Author: Robert Hyatt
Date: 15:04:51 01/25/05
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On January 25, 2005 at 16:32:58, Duncan Roberts wrote: >On January 25, 2005 at 16:25:28, Robert Hyatt wrote: > >>On January 25, 2005 at 16:13:01, Duncan Roberts wrote: >> >>>My understanding of dann corbit is that a 32 piece tablebase needs a 2.5 * 2.5 >>>cube of crystal. >>> >>>http://www.talkchess.com/forums/1/message.html?407489 >>> >>> >>>This is considerably less than a galaxy and perhaps could be slipped pass >>>greenpeace, although I think you were referring to all games. >>> >>>anyway is this calculation anywhere near right ? >>> >>> >>>duncan >> >> >>I honestly have no idea. First, I really don't know how big the actual game >>tree for chess will be. It could be _very_ big if the game goes on and on with >>every 50th move being a pawn push or capture to restart the 50 move rule. Or it >>might be that it is a forced win or draw or loss inside 50 move, with best play. >> Until we know how big the tree really is, it is hard to predict how much >>storage will be required to hold it. For the worst case, where some 5500 moves >>are possible before it becomes a forced draw (forced in that I assume one side >>will claim the draw if the other side will not, otherwise the game becomes >>infinite and all bets are off) that is so big that it is impossible to estimate >>anything about it. There are positions with a branching factor of one (one >>legal move) as well as positions with a branching factor of over 200. When >>talking about W^D where D is big and W can get big, I personally lose focus. :) > > >but to store a 32 piece tablebase would be a lot 'smaller'. > >might a 2.5 by 2.5 kilometre crystal do the trick ? > > >duncan The size of that is easy to compute. you start off with one piece on any of 64 squares. That takes 6 bits. Another piece on any of the remaining 63 squares. This turns into 64*63*62*61...*33... which is about 2e55 if I did my math right. Or another way is 6 bits * 32 pieces = 192 bits = 2^192 = 6e57. Both are big numbers. If you can store that many _values_ in a crystal of that size, then you are set. note that win/lose/draw is not good enough here, you need a mate in N value, not just win/lose/draw or you can't play the game and win when you should.
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