Author: chandler yergin
Date: 18:36:05 01/12/05
Go up one level in this thread
On January 12, 2005 at 21:28:02, Michael Yee wrote: >On January 12, 2005 at 21:07:42, chandler yergin wrote: > >>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. > >Actually, I don't think I'm missing your point. What you seem to be saying is >this: > >(1) There are approx 10^120 chess positions in the *tree* of moves >(2) There aren't even that many atoms in the universe >(3) Therefore, it's impossible to "mathematically prove" anything about chess >(i.e., solve it) > >And these are my points: > >(1) For solving chess, you only need to consider unique positions >(2) You can prove things about infinite sets of things without having to "touch" >each item. For example, we can even stay with your move tree and consider a K >and Q versus K ending. Ignoring the 50-move rule, there are infinitely many >move-paths (in your model) starting from some root position. By your thinking (I >think), it would be impossible to prove that K+Q is a win because you couldn't >possibly deal with an infinite number of move paths. But I think you would agree >that it's easily shown to be a win. End Game Tablebases Prove it... of course... What was the Topic? Solving.. the Game of Chess. Try reading with comprehension, and stick to the subject! Too complicated for ya?? > >Michael
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