Opposition is part of a much more complicated theory Keres developed, the "theory of the related squares".The theory applies in pawn endgames and only if white(attacking side) doesn't have already a winning position.According to that theory:
"For every move white does there is a related Black move that draws."
and vice-versa
"For every move black does there is the related white move that wins."
The theory of the related squares and opposition are actually exactly the same thing but with more pawns the simplicity of opposition is no longer enough.It is known for many years that the restricted theory of opposition is inadequate to explain a lot of the complexities of pawn endgames(if it is possible to be explained).In their last book "Fundamental Chess Endings", Karsten Muller and Frank Lamprecht present a new opposition("virtual opposition"). There is no need to examine so much complicated concepts but if we want to develop an understanding for endgames we must develop our ability to think schematically.This means being able to spot specific placement of the pieces in a given position that give us the win(if we are the attacking side) or the draw(if we are the defending side).
Let's explain that with 2 examples:
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Theory of the related squares and opposition are the same thing when there is only one pawn no the board.
At the above position , how can black draw?
He must examine what white must do to win.Let's see it one by one:
1)When black plays to e5,if white plays to e3(related square), black is forced to move and white penetrates and win.The same position is also a winning opposition for white
2)When black plays to f5 , white must play to f3 to win(related square and opposition)
3)When black plays to e6 white must to play e2 to win(related square and distant opposition)
But the pawn is at e2 and that means that white can't play Ke2.That immediately gives us the move with which black draws, 1...Ke6
The related squares can help us in more complicated positions
White has the move , but can he win?
To answer that White must think schematically.The related squares are determined by the zugzwang positions.
We say that a player is in zugzwang when every move he makes , loses. In other words passing would be by far the best move if the rules allowed such a thing.In pawn endgames there are positions that are called "reciprocal zugzwang" because both sides have no move to play.Every opposition is a reciprocal zugzwang position because the side that has the move , loses(defending side loses the game , attacking side loses the win).
By determining the reciprocal zugzwang positions(RZP) we determine the related squares.In our example, the following position is the RZP
In that position the side that has the move , loses the game.If we translate that to related squares it means that when black plays Kf4 white has to play Kd5(related square) or from Black's point of view, when white plays Kd5 , black must play to Kf4.That easily gives the answer....
We will examine some advanced concepts here and maybe share some thoughts.
I don't advise anyone that doesn't kunderstand very well the basic endgame concepts (like opposition) to read this because he/she , probably, will be confused.
p.s. I have seen though people having trouble understanding simple things while at the same time they can understand very difficult and complicated concepts with the first try.