King and Pawn Endings: Key Squares
Key Squares are what we call those squares whose occupation by the king assures victory, regardless of whose turn it is to move.
In other types of endgame, we may also speak of key squares for other pieces besides the king.
In general a pawn has its three key squares located two ranks above its current position. Although when this pawn has crossed over into the opponents half of the board it generally has six key squares. (three squares two ranks up and another three on the next rank up).
Capablanca summed it up simply in his book titled 'A Chess Primer':
The King must be, generally speaking, ahead of its pawn with at least one intervening rank between them.
The d5-square on which the king now stands is not a key square - White to move does not win. The key squares are c6, d6 and e6. Black to move must retreat his king, allowing the enemy king onto one of the key squares. With White to move, the position is drawn, since he cannot move to any key square.
With the pawn on the 5th rank, the key squares are not only a7, b7 and c7, but also the similar 6th rank squares a6, b6, and c6. White wins, even if he is on move.
1.Ka6 Ka8 2.b6 Kb8 3.b7 +-
Note that 1.Kc6 is inaccurate, in view of 1...Ka7, when White has to return to the starting position with 2.Kc7 (2.b6 Ka8 =) 2...Ka8 3.Kb6 (again, 3.b6 is stalemate) 3...Kb8 4.Ka6
The Key squares are a6,b6 and c6. The sensible thing here is to head for the square furthest from the enemy king, since that will be the one hardest to defend.
1.Kc2 Ke7 2.Kb3 Kd6 3.Ka4 (3.Kc4? Kc6 =) 3...Kc6 4.Ka5 Kb7 5.Kb5