Richard Chen

Chess Endgames 5: King + Pawn vs. King, Part 2

Last Edited January 3, 2016
Created April 9, 2016

Hey y'all, so I figured that the concept of the opposition requires a little more explanation, given how confusingly it was presented in the previous example. It takes a little time to wrap your head around, but in the end you'll find that more than not, seizing the opposition is more often a way to win than a waste of time.

Recall that, in a chess game, a player has the opposition if:

  1. There is an odd number of spaces between the enemy kings;
  2. It is the other player's turn to move.

It's a simple enough idea, but somewhat forgettable without any context. The basic intuition behind why it works is because the side to move must move his/her king, and as a result, cede territory to the opponent's king. Although in the example below (as well as in most pre-endgame situations) it doesn't mean much, with a small number of pieces on the board, having the turn to move can, in many cases, become a liability.

Let us turn our attention to Figure 1 again:

Let's first examine the position with white to move. Pushing the pawn, in this case, is really, really bad...
1. e6?
For those of you who read the post before this, you know this is not good, because not only can Black now oppose the pawn, but (s)he can also draw the game altogether!
1. ...Ke7!
2. Ke5Ke8!
Once again, preventing the opponent from taking the opposition is a key idea here. If Black plays 2. ... Kd8?, then (s)he's screwed because White can seize the opposition with 3. Kd6! There is one square between the kings and it's Black's move, and so follows 3. ... Ke8 4. e7 Kf7 5. Kd7, squeezing the king out and allowing a promotion for White to win. See how the principle works?

White now has nothing better than to offer a draw, as (s)he can't get further than that by moving:
3. Kd6Kd8!
Again, notice how Black seizes the opposition, preventing advance. Similar is 3. Kf6 Kf8!

Might as well...
4. e7+Ke8
5. Kd6
½ - ½
...and Black succeeds in defending against White's passed pawn.

White's first move here was clearly in violation of the idea of taking the opposition. If White plays 1. Ke6! here instead, notice what happens. He seizes the opposition, because (1) there's an odd number of squares between the kings, and (2) it's Black's move. Let's have a look at this alternate path:
1. Ke6!
Now Black is forced to yield to White's king, allowing it to guard several critical squares:
1. ...Kd8
2. Kf7Kd7
Even a 5-year-old could see the writing on the wall: Black is lost, because White's king now protects every square in the e-pawn's path, and there is nothing Black can do to nab the pawn or prevent its progress.

3. e6+Kd8
4. e7+Kd7
5. e8=
Q +
1 - 0
As you can see, seizing the opposition is often more advantageous than not, and often revolves around the intuitive premise of having to move and yield territory. Here White played smartly, and as a result, was able to queen his pawn easily.

We now turn our attention to another critical idea regarding king and pawn vs. king endings: critical squares.

Critical Squares

In king and pawn vs. king endings, critical squares refer to squares that, for the side with the sole pawn, guarantee the pawn's promotion if the advantageous side's king is on them. If a pawn is on a certain square, then any square that is two squares up, or two squares up and to the left/right are critical squares for the king: for the side with the pawn, if his/her king stands on any of those squares, it is guaranteed that (s)he will promote the pawn.

It's easier to show than explain. Here's an example:

If White's king, for instance, is on c4 (this is assuming the other pawns aren't on the board, and Black only has his/her king), then White can guarantee the promotion of his b-pawn. If White's king is on c6, d6 or e6 (under the same assumptions), then (s)he can guarantee the promotion of his d-pawn; and if Black's king is on f3, g3 or h3 (under the same assumptions but with colours swapped), then (s)he can guarantee the promotion of his g-pawn.

The rules behind this are somewhat different for pawns on the 5th, 6th and 7th rank. For pawns on the 5th rank, the critical squares are one rank upwards (or downwards for black) rather than 2, so a White pawn on c5 has critical squares on b6, c6 and d6. For pawns on the 6th rank, the critical squares are also one rank upwards or downwards. For pawns on the 7th rank, the critical squares are on the seventh rank beside the pawn, and the 8th in front of or behind the pawn.

Let's see yet another example of this in action:

All Black needs to do is guarantee that (s)he can occupy f3, g3 or h3 for the pawn, as these are all critical squares for the g-pawn. Otherwise, White can draw the game with perfect play. That's why White to move first draws:
1. Kg2!
White has prevented Black from coming to the critical squares, and can now defend without difficulty:
1. ...Kf4
2. Kf2Kg4
3. Kg2
Black can try to "seize the opposition":
3. ...Kf4
4. Kf2g4
Now it's White to move and there's an odd number of squares between the kings. But that doesn't work because Black can't maintain the opposition:
5. Kg2g3
Black can't play 5. ... Kg4 because his/her pawn blocks the way. There's not much left for Black now other than a compromise:
6. Kg1
Again White must be careful. (S)he shouldn't play 6. Kf1? because then Black has 6. ... Kf3!, which seizes the opposition. After 7. Kg1 g2! 8. Kh2 Kf2!, Black wins by promoting the pawn and mating. So White must play NOT to let Black have the opposition, as he can respond to Black's attempting entrance as follows:
6. ...Kf3
7. Kf1g2+
8. Kg1Kg3
½ - ½
This example once again highlights the importance of seizing the opposition, as White preventing the opponent from doing so is successful here and leads to a draw. White also took the critical concept to heart, moving to stop Black from reaching the critical squares and thus reaching an unfavourable positioning when the time came to support his/her pawn to promote.

Thus, all Black needs to do in Figure 8 is take the same advice to heart. By moving to any of the squares highlighted, (s)he can guarantee a victory:
1. ...Kf3!
2. Kf1
½ - ½
Taking the opposition, but that fails here because Black doesn't have to move his/her king. He can burn time by moving his pawn...
2. ...Kg4!
Now Black has the opposition again! Thus, one important concept of the opposition is that while getting the opposition is easy, taking advantage of it or maintaining it is much harder. White must eventually step aside...
3. Kg1Kg3
4. Kh1Kf2
All White can do now (besides resign) is prolong the agony as the g-pawn steamrolls forward.
5. Kh2g3+
6. Kh1g2+
7. Kh2g1=Q+
8. Kh3Qh3#
The ending of the game has now preceded in Black's favour; by using his/her own pawn to burn one turn and seize the opposition from White, he was able to outflank White's king and escort the pawn to queendom.

Postscript

Thanks for reading everyone; I think next time I'll look at some miscellaneous cases of King and Pawn vs. King endings to examine what to do in certain tricky situations that aren't covered by the above posts. Stay tuned!