Author: Robert Hyatt
Date: 09:50:52 01/13/05
Go up one level in this thread
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. >>>>>>>>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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