Author: Duncan Roberts
Date: 12:52:19 01/13/05
Go up one level in this thread
On January 13, 2005 at 12:50:52, Robert Hyatt wrote: >On January 12, 2005 at 21:47:05, Les Fernandez wrote: > >>On January 12, 2005 at 21:21:34, Dann Corbit wrote: >> >>>On January 12, 2005 at 21:18:22, chandler yergin wrote: >>> >>>>On January 12, 2005 at 21:13:08, Dann Corbit wrote: >>>> >>>>>On January 12, 2005 at 21:09:16, chandler yergin wrote: >>>>> >>>>>>On January 12, 2005 at 21:02:01, Dann Corbit 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! >>>>>>> >>>>>>>You do not have to solve every game. Only every position. Look at the two >>>>>>>chess games that I posted. The end position for both was identical. In fact, >>>>>>>despite the many moves, there are only a very few positions that are distinct. >>>>>>>For each of those positions, if you know the best move, you do not care how you >>>>>>>got there. >>>>>>> >>>>>> >>>>>>How do you now the "Best Move" until you have calculated them ALL? >>>>> >>>>>The miracle of alpha beta is that it allows you to prune away huge chunks of the >>>>>tree and get EXACTLY the SAME answer you would get if you examined every single >>>>>leaf. >>>>> >>>>>>Hmmm? >>>>> >>>>>Read a paper on alpha-beta and you will find the answer. >>>> >>>>Still doesn't come CLOSE to 10^ 120th Power for Solving ANYTHING! >>>>Also.. there are positions for "Underpromotion" which you don't take into >>>>account. >>> >>>Underpromotion is also completely irrelevant. Each of the possible outcomes of >>>promotion is simply a new position. Those positions have already been counted >>>in the set of 10^43 distinct positions. So you see, underpromotion does not >>>even complicate things at all. >>> >>>>That's WHY 7 man EGTB'S will NOT jump the ELO Rating... >> >>#1 Chandler just because we do not see a measurable advantage that 6 piece >>egtb's offer a computer doesnt mean that a larger,ie 10 piece egtb, wouldnt be >>measurable. Think about it. With only 6 pieces on the board most GM's I >>suspect would know how to handle that even though some of the 6 piece egtb's can >>be very tough even for them. Now if that GM was to try and develope a workable >>approach to survivng an endgame for which we have perfect information for 10 >>pieces I doubt in most cases he could survive (IMHO). I suspect the benefits of >>egtb's will become more obvious as we develope large sets. >> >>#2 In one of the other threads of yours you mentioned the incredible magnitude >>of chess positions and that there was 0% chance of solving chess. Well in >>support of Dann's statement where he corrected your figure of 10*120 let me just >>say that although perfectly ordered alpha-beta solution will reduce this number >>I can probably also reduce that number quite a bit further when we talk about >>unique positions vs positions. Although the task "seems" unattainable you just >>probably have not looked at all kinds of methods that may offer ways of trimming >>down that one number that you are baseing all your thoughts on. Keep an open >>mind, we see this stuff happen every day in technology. >> >>Les >> > > >This is irrefutable: Each successive generation of tables provides a _higher_ >strength improvement than the previous generation, until we get the 32 piece >tables done at which point perfect chess will be played. We won't reach there >for a long time, if ever (never is such a long way away I try to not use it) but >from personal experience, having started off with just 3-4 piece files, then >adding all the 5's, I can assure you that the 5 piece files added much more to >my program than the 3-4 piece files did. And the 6's have added even more even >though all are not done. I can't say it is an exponential growth with so few >data points, but I can say without fear of being proven wrong later that it is >just as clearly more than a linear growth in playing strength. could you comment about the table base searches slow the software down a lot. duncan > > > > >>>>>>>>>tree >>> >>>That has more to do with disk access time. But I expect that judicious use of >>>the data will increase Elo ratings. >>> >>>>They, can't even be solved yet.. and NOT in your lifetime either.. will they.. >>>>or for future generations to come. >>>>STOP! The NONSENSE!
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