Author: Bruce Moreland
Date: 19:08:03 11/09/99
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On November 09, 1999 at 18:51:52, Marc Plum wrote: >Two Knights and a King can never mate a lone King. You may well be thinking of >the ending King and two Knights vs. King and one pawn. This is often a win for >the two Knights if the pawn is blocked and isn't too far advanced. The reason >is that the availability of pawn moves at a critical juncture will prevent >stalemate. The ending is horribly difficult for humans, and at one time, the 50 >move rule draw was extended to 100 moves for some positions with this material >balance. > >There are, I believe, endgame tablebases available for this, and other people >may be able to tell you what they show, but let's also give due credit to a >human who worked before computers. The Russian endgame composer Alexei Troitzky >(1866-1942) did a lot of work on this ending, I haven't heard that any of his >work has actually been refuted by computers, although I'm sure many details have >been filled in. It was his analytical work, according to the "Oxford Companion >to Chess" that led to that revision of the 50 move rule, mentioned above. The major elements of Troitsky's work were proven correct. In particular he defined some zones that the weaker king must be in in order to draw, and these were proven correct. I believe that even this ending is subject to the 50-move rule now. The reason is that Thompson found many other endings that could conceivably take more than 50 moves to win, and the professional players balked at having a huge number of exceptions to the rule in order to cover these cases. bruce
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