Author: chandler yergin
Date: 18:33:06 01/12/05
Go up one level in this thread
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? If there are 10^120 Games.. then 'every move' in those 10^120 games ARE Positions. NOW, how many Nodes are there? I have given the Statistics.. YOU, Uri & Dan Have NOT refuted it. You can't... So STOP the Opinions..... Post Facts, not Bias, NOT prejudice, admit, you don't know; "What the Hell you are talking about!" (you may need to multiply it by a small >constant like 1000 so it may be 10^43 nodes) but not by sqrt(10^40) nodes. > >I disagree both with you and Dann about solving the game. > >Dann claim possible in the life of part of the readers >You claim impossible in the life of part of the readers. > >I claim unknown if possible or impossible in the life of part of the readers. > >I do not know if it will be possible to build the 32 piece tablebases in the >next 100 years(you need something in the order of 10^40 both in memory and in >speed). > >I do not know if it will be possible to solve chess by other means like finding >that only 10^30 of the possible positions are relevant to build tablebases for >them. > >Uri
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