Author: Dan Newman
Date: 14:20:28 12/24/00
Go up one level in this thread
On December 24, 2000 at 13:21:38, Uri Blass wrote: >On December 24, 2000 at 12:56:31, Robert Hyatt wrote: > >>On December 24, 2000 at 02:58:19, Uri Blass wrote: >> >>>On December 23, 2000 at 18:41:53, Joshua Lee wrote: >>> >>>>Chances are against ever solving chess let alone calculating over 10^120 >>> >>> >>>Programs do not need to calculate over 10^120 in order to be unbeatable in games >>>when the opponent is not important. >>> >>>Uri >> >>I disagree. to be "unbeatable" the program will _have_ to see to the end of >>the game. Anything less leaves the opportunity for an unseen loss. > >The 32 piece tablebases is enough to be unbeatable and you need less than 10^120 >positions in this tablebases. The 32 piece tablebase is enough to make the first few moves, but after the first capture (assuming the perfect game isn't a mate without any captures :) you need the 31 piece tablebases, and so on. The 32 piece tablebase alone would probably take more than all the matter in the universe to store it though. But even it it only took, say, all the matter in the Earth or Mars to construct, I doubt if anyone would ever be willing to do this experiment :). [The above ignores possible (though improbable) breakthroughs in storage technology that can store many bits/atom.] > >It is also possible that calculating 80 plies forward with the right evaluation >function is enough in order to be unbeatable. > >Calculating 1 ply is enough to be unbeatable if you have the perfect evaluation >function but it is clear that it is not practical to have it. > >It is not clear that the case of 80 plies is the same and it is possible that 80 >plies is enough to play perfect when you use Crafty's evaluation function. > >You do not need to know to play every position perfect in order to be unbeatable >but only the positions that you can get practically in games so finding a >position when 80 plies is not enough to play perfect proves nothing. > >Uri Are we searching out 80 plies full width w/o null moves? If so then we have a branching factor of about 5 or 6 and we must vist approximately 5^80 == 8x10^55 nodes. If we take 1000 years (3.15x10^10 seconds) to do this calculation, we must visit 2.6x10^45 nodes/second. If we take a million years it goes down to 2.6x10^42 nodes/second--not much help. Imagine we have a computer a trillion times more efficient than a 1 GHz PIII (which is likely physically impossible) which can do this calculation in one million years, and let's say a PIII consumes 10 W of power. Let's also say the chess program executes at 1 Mnps on the PIII. Then this computer will consume 2.6x10^25 W of power, or the combined output of 26 million billion one-gigawatt electric power plants. Quite an environmental problem :). Also the computer (which must be extremely small) would instantly explode and utterly destroy any nearby city :). [Again, the above ignores the possiblility of breathroughs with, say, quantum computing or whatever...] -Dan.
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