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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