Author: Les Fernandez
Date: 18:47:05 01/12/05
Go up one level in this thread
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 >>>>>>>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!
This page took 0.02 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.