Author: Urban Koistinen
Date: 08:15:04 04/08/01
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On April 08, 2001 at 08:41:19, Uri Blass wrote: >1)I tried to explain the paper in more words in order to understand it and the >first part that I did not understand was the sentence: >"t4 depends on t3 and d" >It seems to me that t4 is dependent also on t1. > >Here is an example of position in t4 > >[D]2k5/8/2K1Q3/8/8/8/8/8 b - - 0 1 > >The position after Kb8 is in t3 but the position after Kd8 is in t1. Any position in t1 is also in t3 and t(2n+1) because if a position is a win for white with g50=x it is also a win for white with g50>x. >I prefer not to try to understand the rest of the paper before I understand this point. > >2)Here is my explanation of the part that I did understand: > >I call capturing or pawn move in the same word conversion. > >tables ti are clear >They include all the positions when it is a win for white but white need i plies to get the conversion. For even i: ti is legal and a loss for black with g50=i For odd i: ti is illegal or a win for white with g50=i If white win with g50=i, white obviously win if g50>i. >Table d include only legal positions that are not stalemate and black cannot >save itself by conversion. Include <=> value=1 >We want to find positions that are win for white. >other positions are not intereting because it is obvious that they are not win >for white. > >It is clear that t1 depends on t0 and previous tables that can be reached by a >conversion(a position is in t1 only if white wins by conversion or by checkmate >in 1 ply). > >t2 are positions when black is to move. >The position is legal and black cannot save itself by conversion and it means >that t2 is included in d. >If black try to play a move that is not conversion it gets to position in t1 so >it depends also on t1. > >t3 are positions when white is to move. >White cannot win by conversion otherwise the position is in t1. >White can get by a move that is not conversion to position in t2. > >This is the reason that t3 is dependent on t2 and t1. Yes, t3 can be computed by computing: or(t1,max(reachable(t2))). Urban Koistinen
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