Author: chandler yergin
Date: 23:03:42 01/12/05
Go up one level in this thread
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! > >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 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!
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