Author: Uri Blass
Date: 04:16:09 05/18/01
Go up one level in this thread
On May 18, 2001 at 04:32:14, Graham Laight wrote: >On May 18, 2001 at 00:50:30, Robert Hyatt wrote: > >>On May 17, 2001 at 19:08:15, J. Wesley Cleveland wrote: >> >>>On May 17, 2001 at 05:44:03, Uri Blass wrote: > >>>>You need to write a special program to generate random board even if you want >>>>only 20 samples because there is no easy way to choose a random position when >>>>every position gets the same probability without a special program. >>>> >>>>Uri >>> >>>This seems overly complicated. If you have an encoding method, say, that encodes >>>all positions into 168 bits, then generate random 168 bit numbers and see what >>>percent of the corresponding positions are legal. >> >> >>This is actually very difficult. IE for a position to be legal, you need to >>prove the following: >> >>1. side on move is not in check; >>2. pieces could actually reach the given position (ie if you have 3 pawns on a >>single file, the opponent must be missing at least two pawns/pieces; >>3. the side not on move actually could have made a legal move to get us to the >>current position. >>4. then the side on move actually could have made a legal move to get us to >>that previous position. >> >>IE 3 and 4 are recursive and could be restated: >> >>3a. The position must be reachable from the opening position of the game. >>That is yet another exponential problem. Or is that O(1) too. :) > >This isn't necessarily so (though I admit it might be) - because we're talking >about statistical sampling here. > >In view of Bob's constraints 1. and 2. above, my approach would be to generate >random positions and classify them in one of 3 ways: > >a) Obviously legal >b) Obviously illegal >c) Not sure > >Whether or not this simple approach works depends on the size of c). If it's >relatively small, there's no problem. If it's relatively large, then it >threatens the integrity of the exercise. > >-g I agree I guess that the work about it can be done. You should generate a program to decide if the position is in class a ,b or c and after it to try to find manually for positions in class c if they are in class a or class b. I guess that in almost all the cases it can be done. I guess that composing a position when no human can prove that it is illegal and no human can construct a game to prove that it is legal is not a simple task. Uri
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