Author: Dann Corbit
Date: 15:31:38 12/10/02
Go up one level in this thread
On December 10, 2002 at 18:19:43, Ingo Lindam wrote: >On December 10, 2002 at 18:12:53, Dann Corbit wrote: > >>On December 10, 2002 at 17:55:51, Dann Corbit wrote: >> >>>On December 10, 2002 at 17:51:40, Ingo Lindam wrote: >>> >>>>On December 10, 2002 at 17:30:47, Dann Corbit wrote: >>>> >>>>>On December 10, 2002 at 13:42:36, Bernardo Wesler wrote: >>>>>[snip] >>>>>>THE ALGORITHM. A MATHEMATICAL FORMULA THAT , FOR EXAMPLE, ASSURE YOU THAT IF YOU >>>>>>DO THE FIRST MOVE YOU ALWAYS WIN. >>>>>>I MEAN TO THINK ABOUT DISCOVERING A CHESS ALGORITHM IS AN UTHOPY? >>>>> >>>>>Provably impossible on current hardware and software systems. >>>>>Maybe in 100 years the game will be formally solved. Not in the near futre. >>>> >>>>provably impossible on current hardware...? >>>>are you sure? >>> >>>Absolutely sure. >>> >>>To solve chess you must store at least the square root of nodes of the solution >>>tree. Considering the half move clock and castle rights, it easily exhausts any >>>possibility of solution. >>> >>>>without assuming anything about the kind of solution? >>> >>>No assumptions are necessary. We pick an adversary in the tree. It's just like >>>how you would prove a sort works in O(f(n)). >>> >>>>atleast you are assuming the use of hardware... >>>>(an assumtion I could live with because I wouldn't bet on find the solution >>>>faster by using just a pencil and a sheet of paper :-)) >>> >>>I am assuming that if you turned the universe into silicon chips and devoted >>>half of them to CPU's and the other half to memory storage that all the stars >>>will go out before you find the answer. >>> >>>>me would like to see the proof for 'provably impossible' as much as I would like >>>>to see the solution for chess >> >>10^48 formations * 100 states for half-move clock * 4 bits for castle state. >>sqrt(1.5e+51) = 38729833462074168851792654 [64 moles of positions ;-)] >> >>Assume that you can access one position in one nanosecond -- better yet, we will >>assume that we can correctly compute the value in one nanosecond, access the >>relevant parts and save the result in one nanosecond. We will assume that our >>algorithm is totally optimal and move ordering is perfect so that we can achieve >>the square root of the tree factor. >> >>It would take 38729833462074169 seconds to fill the tree. That is 448261961366 >>days and 1,228,114,962 years. >> >>This is an incredibly conservative estimate. It would probably take at least >>one thousand times that long. > >yes, >this IS an incredible conservative estimate of SOMETHING... >BUT NOT... >of the size/time of a proof/solution. > >the esitmation has completely nothing to do >with the question whether chess is solvable in general or not... > >just try to get the point :-) Happy solving fellows. Don't say I didn't warn you.
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