Principle 1 – Rule of the Square
In King and Pawn endgames the King plays the part of both the attacker
and defender. This endgame principle looks at both of these aspects. The
King has to both attack the Pawn whilst defending the Pawn's promotion
square.
In this example, the Pawn is advanced on the f5 square, but cannot be
protected by the White King. The Pawn has to try and advance to f6, f7
and f8 to promote. However, the Pawn the can be caught by the Black
King.
To tell whether the King is close enough to the Pawn to catch it before it
promotes we have two choices. One way, is that we can count the number
of squares and work out the possible variations. For example, the Pawn
takes 3 moves to promote (on the f8 square). The King also needs at least
3 moves to reach the promotion square. In this case we can see the King is
quick enough to catch the Pawn before it promotes. However, in a more
complicated position with numerous pawns counting squares can take
value time and lead to mistakes.
A quicker way to check whether the King is close enough to the Pawn is to
draw a line from a Pawn to the promotion square. Use this line as one
side of a square, which must be drawn towards the side of the board that
is furthest away from the Pawn. If the King is inside the drawn square he
is close enough to the Pawn to capture the Pawn. This is shown below.
Note that if the Pawn advances to f6 the Black King must go to either d6
or d7 to remain inside the square, which will now be a 3 by 3 square.
If the Black King was on b4, in this example, he would be outside the
square. Here, with the Black King on b4 and White Pawn on f5 whoever
moves is important. If White was to move, there would be a win for White,
if Black was to move then after bringing his King to c5 (inside the square)
a draw is possible.
This principle and the understanding of the square rule becomes
extremely important when examining endgames where Pawns are used as
decoys or sacrificed, so that other pawns can promote.
Principle 2 – Opposition
Opposition is one endgame principle that cannot have its importance
overstated. Whilst primarily a defensive tool, opposition can also be used
to put your opponent in zugzwang.
Having the opposition can allow the King to gain better control of squares
and advance to a better position. There are numerous types of opposition
(some of which shown below) that occur when the Kings are on the same
colour square with an odd number of squares between them. Whichever
King was last to move has the opposition.
Looking through the King and Pawn endgames will show how opposition
can be used.
Vertical (near) Opposition
Diagonal (near) Opposition
Horizontal (near) Opposition
Distant Opposition
Virtual Opposition
Principle 3 – Key Squares
In King and Pawn endgames there are a number of important principles
to follow. The importance of obtaining the opposition and keeping the
King in reach of the promotion square (see: Pawn Endgame Principles 1
and 2). Another principle that cannot be over-stressed but of equal
importance is understanding the key squares, which depends on the
Pawn's position on the board.
Key squares are those squares, which when occupied by a King, force a
win for the attacking side and a draw for the defending side. Key squares
are best illustrated in simple diagrams, but as you work through the
positions on this site you will see arise in more complicated endgames.
Key squares depend on the position of the Pawn or Pawns in question.
Position 1 - Pawn in Attacker's Half of the Board (Files b to g)
In this first example the pawn is in the attacker's half of the board, i.e. on
the 2nd, 3rd or 4th rank. When this is the case the key squares are the
square 2 ranks in front of the pawn, on the same file, and one square
adjacent to this. In this example, the pawn is on c3: the key squares are
b5, c5 and d5.
If the Pawn was on g2 the key squares would be f4, g4 and h4. Similarly,
if the pawn was on e4 the key squares would be d6, e6 and f6.
If the attacker (White in this case) can manoeuvre his King onto any of the
key squares, whilst protecting his Pawn, the attacker can force a win. It is
worth noting that these positions rely heavily on gaining or maintaining
opposition.
It should also be noted that if the pawn moves the key squares change.
In the example shown, if the White King was on the d6 square there are
three possible moves to get the White King onto a key square. Moving
the King from d6 to either c5 or d5 are two moves. An alternative would
be to move the Pawn from c3 to c4. If the Pawn moves to c4 the King
would be already standing on one of the key squares, which would have
changed to b6, c6 and d6.
Position 2 - Pawn in Defender's Half of the Board (Files b to g)
The closer a pawn gets to the 8th rank the greater it's value. It therefore
makes sense that once a pawn has passed into the defenders side of the
board it becomes harder to defend. The result of progressing passed the
4th rank is that the number of key squares doubles. The original key
squares are the same key squares as a pawn in the attacker's half plus the
3 squares directly in front of the pawn. In this example, the pawn is on c5:
the key squares are b6, c6, d6, b7, c7 and d7.
If the Pawn was on g6 the key squares would be f7, g7, h7, f8, g8 and h8.
It is the objective of the attacking king to manoeuvre onto one of the key
squares, whilst protecting the pawn.
The pawn's "force of radius" (squares it attacks) being the ones directly in
front of it on the diagonals. In the example the pawn being on c5 means
the force of radius is on the squares b6 and d6 (both key squares). The
opposition King cannot occupy these squares, making them natural
targets for the attacking King, but they can be defended by the defending
King (usually by occupying the square directly in front of the pawn).
If the pawn progresses to the 7th rank the 3 squares directly in front of
the pawn on the 8th rank are the key squares. For example a pawn on e7
has the key squares d8, e8 and f8.
Position 3 - Pawn on the Flank (Files a or h)
The number of key squares for flank pawns drops dramatically, and more
importantly do not exist until the pawn has progressed to the 6th rank.
The reason for both of these principles is that flank pawns are harder to
promote.
If the defending King can get to the promotion square there is no way of
forcing the King out of the corner, and the pawn cannot promote, because
both key squares are covered.
The promotion square and square directly in front of the Pawn are also
not key squares, in the example the squares a7 and a8. This is because
the defending King can trap the attacking King on the flank by gaining
direct horizontal opposition, by occupying the squares c7 and c8
respectively.
The defending King should be aiming to occupy the one key square it can,
in the example above this is the square b8.
It is worth noting that even if the pawn is not as advanced as the 6th rank
the defending King does not have to "attack" the pawn. Simply moving
between the corner square and adjacent square, on the same rank, will
result in a draw. For example a pawn on h2 can be stopped from
promoting by the defending King moving between g8 and h8, repeatedly.
For examples of where these principles are applied in order to win or draw
games see www.michael-quigley.com .
– Michael Quigley