Author: stuart taylor
Date: 17:52:38 10/24/02
Go up one level in this thread
On October 23, 2002 at 11:18:03, Robert Hyatt wrote: >On October 23, 2002 at 04:01:37, Tony Werten wrote: > >>On October 22, 2002 at 23:25:36, Robert Hyatt wrote: >> >>>On October 22, 2002 at 22:45:44, stuart taylor wrote: >>> >>>>On October 22, 2002 at 16:21:40, Robert Hyatt wrote: >>>> >>>>>On October 22, 2002 at 14:53:21, stuart taylor wrote: >>>>> >>>>>>On October 22, 2002 at 11:40:40, Robert Hyatt wrote: >>>>>> >>>>>>>On October 22, 2002 at 01:13:43, Timothy J. Frohlick wrote: >>>>>>> >>>>>>>>Sandia Labs is just down the street from me on Kirtland Air Force Base. >>>>>>>>I lived about 1 kilometer from the labs when I lived on base. This "Red >>>>>>>>Storm" machine will do 40,000,000,000,000 operations per second. Put Fritz X >>>>>>>>on that and smoke it. >>>>>>>> >>>>>>> >>>>>>>Put fritz on that and it will use exactly one cpu. That machine is pure >>>>>>>message-passing. >>>>>> >>>>>>If it would use all, I think it should solve chess. >>>>> >>>>>Chess is exponential. Even if it had 16,000 X 16,000 processors, it would not >>>>>be anywhere near enough. >>>> >>>>I know that required speed would be extremely great. But there must be a limit >>>>at which chess would actually be solved, even if impossible to arrange. >>>> And with the application of enough intelligence, that amount of speed could be >>>>reduced significantly to still get the playing strength to a level that will >>>>never lose any game to any machine or man. >>>> I'm not speaking about if it is possible to arrange that in existing levels of >>>>hardware in a PC of today. >>>>S.Taylor >>>>> >>> >>>The math is not so hard. If we take the relatively low estimate of 2^168 total >>>possible >>>positions, which ignores repetition issues and the like, then alpha/beta needs >>>to search >>>roughly 2^84 positions. that turns into 10^25 nodes. If you search 1M nodes >>>per second, >>>you need 10^19 seconds. If you go 1B nodes per second, 10^16 seconds. One >>>trillion nodes >>>per second, 10^13 seconds. >>> >>>10^13 seconds is 318,000 years. A _long_ time. even at 1 trillion nodes per >>>second, which >>>is actually doable should someone like Hsu decide to build a new DB-3 machine... >> >>If the math is correct. Suppose the goal of chess was not to checkmate but to >>get a pawn on e4. The amount of possible positions would be the same except that >>it would be trivial to solve. >> >>Unfortunately we can only tell this when chess is actually solved. If somebody >>finds the 42 ply winning sequence for white then we can say how much positions >>had to be searched. >> >>Tony > >This is like the "decidability issue" in computing theory. > >If the answer to a question is yes or no, then one of the answers might be >computable >while the other is not. > >For example, your case above comes to mind. It might well be that there is a >forced mate >in 30 plies. And if there is, when we can search 30 plies deep we will see the >mate and know >the game is a win for that side. But if there is no forced mate for 80 plies, >we will have to >search 80 plies to prove that, and that is going to take a _long_ time. > >My "math" was based on the premise that we don't know the outcome and that we >will >probably have to search every last possible position, if it turns out that the >game is not a >forced win... That's alot. I would have hoped/thought it would be much sooner than that. But with a significant amount of intelligence, I'm sure it can be reduced to about a 1,000,000,000th of that or less, and confidently never lose a game, or the most, lose one in 500-1000 of top class oposition. S.Taylor
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