Author: chandler yergin
Date: 18:07:42 01/12/05
Go up one level in this thread
On January 12, 2005 at 21:03:54, Michael Yee wrote: >On January 12, 2005 at 20:57:40, chandler yergin 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. >>> >>>If there were 10^120 in the full tree, then about 10^60 would be in the solution >>>tree. >>> >>>It can be less than that. >> >>It "Can't be LESS than that! >> >> But it cannot be more. >> >> >>It Certainly CAN! >> >>In any TREE.. the TREE ONLY represents "What HAS Been PLayed." >>REFUTE THAT! >>Can't HUH? >> >>Give it up! > >What you just said is correct since you're talking about the *tree* of moves. >But Uri and Dann are talking about the *set* of unique positions (many of which >can arise through different move orders). So you and they are talking about >different (mathematical) objects--trees (or paths in a tree) and graphs (or >nodes in a graph). > >By the way, just because some quantity is large (or infinite) doesn't mean you >can't prove something about it mathematically. For instance, you can prove that >a geometric series (e.g., 1/2 + 1/4 + 1/8 + ...) convergences to a number even >though their are an infinite number of terms. > >Michael Yeah.. ya can compute Pi to a Billion or so digits... I round off at 3.1416... Close enough for me.. So What? Ur missing the point.
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