I would play Kc3. Then, whatever White’s next move is, Black should go Kc2. If White then plays e3, Black goes back to c3 and plays for the draw. Otherwise, d2 and White’s king is forced out of the scrum, losing the d3 pawn.
If 2. Ke1 Kc3 again forces 3. Ke2 and Black forces the White King away from the pawns as in Anon’s analysis.
If 2. Kf3 Kc1 3. Ke3 Kd1 transposes to the 2. Kf1 line given by Anon. White can’t maintain the opposition by playing 4. Kd3 because the pawn is in the way, and if he maintains the opposition by playing 4. Kf3 then 4. … Kd2 wins the pawn.
If 2. Kf3 Kc1 3. Ke2 Kc2 Black has the opposition and White must either give up the pawn immediately or transpose to the above line.
If 2. Ke3 Kc1 3. Ke2 (if 3. Kf3 Kd2 wins even faster) Kc2 again maintains the opposition and transposes to the above lines.
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But 1. … Kc3 suggested by GLI allows White to maintain the opposition.
1. … Kc3 2. Ke3 Kc2 3. Ke2 Kc3 4. Ke3 and draws.
Establishing the opposition may not always be the best move, but it’s usually a good place to start in your analysis.
Of course
1… Kb2 wins easily
for example:
2. Kf1 Kc3
3. Ke2 Kc2
4. Ke3 Kd1
5. Kf3 Kd2
Black king to his pawns: “yes we can!”
I would play Kc3. Then, whatever White’s next move is, Black should go Kc2. If White then plays e3, Black goes back to c3 and plays for the draw. Otherwise, d2 and White’s king is forced out of the scrum, losing the d3 pawn.
Straightforward opposition + Zugswang endgame.
To expand on Anon’s solution:
If 2. Ke1 Kc3 again forces 3. Ke2 and Black forces the White King away from the pawns as in Anon’s analysis.
If 2. Kf3 Kc1 3. Ke3 Kd1 transposes to the 2. Kf1 line given by Anon. White can’t maintain the opposition by playing 4. Kd3 because the pawn is in the way, and if he maintains the opposition by playing 4. Kf3 then 4. … Kd2 wins the pawn.
If 2. Kf3 Kc1 3. Ke2 Kc2 Black has the opposition and White must either give up the pawn immediately or transpose to the above line.
If 2. Ke3 Kc1 3. Ke2 (if 3. Kf3 Kd2 wins even faster) Kc2 again maintains the opposition and transposes to the above lines.
——
But 1. … Kc3 suggested by GLI allows White to maintain the opposition.
1. … Kc3
2. Ke3 Kc2
3. Ke2 Kc3
4. Ke3 and draws.
Establishing the opposition may not always be the best move, but it’s usually a good place to start in your analysis.
1.- Kb2 and black has distant opposition and wins easily.
1.- Kc2 or – Kc3 and white gets the opposition and dead draw.