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Distant Opposition Confusion

I'm checking this one out: lichess.org/practice/pawn-endgames/key-squares/xebrDvFe/S8rbDQmn

I don't understand the distant opposition. How can I easily understand why only c2 is a win for white here?

I found this blog, which I thought saved me: http://www.rolandbesblogs.com/opposition.html

The bottom of the blog talks about making a rectangle or square with all the same color corners as the kings and you'll have the opposition. However, in this case above, that move is d2. But, d2 is a blunder.

So...I'm lost. Can someone please straighten me out?
OK. So, I just read something in wiki that struck a chord with me. Opposition is a means to an end. Penetration to a key square is the end. So, in this case, with b5, c5, and d5 being the key squares, I guess I must find a route to one of those key squares that is the same or shorter in number of squares. Black has 3 moves to c5 or d5, and I have 4. However, we both have 4 moves to b5, so I should head that route. I guess it's just that simple.

However, I need to use that concept to understand when i need to keep the opposition or go for the key square and abandon the opposition.
So, I guess the practice one I gave is a situation in which you can get the opposition and still lose because it's giving up the goal of the key square.

Wiki gave this example with the same idea: 8/8/4k3/8/2PK4/8/8/8 w Q -
In order to win a K+P vs K endgame, you must take the opposition with your king in front of the pawn. 1.Kd2 does take the distant opposition, but the king stands behind the pawn. On the contrary, 1.Kc2 manages to take the diagonal opposition with White's king in front of the pawn or (that's equivalent) to reach one of the so-called "key squares" before pushing the pawn. Both formulations of the solution hold.
@QTipPoker

When having the opposition I don't think it's possible to lose as long as you maintain the opposition.

When you play 1. Kd2 Black has 1. ... Ke7 and now if you try 2. Kd3 Black has 2. ... Kd7 distant opposition. Now if you try 3. Kc4 then Black has 3. ... Kc6 gaining the opposition and asking you to move your king.

But when you start with 1. Kc2 Black has 1. ... Ke7 and now when you play 2. Kb3 if Black tries 2. ... Kd7 you can play 3. Kb4 and if Black plays 3. ... Kc6 then you play 4. Kc4 with the opposition and asking the Black king to move. If 3. ... Kc7 then 4. Kc5 opposition and asking the Black king to move again.
Key squares is the more general notion. Opposition and distant opposition are useful shortcuts. Nimzovich in 'My System' disapproves of teaching opposition and advocates using key squares only.

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