Author: Guido
Date: 07:33:04 03/14/05
The EGTB of KQK shows that there is one only position on the board where white, having the move, wins in 10 moves. The position is the following: wKa1, wQb2, bKf5. In this position the results of the possible legal moves are: - 22 moves: win in 10 moves - 2 moves: draw The last two cases (wQb2-e5, wQb2-f6) are clearly related to the possibility of bK capturing wQ. Now the question is: is it only casual (or better pseudocasual) that all the winning moves are perfectly equivalent, i.e. victories in 10 moves, and have we to wonder at this? My answer is no, as it is easy to demonstrate. In fact, if it is evident by hypothesis that no win can be shorter than 10 moves and that, if the wQ is captured, only a draw is possible, we can suppose by absurd that a victory for white exists in 11 or more moves. But after the white has done such move and the black has answered with another move, the new reached position will never be a 10 or more moves victory position for the white because such position will be different from the only one winning position in 10 moves reported above. So what we suppose is absurd and the demonstration is complete! At a first sight it seems a strict reasoning and actually I can confirm that it is correct for KQK but it is not right in two cases: - when the move of the white and the answer of the black can change the composition of the ending by capture or promotion. In KQK this happens in the two draw cases but without influencing the winning moves. In other ending it could happen that some moves of the white are still victories but in more moves than the maximum DTM, or are draws or also are losses. - when after the move of the white and the black the original position has again reached! This second case would seem impossible but suppose that the KQK position of victory in 10 moves had been wKa1, wQb1, bKf5 than the white move wQb1-a2 would be a victory in 11 moves, because black would have answered with bKf5-e6 obtaining a position equivalent by symmetry to the initial. But this doesn't happen with KQK, where the above mentioned position doesn't offer this possibility, because wK and wQ are both on the main diagonal. For association of ideas I finish noticing that the three repetition rule doesn't keep into account positions equivalent by symmetry, even if I think that a similar case would be extremely unlikely. Guido
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