/5k1K b - - ce 32762; pv Ra1;
>>>>>8/8/r7/8/8/8/8/5k1K b - - ce 32762; pv Ra1;
>>>>>8/r7/8/8/8/8/8/5k1K b - - ce 32762; pv Ra1;
>>>>>r7/8/8/8/8/8/8/5k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/8/8/8/8/1r3k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/8/8/8/8/2r2k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/8/8/8/8/3r1k1K b - - ce 32762; pv Ra1;
>>>>>8/8/8/8/8/8/8/4rk1K b - - ce 32762; pv Ra1;



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