More concrete

 

Have a good look at the following position.

White to move wins. Black to move draws

4R3/8/7K/8/1kp5/8/8/8 w - - 0 1

Moves are low level concepts. They are mainly geometrical. We have been long on the wrong foot by giving geometrical patterns way too much attention. Geometrical patterns transfer poorly to other positions. Concepts do a much better job for transferring knowledge between positions.

What is going on in this position? What concepts can we distill from it which transfer to similar positions?

• White wants to win by conquering the pawn without the need to give up the rook
• Black wants to promote the pawn, thus forcing white to give up the rook
• This is a kind of freak position, since white to move wins and black to move draws with best play. With the white king in an other position it is always a win or always a draw, no matter who is to move.
• The same techniques apply for similar positions, if the black pieces are translated a file to the left or the right, for instance. Or a rank up or a rank down
• White can only win the pawn when both his king and his rook attack it
• Black can try to prevent the contact of the white king with the pawn by shouldering him away
  
• Black can only draw by promoting his pawn
• In tempo positions like these, one tempo makes the outcome of the game. Who has the first move decides the game.
• If white makes an error, black can gain a tempo. If for instance white plays 1. Rc8, black is in time to shoulder away the white king and promote by 1. ... Kc3!

Most listed concepts are applicable to a host of endgames. The amount of concepts don't seem endless at all. What is needed is awareness of the concepts that play a role. And a clear idea what you are after and why. The real work is done by calculation. But you MUST know what you want to achieve in any endgame position. As concrete as possible!