Author: Uri Blass
Date: 00:30:48 01/13/05
Go up one level in this thread
On January 13, 2005 at 02:03:42, chandler yergin wrote: >On January 13, 2005 at 01:35:44, Uri Blass wrote: > >>On January 13, 2005 at 00:50:00, chandler yergin wrote: >> >>>On January 12, 2005 at 22:07:58, Uri Blass wrote: >>> >>>>On January 12, 2005 at 21:33:06, chandler yergin wrote: >>>> >>>>>On January 12, 2005 at 21:17:58, Uri Blass wrote: >>>>> >>>>>>On January 12, 2005 at 20:58:47, chandler yergin wrote: >>>>>> >>>>>>>On January 12, 2005 at 20:55:42, Uri Blass wrote: >>>>>>> >>>>>>>>On January 12, 2005 at 20:33:25, Dann Corbit wrote: >>>>>>>> >>>>>>>>>On January 12, 2005 at 20:25:24, Uri Blass wrote: >>>>>>>>> >>>>>>>>>>On January 12, 2005 at 19:56:25, Dann Corbit wrote: >>>>>>>>>> >>>>>>>>>>>On January 12, 2005 at 19:37:29, Steve Maughan wrote: >>>>>>>>>>> >>>>>>>>>>>>Dann, >>>>>>>>>>>> >>>>>>>>>>>>>Things that seem impossible quickly become possible. >>>>>>>>>>>> >>>>>>>>>>>>I recon about 300 years before a computer will solve chess. This assumes >>>>>>>>>>>> >>>>>>>>>>>>1) 10^120 possible positions >>>>>>>>>>> >>>>>>>>>>>This is far, far too large. Chess positions have been encoded in 162 bits, >>>>>>>>>>>which puts an absolute upper limit at 10^58 (and it is probably much less than >>>>>>>>>>>that). >>>>>>>>>>> >>>>>>>>>>>>2) Alpha-beta cutting this down to 10^60 sensible positions >>>>>>>>>>> >>>>>>>>>>>The incorrect first assumption renders this and all following assumtions as >>>>>>>>>>>moot. >>>>>>>>>> >>>>>>>>>>The second assumption is also not correct. >>>>>>>>>> >>>>>>>>>>By the same logic alphabeta can cut less than 2^30 positions in KRB vs KR to >>>>>>>>>>2^15 positions but it does not happen and solving some KRB vs KR position with >>>>>>>>>>no KRB vs KR tablebases is not something that you need 2^15 nodes for it. >>>>>>>>> >>>>>>>>>No. The second assumption would be true if the first was true. This was >>>>>>>>>formally PROVEN by Donald Knuth. In a perfectly ordered alpha-beta solution >>>>>>>>>tree, the number of nodes is proportional to the square root of the nodes in the >>>>>>>>>full tree. >>>>>>>> >>>>>>>>The problem is that the number of nodes in the full tree is bigger than the >>>>>>>>number of positions because the same position can happen in many branches of the >>>>>>>>tree. >>>>>>>> >>>>>>>>Even with perfect order of moves you cannot solve KRB vs KR by alpha beta with >>>>>>>>sqrt(2^30) nodes. >>>>>>>> >>>>>>>>Uri >>>>>>>>Uri >>>>>>> >>>>>>> >>>>>>>I think you are on my side... >>>>>>>;) >>>>>> >>>>>>I disagree both with you and Dann. >>>>>> >>>>>>If you want to generate tablebases you cannot use sqrt like Dan suggest. >>>>>>If you want to analyze possibility in games then sqrt is enough. >>>>>> >>>>>>In case that there are 10^120 games and 10^40 positions then chess can be solved >>>>>>by sqrt(10^120) nodes or by 10^40 nodes >>>>> >>>>> >>>>>A NODE, IS a Position! Correct? >>>> >>>>Node is a position that is searched by the chess engine. >>>> >>>>> >>>>>If there are 10^120 Games.. then 'every move' in those 10^120 games ARE >>>>>Positions. >>>> >>>>Yes but not all of them are different so it is possible that there are only >>>>10^40 different positions in a tree of 10^120 positions. >>>> >>>>There are too way to try to solve chess >>>> >>>>1)search(in this case you may search the same node in a lot of branches and you >>>>search both 1.e4 e6 2.d4 d6 or 1.e4 d6 2.e4 e6 or 1.d4 e6 2.e4 d6 or 1.d4 d6 >>>>2.e4 e6) >>>> >>>>In 4 plies you can get the same position 4 times and in 80 plies that are 40 >>>>moves you may get it trillions of times in different branches of the tree. >>>> >>>>In tree alpha beta help to get sqrt of the number of games but it is not a good >>>>idea to solve chess. >>>> >>>>2)tablebases that seems a better idea and the problem is that today there is not >>>>enough memory. >>>> >>>>In this case you do not build a tree. >>>> >>>>you look at all the position first time and mark all the mates. >>>>you look at all the position second time and mark all positions that you can get >>>>mate in 1(position that is already marked) >>>> >>>>you look at all the position and mark all the positions that you cannot prevent >>>>mate in 1(every move will need to position that is marked as mate in 1) >>>> >>>>There is no mate in 5000 because of the 50 move rule. >>>>so after repeating this process 10,000 times you can continue stop it and every >>>>position was searched only 10,000 times. >>>> >>>>This means that if the number of positions is 10^40 then time of searching >>>>10^40*10,000 positions is going to be enough but you need also memory of 10^40 >>>>positions and this is the another problem with using this solution today. >>>> >>>>I do not know if we will be able to use memory of 10^40 positions or search >>>>10^44 nodes in the next 100 years but I cannot say that I am sure that it is >>>>impossible. >>>> >>>>10^40 positions is only an estimate and I do not know the exact number of >>>>positions. >>>> >>>>I remember that I proved that it is less than 10^50 and even less than 10^47 in >>>>the past by a computer program that counted the number of possible positions for >>>>every possible material configuration and part of the positions that I counted >>>>are also illegal because both kings are in check so the estimate of 10^40 seems >>>>to me a good estimate. >>>> >>>>Uri >>> >>> >>>Argue with Dr. Hyatt, Dr. John Nunn & Frederick Freidel! >>> >>>THEY agree with ME! >> >>I need to hear from them that they agree with you. > >The Article is self-evident! R-E-A-D! >Comprehend! > >You are suckin hind Tit here! I read the post of hyatt but I read nothing of Nunn. > > >> >>It is possible that they have the opinion that chess will not be solved in the >>next 100 years(I only said that I do not know) but I believe that they do not >>claim that it is a proved fact. > >DR. John Nunn does the Math.. the fact you cannot comprehend it.. is 'your' >problem. I have B.sc in mathematics and M.sc and doctor of philosophy in related subjects. I certainly can understand mathematics but I saw no post of John nunn there. >> >>I do not think that they agree that it is impossible to solve chess if you have >>enough memory >>to store 10^50 positions with distance to mate or conversion and machine that >>can search 10^45 nodes per second. >> >>The question if this will be possible in the next 50 years or in the next 100 >>years is an open question. >> >>Uri > NO Question! Among those who know.. >You, have a Biased Opinion and an agenda, and you are misleading people! No I am not misleading people. I say that we cannot know and that mathematics does not answer it. I say that you are misleading people when you say that we need to search 10^120 to solve chess. Uri
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