Author: Dann Corbit
Date: 15:28:08 12/10/02
Go up one level in this thread
On December 10, 2002 at 18:24:20, Uri Blass 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 ;-)] > >Most of the legal positions are irrelvant for solving chess because they can >happen only after both sides play illogical moves. They are still fully relevant. You might throw away your queen and both rooks and still win (in fact, it has been done). >I do not know the number of legal positions but I know no proof that there are >more than 10^40 and I know no proof that the relevant legal positions to solve >chess are more than 10^20 > >positions like 1.a4 a6 may be irrelevant to solve chess if you find that 1.a4 is >losing against 1...e5 when 1.e4 is not losing. In order to prove that they are irrelevant, you will have to solve the tree. In order to solve the tree you will have to compute and store it. >in that case knowing the theoretic result after 1.a4 a6 is going to change >nothing. > >Tree is only one way to prove things. > >It is possible to prove that KQ vs K without the 50 move rule win in n*n chess >board for every dimension n. Believe it or not, you form a tree to solve it. You might have an alternate formulation, but a tree solution will be perfectly equivalent and optimal. >Of course proving that it happens for all n's cannot be proved by tree or >tablebases. Unless the tree is large enough or the tablebase has 32 pieces in it.
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