20 Oct '06 19:02>9 edits
White's turn. What is the only drawing move?
Originally posted by David113My guess is a king move.🙂
[fen]6k1/1p6/1P1p4/3p4/3Pp2p/4P2p/1K5P/8[/fen]
White's turn. What is the only drawing move?
Originally posted by Mephisto2Can you show me where Ka1 draws whereas ka2 loses? I don't see a differance. Like you said, if black gets to g4, from Ka2 the king also gets to e2 just as easily and likewise can still get to b5 after black gets to d7. I can see triangulation ways of getting to b5 or e2 from almost any position on the white side. For instance, 1 kc1, still stops the black king from entering even though it can't get to b5, getting to a5 still stops the black king entering even after getting to c6.
Ka1. White needs to make sure he can reach the 'corresponding' squares of the black king (extension of 'remote opposition'😉 in order to be able to counter every black king move to either side: Kg4 must be met with Ke2, and Kc6 must be met by Ka5. I am not an expert, but I think this is an example of 'heterodox' opposition: away from the pawns, either king ...[text shortened]... ive (draw for white, win for black). And b2 and f7 are the starting points to either side.
Originally posted by sonhouseLet's try a few lines.
Can you show me where Ka1 draws whereas ka2 loses? I don't see a differance. Like you said, if black gets to g4, from Ka2 the king also gets to e2 just as easily and likewise can still get to b5 after black gets to d7. I can see triangulation ways of getting to b5 or e2 from almost any position on the white side. For instance, 1 kc1, still stops the black k ...[text shortened]... can't get to b5, getting to a5 still stops the black king entering even after getting to c6.g
Originally posted by Mephisto2That is one interesting problem. I still have to digest it all. I went through most of your notes and still am not totally convinced a1 is the only way to a perfect draw but I am studying it you can be sure!
Let's try a few lines.
1) after 1.Ka1, black can try several things
1a) ... Kf7 2.Kb2! Ke7 (Kf6 then Kc2; Ke6 then Kc3; Kg6 then Kc1; Kf8 then Ka2 etc...) 3.Kb3 Kd7 4.Kb4 and white is in time to reach a5 4. ... Ke6 5.Kc3 and white is in time to follow and reach e2 in time
1b) ... Kg7 2.Kb1 Kf6 3.Kc2 and if Kg5 then Kd1 or if Kf5 then Kd2 or if Kg6 ...[text shortened]... he opposite colour square each move.
This is not comprehensive, but it should give an idea.
Originally posted by sonhouseIt looks more complicated than it is. The starting point is that there are two threats (invasion points for the black king), and there are pivotal squares between the two: a2 and f7 are two of them. If white cannot move Ka2 as a response to Kf7, then he is in zugzwang and has to make a choice, leaving the other way open. From a2 and f7, you can easily derive the other 'corresponding' squares. The idea is not different from the basic 'opposition', extended to 'remote opposition' and 'corresponding squares' up to 'corresponding domain', the latter being the set of connected corresponding squares. The fact that in this case the corresponding squares are of opposite colour, makes it in fact very easy to play this without much thinking, once you determined the correspondence. You could blitz it out.
That is one interesting problem. I still have to digest it all. I went through most of your notes and still am not totally convinced a1 is the only way to a perfect draw but I am studying it you can be sure!
This seems to be the most complicated series of king manouvers that can happen on the board with only pawns and kings. Do you know of any more of equal but differant kinds of manouvers leading to draw?