Author: chandler yergin
Date: 21:41:05 01/12/05
Go up one level in this thread
On January 12, 2005 at 21:56:52, Jason Kent wrote: >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 YOU GOT IT! Thank You! >>>>>(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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