Author: Uri Blass
Date: 17:04:11 01/12/05
Go up one level in this thread
On January 12, 2005 at 19:45:49, chandler yergin wrote: >On January 12, 2005 at 19:41:44, Uri Blass wrote: > >>On January 12, 2005 at 19:27:05, chandler yergin wrote: >> >>>On January 12, 2005 at 19:11:12, Dann Corbit wrote: >>> >>>>On January 12, 2005 at 19:04:31, chandler yergin wrote: >>>> >>>>>So says Mark Twain.... >>>>> >>>>>You Programmers are spreading lies, misinformation, & disinformation. >>>>> >>>>>However I should not attribute to Malice, what can be explained by Ignorance! >>>>> >>>>>Computers will NEVER SOLVE CHESS! >>>>>Stop your Nonsense! >>>> >>>>If man were meant to fly, he'd have wings. >>>>Man will never fly faster than sound. >>>>Man will never go to the moon. >>>> >>>>Things that seem impossible quickly become possible. >>>> >>>>In this particular case, it is even obvious mathematically how it will come >>>>about. >>> >>>If you understood Mathmatics, you wouldn't say that! >>> >>>It IS Obvious, that it's an Impossibility! >>> >>>The Question of "whether or not God exists" is a Philosophical & Meataphysical >>>Question. >>>Would you agree? >>> >>>Some say.. "It can't be Proven". >>>With a Philosophical Question, there are NO 'right or wrong' answers... >>> >>>With Mathmatics, there ARE 'right & wrong' answers. >> >>Mathematics will not tell you if it is practically possible to solve chess. >> >>> >>>Your perception is in error! >>> >>>THINK! >>> >>>"In a tree, from the Starting Position, there are 20 possible moves for white. >>>There are 20 * 20 = 400 possible moves for black, depending on what white does. >> >>Yes but you do not need to analyze everyone of them and no program does it. >> >>>Then there are 400 * 20 = 8,000 for white. >> >>The number of possible games of 3 plies is more than 8000. >>The number of possible positions that you get after 3 plies is smaller because >>1.e4 e6 2.d4 is identical to 1.d4 e6 2.e4 >> >> >> Then there are 8,000 * 20 = 160,000 >>>for black, and so on. If you were to fully develop the entire tree for all >>>possible chess moves, the total number of board positions is about >>>1,000,000,000,000,000,000,000,000, >>>000,000,000,000,000,000,000,000,000,000,000,000,000,000, >>>000,000,000,000,000,000,000,000,000,000,000,000,000,000, >>>000,000,000,000, or 10^120, give or take a few. >> >>No >> >>The number of possible games is higher than 10^120 > > >Give or take a few... > > >> >>The number of total positions is clearly smaller. > >I just proved it isn't! No you did not. > > >>Maybe 10^40 and it is easy to prove it. > >PROVE IT! Stop your absurd assertions! Ok here is a proof it is less than 10^55 For every position you do the following steps: 1)defining place for the kings: less than 64^2=2^12 possibilities 2)defining the empty squares of the rest of the pieces 2^62 possibilities 3)defining the type of the pieces in the non empty squares. Every non empty square has 10 possibilities(5 for white and 5 for black): 1)White queen 2)White Rook 3)White bishop 4)White knight 5)White pawn The total number of cases is 10 for every one of the 30 squares(or less non empty squares so you have at most 10^30 possibilities. 4)defining the side to move 2 possibilities 5)define the ep flag 8 possibilities 6)defining castling rights(16 possibilities in the worst case) 2^74*10^30*2*8*16<10^55 Most of the positions are illegal because position when the side to move is in check is illegal or position when white has 9 pawns is illegal. If you limit yourself only to legal positions than 10^40 seems to be a good estimate. Uri
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