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Prove that a position is legal and reachable.
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H.G.Muller



Joined: 10 Mar 2006
Posts: 12774
Location: Amsterdam
PostPost subject: Re: Prove that a position is legal and reachable.    Posted: Thu May 17, 2012 8:39 am Reply to topic Reply with quote
Uri Blass wrote:
I do not think that unreachable positions are extremely rare.

'Extremely rare' should be understood in the context of the total number of positions. So there coud be billions, and they could still be extremely rare, because the state space of Chess is so large.

Quote:
There are many positions when the pawn structure is illegal
or it is simply impossible for pieces to go to the relevant square(for example white Bh8 black king g7).


Testing if a Pawn structure is reachable is actually quite feasible. For one there are a few easy heuristics to establish that a structure is not reachable, (e.g. white pawns on a2, a3 and b2) based on Pawn counts below each diagonal, in each file, and number of missing opponent pieces. Exhaustive (retrograde) search is qite possible with only Pawns.

The in-check problem is a short-term one. Positions like you describe, or triple checks, etc., are immediately caught because you cannot even do a single retro-move to a legal position.
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Subject Author Date/Time
Prove that a position is legal and reachable. Dustin Yoder Wed May 16, 2012 11:23 am
      Re: Prove that a position is legal and reachable. Julien MARCEL Wed May 16, 2012 11:45 am
            Re: Prove that a position is legal and reachable. Arpad Rusz Wed May 16, 2012 1:22 pm
      Re: Prove that a position is legal and reachable. Uri Blass Wed May 16, 2012 1:28 pm
      Re: Prove that a position is legal and reachable. Ricardo Barreira Wed May 16, 2012 1:49 pm
            Re: Prove that a position is legal and reachable. Julien MARCEL Wed May 16, 2012 1:55 pm
                  Re: Prove that a position is legal and reachable. Sven Schüle Wed May 16, 2012 2:43 pm
                  Re: Prove that a position is legal and reachable. H.G.Muller Wed May 16, 2012 6:25 pm
                        Re: Prove that a position is legal and reachable. George Tsavdaris Sat May 19, 2012 2:22 pm
      Re: Prove that a position is legal and reachable. Edmund Moshammer Wed May 16, 2012 2:49 pm
            Re: Prove that a position is legal and reachable. George Tsavdaris Sat May 19, 2012 1:50 pm
      Re: Prove that a position is legal and reachable. Joona Kiiski Wed May 16, 2012 6:39 pm
            Re: Prove that a position is legal and reachable. H.G.Muller Wed May 16, 2012 6:50 pm
                  Re: Prove that a position is legal and reachable. Alex Brown Wed May 16, 2012 10:57 pm
                        Re: Prove that a position is legal and reachable. Sven Schüle Thu May 17, 2012 9:01 pm
                              Re: Prove that a position is legal and reachable. Sven Schüle Thu May 17, 2012 9:27 pm
                                    Re: Prove that a position is legal and reachable. Arpad Rusz Thu May 17, 2012 9:58 pm
                              Re: Prove that a position is legal and reachable. George Tsavdaris Sat May 19, 2012 2:40 pm
                                    Re: Prove that a position is legal and reachable. Sven Schüle Sat May 19, 2012 8:56 pm
                                    Re: Prove that a position is legal and reachable. Alex Brown Sat May 19, 2012 9:27 pm
                  Re: Prove that a position is legal and reachable. Uri Blass Thu May 17, 2012 2:55 am
                        Re: Prove that a position is legal and reachable. H.G.Muller Thu May 17, 2012 8:39 am
      Algorithm Ideas Dustin Yoder Wed May 16, 2012 6:48 pm
            Re: Algorithm Ideas fernando Sat May 19, 2012 5:12 pm
      Re: Prove that a position is legal and reachable. Robert Hyatt Thu May 17, 2012 9:59 pm
            Re: Prove that a position is legal and reachable. George Speight Fri May 18, 2012 2:34 am
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