Author: Jason Kent
Date: 18:56:52 01/12/05
Go up one level in this thread
On January 12, 2005 at 21:47:23, chandler yergin wrote: >On January 12, 2005 at 21:41:47, Michael Yee wrote: > >>On January 12, 2005 at 21:36:05, chandler yergin wrote: >>>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: >> >>[snip] >> >>>>>>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?? >>> >> >>I know the topic is solving chess. My point was that your logic/argument applied >>to even a simpler subproblem of chess goes haywire (and thus must be flawed). >>(That is, if my summary of your points was accurate.) > >Refute the Mathmatics! >I have Posted them... >Otherwise.. Opinion doesn't count. Currently, the way tablebases are solving the game seems like the best method to me. Start with known wins, draws, or losses and calculate backwards. This method seems to require brute force checks. This is a big question for me... Do repeated positions (like dann is talking about) help save time solving the tablebases? Jason
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