Richard Chen

Chess Endgames 4: King + Pawn vs. King

Last Edited January 3, 2016
Created April 9, 2016

In chess, the closest thing you can get to a gun battle in the Wild West is the endgame of the King and Pawn vs. King. In these endgames, White can only win if (s)he promotes his/her pawn to a queen (or, in some cases, a rook), and the best that Black can do is try to prevent White from accomplishing that at all. Either case is likely to occur, and what happens depends largely on whose move it is and how the pieces are positioned. In fact, given some circumstances, having the move is more of a disadvantage more than an advantage, with extreme cases resulting in zugzwang, the German term for "train stuck", which means that the side to move otherwise does not have a bad position, but regardless of how (s)he moves, (s)he is lost.

Black to Move Loses

Let's examine Figure 1a in detail to show this. If it is Black to move:
1. ...Ke8
...then this is the only move (s)he can play. White is actually doing better here:
2. e7
Regardless of Black's response, White can promote the queen on the next turn. Black's king would then be unable to come back to d8 or d7, since both squares are guarded by White pieces.

Now Black's next move is forced.
2. ...Kf7
Note that, in Figure 1b, that if it was White's move, then the game would be drawn. White must play Ke6, as any other move relinquishes protection of the pawn, allowing Black to capture it and claim a draw, since both sides only have their Kings left and it is impossible to checkmate the opponent with just a King. But Ke6 is no better because it also results in a draw, by stalemate: both f8 and d8 are guarded by the White e-pawn, and d7 and f7 are guarded by the White king. Bear in mind this recurring theme of moving first and losing.
3. Kd7Kf6
4. e8=Q
1 - 0
...and the White pawn queens. This victory is straightforward to explain, done simply by "squeezing" the Black king off the e8 square so that the White king can make an entrance. What happens if White moves first, however, is a different story.

White to Move Draws

Suppose White now has the move. (S)he could try pushing the pawn...

Attempt #1:
1. e7+Ke8
...but that leads to the same scenario described above, forcing White to guard the pawn and creating stalemate!
2. Ke6
½ - ½
So, White now has to try another approach. The only (s)he can do at best is to mark time with passive King moves (remember these are what we call waiting moves, moves used to mark turns by doing nothing):

Attempt #2:
1. Kd5Ke7
2. Ke5Ke8
3. Kd6Kd8
This first attempt leads back to the exact same position as before. White must now try yet another route:

Attempt #3:
1. Ke5Ke7
2. Kd5Ke8
3. Kd6Kd8
...and another:

Attempt #4:
1. Kc5Ke7
2. Kd5
Clearly, any attempts to move away from the pawn result in Ke7, forcing the King to come back to d5 and recreating variation #3. As long as the Black king can hold the White king at bay...
½ - ½
The game is drawn.

It's Not Magic! — Why This Works The Way It Does

Now you may be wondering, "Richard, so far it looks really convicing, but I'm a little confused to why this works the way it does." You're right, there's a critical concept to understand here that explains why it is not possible for White to win if (s)he is the one to move (if Black plays carefully, of course). To see this, let's look at a way that Black could possibly go wrong in the above example, in attempt #2:
1. Ke5Ke7
2. Kd5
If Black plays...
2. ...Kd8?
He is now officially screwed, because White can now manipulate the position into his/her favour:
3. Kd6!Ke8
...and we are back to where we once were (see Figure 1a), except that it is Black to move, and thus to lose!
4. e7!Kf7
5. Kd7
1 - 0
Therefore, to maintain a draw, Black must make sure that White cannot achieve Figure 1a while it is Black to move, otherwise Black loses.

Ensuring that such an event occurs is difficult to do, unless you consider a concept that is extremely common in chess called the opposition. Here is the concept in detail:

The Opposition (and we're not talking about the NDP here...)

In chess endgames, for either White or Black to have the opposition means the following:

  1. The white king and the black king are separated by an odd number of squares, either horizontally, vertically or diagonally;
  2. It is the other side's turn to move.

In Figure 2, the kings are separated by one square (an odd number), so whoever's turn it is to move does NOT have the opposition, while his/her opponent DOES have the opposition. For example, if it's White's move, then Black has the opposition; if it's Black's turn, then White has the opposition.

The reasons why this is advantageous for the side that has the opposition are not immediately clear. However, one way of reasoning this is to treat it as if the moving side is ceding territory to the other. Whoever's turn it is to move in the diagram above, for example, must allow the other king to "invade" by stepping either left or right. For example, if it's White's turn...
1. Kf2Kd3
White has essentially granted Black additional territory by being forced to move. It's hard to see at this point, but with additional pawns on the board, sometimes the ability to outflank can be really dangerous for the side without the opposition.

(Note: The position above, and the demonstration positions following, are obviously drawn; it is merely used as a demonstration as to what the opposition is.)

In this example, the kings are not separated by an odd number of squares, so neither side has the opposition. However, it is possible to either White or Black to seize the opposition in this case. White simply plays:
1. Ka2
...and now, there are an odd number of squares between the kings, and it is Black's move, meaning White has the opposition.

So, how does this pertain to Figure 1?

Well, think. What happens if it's White's turn to move? Then the kings are a square apart, and since that is an odd number of squares, then Black has the opposition! As a result, White cannot make any progress against the Black king, unless Black slips up and gives White the opposition.

Conversely, if it's Black to move, then by definition, since there are an odd number of squares between the kings, then White has the opposition. As a result, Black is compelled to move, allowing White to push the e-pawn forward and squeeze Black's King out!

Chess endgames, while not always necessarily complex, can take some time to understand and analyze. Important concepts such as seizing or having the opposition can make or break a game at critical moments where the sides differ in material by only one pawn, or in many cases, differ by whole piece values. As the pieces on the board are traded off, it becomes easier for the side down in material to obtain a draw, sometimes even come back from a loss if his/her opponent is careless. Although games don't always end in a King and Pawn vs. King endgame, many different types of endgames often reduce to this type of endgame, or require understanding of how to promote pawns in these sorts of situations.

Thanks again for reading, y'all. Get out there and maintain an opposition!