Author: Bruce Moreland
Date: 13:16:34 10/10/00
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On October 10, 2000 at 10:52:54, Pekka Karjalainen wrote: > > Hi folks, > > there were some postings some time ago by Bruce Moreland, I believe, about >tablebases for chess on the 6x6 board. That seemed quite interesting actually >and I started to wonder: Could we solve 6x6 chess? If not, how about an even >smaller variant? I don't believe that we can solve 6 x 6 chess via retrograde analysis, since powers of 36 are not shockingly better than powers of 64. I built a 6-man table and it was well under a gigabyte, but if you try to add a seventh you are doing multiple gigabytes again, and there are 24 pieces on a full board. In case anyone has a burning desire to know, there aren't any huge long wins in KRR vs KRN on a 6 x 6 board. This s contrasted with 8 x 8 chess, where there is some godawful huge conversion case. It seems intuitively obvious that a knight is stronger on a 6 x 6 board than it is on an 8 x 8 board, and perhaps this is enough to draw if there isn't a way for either side to win immediately. You must be right that it would be possible to solve chess on a board that's small enough. I haven't tried to figure out what that size would be. It might be practically impossible to do it for any interesting case. bruce > > You can find several actual small chessvariants from this URL: >http://www.chessvariants.com . Basically you can make them up yourself by >taking a smaller board (any size from 3x1 upwards is possible). Just set the >starting position as you please and call it <foo>chess. The smallest ones are >obviously trivial and can be solved even on the back of an envelope. You might >want to remove the castling rule and double pawn moves, and even treat stalemate >as a win to avoid total drawishness. > > But this is not what I am after really. I was thinking that would it be >interesting to try to solve these? Could we get a program that would search all >the way from a starting position to its (smaller NB) tablebases? > > One might even get a little feeling about the actual (and huge) computing >resources that would be needed to solve standard chess. If 5x5 takes this much >effort and 6x6 takes that much then 8x8 takes SO much (exponentially more of >course). What would a solution to a 5x5 chess variant really look like? > > As I am not much of a chess programmer I do not want to take on this challenge >myself. But if it interests anyone at all, maybe it was worth mentioning. > > Comments? > > Pekka K.
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