Author: Angrim
Date: 21:13:33 05/12/01
Go up one level in this thread
On May 12, 2001 at 01:49:19, Robert Hyatt wrote: >On May 12, 2001 at 00:48:17, Angrim wrote: > >>On May 11, 2001 at 22:24:21, Robert Hyatt wrote: >> >>>On May 11, 2001 at 15:49:19, Angrim wrote: >>> >>>>On May 11, 2001 at 03:29:43, Dann Corbit wrote: >>>> >>>>>On May 11, 2001 at 01:49:03, Angrim wrote: >>>><snip> >>>>>>If your goal is to determine how hard it is to solve chess, then yes. >>>>>>Rather then go into a lengthy rant here, let me give an example. >>>>>>The following position has pawns advanced a total of 4 squares, so >>>>>>subtract 4*50 from the max depth, and your math suggests that there are >>>>>>38^(5900 -200) total games of chess that can result from this position. >>>>>>However, the position is trivial. No need for sqrt(38^(5900 -200)) >>>>>>positions to be searched or stored... >>>>>> >>>>>>[D]rnbqkbnr/pppp1ppp/4p3/8/6P1/5P2/PPPPP2P/RNBQKBNR b KQkq g3 0 2 >>>>> >>>>>Yet there are many quintillions of quintillions of qintillions of games that can >>>>>sprout from here. >>>>> >>>>My point being that if your goal is to solve this position, then all >>>>but 1 of those games is totally irrelevant.\\\\\ >>> >>> >>> >>>Unfortunately they are _not_. Because you have to _prove_ that the best >>>move is best. And to the best of my knowledge, there is no "oracle" that >>>will give us perfect move ordering so it is not just likely, it is highly >>>probable that the winning move won't be searched first. Maybe it will be >>>searched by the 1/2 way mark at this play, maybe it will be last. But >>>if it isn't first, you have a HUGE tree to search first... >>> >>>That's the way alpha/beta works... not best-first but alpha/beta... >>> >>> >> >>did you happen to look at the position? >>You need to look at exactly 1 line to prove that it is the best line. >>If you are unlucky you might need to look at 30 or so other lines first >>to find this line, > > >Do you understand how a tree search works in the "depth-first" world of >alpha/beta and minimax? If you do, then you would realize your question >is not sensible in that context. > > > >>but my point was that the "many quintillions of quintillions of >>qintillions of games" that can result from this position are irrelevant. > > >Not to alpha/beta minimax they are not. If we could assure "perfect" move >ordering, then we would be able to find the instant mate and simply have to >prove that no other move here can mate in a shorter distance than 1 which >is impossible of course. But without perfect move ordering, we might not >find the check/mate first, and then we do search zillions of games following >_another_ move first... we will eventually find the mate, but only after we >search one or more other moves first... > > > >>The fact that with worst play games thousands of moves long could result >>from this line is also irrelevant. > > >Again, no they aren't. That is not the way minimax works. > Carefully forgetting about iterative deepening? I lack the patience and stamina to continue this thread. Both sides of the case have been clearly stated already, so anyone who cares who is right can come to their own conclusions. Angrim
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