How to defend this?

Hello, everyone, 
would anyone be so kind and try to explain me how to correctly defend this position, if white king doesn’t go a2 in next move? 

I find it pretty hard.  I don’t entirely understand the concept of this endgame.

Thank you very much!

 

wait is you defending as white or blak?

honestly by now I would call a stale / draw it's not going to go well for anyone just kings moving around a lot.

This should be winning for white (there is c5-e7 and f4-h5), but white must play Ka2 next move and then it depends. 1. ...Kg8 2. Ka3 Kf8 3. Kb2! Kg7 4. Kb3 Kf7 5. Kb4 Kf8 6. Kc4 Kf7 7. Kd4 Kf8 8. Ke3. (after 1...Kg7 Kb3). 

But I don’t understand it as I would like to. So my question is: If I was Black and white didn’t find Ka2, What should I do?

 

Edit: apparently the king is on a1 in the original position. You get the idea.

The only thing you'll need to defend is the white King coming in. The white king can enter via c5-d6 of via f4-xg4. We need to prevent that from happening. How can we do that?

If Kc5, we need to play Kd7 or Ke7 to prevent white from playing Kd6. If Kf4, we need to play Kh5, otherwise we lose our pawn. Also, to reach h5 in time, we need to play Kg6 or Kh6 after white plays Ke3.

Now if you combine the two threats, you'll notice that if white plays Kd4 we need to be ready for both threats. We both need to be able to play Kg6/Kh6 after Ke3 by white, but we also need to be able to play Ke7/Kd7 if white plays Kc5. You'll notice that this can only be done from f7. 

What we've done is we've found 'corresponding squares'. If white plays move A, black must move B. 
- If white plays Kc5, black must play Ke7
- if white plays Kd4, black must play Kf7
- if white plays Ke3, black must play Kg6
- if white plays Kf4, black must play Kh5

There are more corresponding squares. If white plays Kd3, he's threatening to play Kd4. We know that after Kd4 our corresponding square is f7, so we need to be able to play Kf7 after Kd4. But white is also threatening Ke3 after which we need to be able to play Kg6. You'll notice that to be able to do both, we need to play Kg7 after Kd3. Again, d3 and g7 are corresponding squares. 

So if c5-e7, d3-g7 and d4-f7 are corresponding squares, there are more. If Kc4, then black needs to be on f8. Otherwise he can't be ready to meet Kd3 with Kg7, Kd4 with Kf7 and Kc5 with Ke7. If that's the case, c3 corresponds with g8. With Kc3, white is threatening Kc4, Kd4 and Kd3 and we know that those squares correspond with f8, f7 and g7. To be able to respond to all of those threats, black's king can only be on g8. If black can't play Kf8 after Kc4, he will lose, but if he steps on a mined square with Kf7 or Kg7, he'd lose to Kd3/Kd4 by white. Again, after Kc3, Ke7 would not be possible, cause white then just plays Kd3 and black can't play Kg7 (the corresponding square) after Ke7.

You can see the list growing by working backwards. We have: 
- on Kd4 black needs to play Kf7
- on Kd3 black needs to play Kg7
- on Kc4 black needs to play Kf8
- on Kc3 black needs to play Kg8

And this continues. You'll find that after Kb4, black would need to play Kf7 (to be in time to play Kg8 on Kc3, Ke7 on Kc5 and Kf8 on Kc4). You'll find that if Kb3, black better not play Kf7 (losing after Kb4), Kf8 (losing after Kc4) or Kg8 (losing after Kc3), so Kb3 corresponds with Kg7 by black.

So we've found the additional corresponding squares: 
- on Kb4 black needs to play Kf7
- on Kb3 black needs to play Kg7

With Kd2, white would threaten to play Ke3/Kd3 or Kc3. Our corresponding squares are: Kg6/Kg7/Kg8. At first glance it would appear that we can defend Kd2 from 2 different squares: Kh7 and Kf7. But there is an additional threat: Ke2. After Ke2 white is still threatening Kd3 and Ke3, so we still need to be able to play Kg6 or Kg7 next move. If black's king is on f7, he can't play Kf6 because of the pawn on e5. So, Kh7 corresponds to Kd2, because after Ke2, he needs to be able to play Kh6.

Our list: 
- Ke2 - Kh6
- Ke3 - Kg6
- Kd2 - Kh7
- Kd3 - Kg7
- Kd4 - Kf7
- Kc3 - Kg8
- Kc4 - Kf8
- Kb3 - Kg7 
- Kb4 - Kf7

Kc2 threatens Kd2, Kd3, Kc3 and Kb3, so next move we'd need: Kh7, Kg7, Kg8 and Kg7 (again). Therefore after Kc2, we need to be able to play Kh8. 

Then Kb2 threatens Kc2, Kc3 and Kb3, so next move we'd need to be able to play Kh8, Kg8 and Kg7. Our king needs to be on h7. 

From a3 white would threaten to play Kb2, Kb3 and Kb4. We'd need to be able to play Kh7, Kg7 and Kf7, so our king needs to be on g8 or g6. 

From a2 white would threaten Kb2, Kb3 and Ka3, so we'd need to be able to play Kh7, Kg7 and either Kg8 or Kg6. And here we see the problem. On Ka2, Black would need to be able to play Kh8 or Kh6 and that is not possible because the black king is already there. 

So our list of queenside corresponding squares: 
- Kd2 - Kh7
- Kd3 - Kg7
- Kc2 - Kh8
- Kc3 - Kg8
- Kb2 - Kh7
- Kb3 - Kg7
- Ka3 - either Kg8 or Kg6
- Ka2 - either Kh8 or Kh6

Now you can see why the other moves are wrong. 
A. if 1. Kb2, black plays 1. ... Kh7, which is a corresponding square
B. if 1. Kc2, black plays 1. ... Kh8, which is a corresponding square
C. if 1. Kc1, black needs to defend against Kd2, Kc2 and Kb2, so defend the squares Kh7 and Kh8. Apparently we can do that from both Kg8 or Kg7.
D. if 1. Ka1, black needs to defend against Ka2 and Kb2, so defend the squares h8 or h6 and Kh7, so Kg8, Kg7 and Kg6 all seem to work
E. But what happens when white repeats the position? Where would black's king need to be to defend Kb1? Kb1 threatens Kc2, Kb2 and Ka2. Black needs to be able to play Kh7 and Kh8 or Kh6. So, Kg8/Kg7/Kg6 are the possibilities.

Therefore the only winning move is 1. Ka2 and we crawl forward with the white king over the squares that correspond to the move black makes.

I can’t thank you enough for this exhausting explanation!  I don’t think I would manage to get it on my own. You really helped me to understand the whole concept of corresponding squares. I can already say that I understand why the other moves are wrong. It took me 90 minutes tho.   

@RAU4ever That's some solid effort right there! I'm just here to praise you. Amazing job!

And THIS is why entire volumes of Chess theory have been written just on Opposition lol

Cheers guys. 

Edit: not wrong after all, just didn't realise the king was on a1, not b1.

The first diagram I sent here was with Ka1 white to move. The second ( Kb1) was meant as a wrong move Ka1 and after black to move (I should have mentioned that, I just flipped the board) (but how? –> I know now.). Maybe that’s the point? Anyway, your explanation of position Kb1 white to move was so helpful! And I think there’s nothing more to say about Ka1 (not Kb1) white to move.  

Oh, the king is supposed to be on a1. I'm so glad! 

Edit: apparently the king is on a1 in the original position. You get the idea.

The only thing you'll need to defend is the white King coming in. The white king can enter via c5-d6 of via f4-xg4. We need to prevent that from happening. How can we do that?

If Kc5, we need to play Kd7 or Ke7 to prevent white from playing Kd6. If Kf4, we need to play Kh5, otherwise we lose our pawn. Also, to reach h5 in time, we need to play Kg6 or Kh6 after white plays Ke3.

Now if you combine the two threats, you'll notice that if white plays Kd4 we need to be ready for both threats. We both need to be able to play Kg6/Kh6 after Ke3 by white, but we also need to be able to play Ke7/Kd7 if white plays Kc5. You'll notice that this can only be done from f7.

What we've done is we've found 'corresponding squares'. If white plays move A, black must move B.
- If white plays Kc5, black must play Ke7
- if white plays Kd4, black must play Kf7
- if white plays Ke3, black must play Kg6
- if white plays Kf4, black must play Kh5

There are more corresponding squares. If white plays Kd3, he's threatening to play Kd4. We know that after Kd4 our corresponding square is f7, so we need to be able to play Kf7 after Kd4. But white is also threatening Ke3 after which we need to be able to play Kg6. You'll notice that to be able to do both, we need to play Kg7 after Kd3. Again, d3 and g7 are corresponding squares.

So if c5-e7, d3-g7 and d4-f7 are corresponding squares, there are more. If Kc4, then black needs to be on f8. Otherwise he can't be ready to meet Kd3 with Kg7, Kd4 with Kf7 and Kc5 with Ke7. If that's the case, c3 corresponds with g8. With Kc3, white is threatening Kc4, Kd4 and Kd3 and we know that those squares correspond with f8, f7 and g7. To be able to respond to all of those threats, black's king can only be on g8. If black can't play Kf8 after Kc4, he will lose, but if he steps on a mined square with Kf7 or Kg7, he'd lose to Kd3/Kd4 by white. Again, after Kc3, Ke7 would not be possible, cause white then just plays Kd3 and black can't play Kg7 (the corresponding square) after Ke7.

You can see the list growing by working backwards. We have:
- on Kd4 black needs to play Kf7
- on Kd3 black needs to play Kg7
- on Kc4 black needs to play Kf8
- on Kc3 black needs to play Kg8

And this continues. You'll find that after Kb4, black would need to play Kf7 (to be in time to play Kg8 on Kc3, Ke7 on Kc5 and Kf8 on Kc4). You'll find that if Kb3, black better not play Kf7 (losing after Kb4), Kf8 (losing after Kc4) or Kg8 (losing after Kc3), so Kb3 corresponds with Kg7 by black.

So we've found the additional corresponding squares:
- on Kb4 black needs to play Kf7
- on Kb3 black needs to play Kg7

With Kd2, white would threaten to play Ke3/Kd3 or Kc3. Our corresponding squares are: Kg6/Kg7/Kg8. At first glance it would appear that we can defend Kd2 from 2 different squares: Kh7 and Kf7. But there is an additional threat: Ke2. After Ke2 white is still threatening Kd3 and Ke3, so we still need to be able to play Kg6 or Kg7 next move. If black's king is on f7, he can't play Kf6 because of the pawn on e5. So, Kh7 corresponds to Kd2, because after Ke2, he needs to be able to play Kh6.

Our list:
- Ke2 - Kh6
- Ke3 - Kg6
- Kd2 - Kh7
- Kd3 - Kg7
- Kd4 - Kf7
- Kc3 - Kg8
- Kc4 - Kf8
- Kb3 - Kg7
- Kb4 - Kf7

Kc2 threatens Kd2, Kd3, Kc3 and Kb3, so next move we'd need: Kh7, Kg7, Kg8 and Kg7 (again). Therefore after Kc2, we need to be able to play Kh8.

Then Kb2 threatens Kc2, Kc3 and Kb3, so next move we'd need to be able to play Kh8, Kg8 and Kg7. Our king needs to be on h7.

From a3 white would threaten to play Kb2, Kb3 and Kb4. We'd need to be able to play Kh7, Kg7 and Kf7, so our king needs to be on g8 or g6.

From a2 white would threaten Kb2, Kb3 and Ka3, so we'd need to be able to play Kh7, Kg7 and either Kg8 or Kg6. And here we see the problem. On Ka2, Black would need to be able to play Kh8 or Kh6 and that is not possible because the black king is already there.

So our list of queenside corresponding squares:
- Kd2 - Kh7
- Kd3 - Kg7
- Kc2 - Kh8
- Kc3 - Kg8
- Kb2 - Kh7
- Kb3 - Kg7
- Ka3 - either Kg8 or Kg6
- Ka2 - either Kh8 or Kh6

Now you can see why the other moves are wrong.
A. if 1. Kb2, black plays 1. ... Kh7, which is a corresponding square
B. if 1. Kc2, black plays 1. ... Kh8, which is a corresponding square
C. if 1. Kc1, black needs to defend against Kd2, Kc2 and Kb2, so defend the squares Kh7 and Kh8. Apparently we can do that from both Kg8 or Kg7.
D. if 1. Ka1, black needs to defend against Ka2 and Kb2, so defend the squares h8 or h6 and Kh7, so Kg8, Kg7 and Kg6 all seem to work
E. But what happens when white repeats the position? Where would black's king need to be to defend Kb1? Kb1 threatens Kc2, Kb2 and Ka2. Black needs to be able to play Kh7 and Kh8 or Kh6. So, Kg8/Kg7/Kg6 are the possibilities.

Therefore the only winning move is 1. Ka2 and we crawl forward with the white king over the squares that correspond to the move black makes.

@RAU4ever da real MVP