Author: Dann Corbit
Date: 13:40:51 01/20/05
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On January 20, 2005 at 10:25:22, Robert Hyatt wrote: >On January 20, 2005 at 07:41:30, Volker Annuss wrote: > >>The number of possible positions as well as the number of possible games is >>limited. > > >Let's do _not_ go there. Chess is finite, for sure. But its space is so large, >that today we can treat it as infinite, because no hardware can search the tree >in any time-frame that is meaningful. It is an exponential problem, which is >beyond the discussion of P/NP type problems, even though it is a finite game. >There is theory and there is reality. Reality is it is effectively infinite >today. And for some time yet to come. > >And theoretically it is an infinite game as well, since the 50 move rule is not >a _forced_ draw, either (or both) sides can continue playing right through the >50 move rule if they so choose, which further makes this a very hard exponential >problem. For that matter, every NP-hard problem will be finite, if we limit the problem size. For instance, the TSP problem is finite, because there are not an infinite number of cities on the earth. But pragmatically, we may as well call it open in size, because we can't solve the minimum path through every city on earth right now. 100 years from now, we may no longer classify it in that way.
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