Learning endgames: King + Pawn vs King
Preface:
I have always been terrible at endgames. Even when I have loads of time on my clock I find myself struggling to calculate all the way through lines to determine if the end game is winning or not, and you better believe I am gonna screw up even a simple endgame under time pressure. As such, I have started slowly working through all the puzzles in Jesus de la Villa’s book: 100 endgames you must know, and will be writing down what I learn in a series of blogs on this page.
This first entry will cover the lessons I have extracted from the first 5 endgames, all of which are King + pawn vs King endgames (shortened to KPVK). In the interest of in-game practicality I have organized these endgames into 3 groups:
1) The weak king is not directly blocking the pawn
Key concepts:
The rule of the square
Shouldering
2) The weak king is directly blocking the pawn
Key concepts:
Opposition, distant opposition & exceptions
Key squares for 5th rank pawns
Key squares for all other pawns
Reserve moves
3) Rook's pawn endings
Key concepts:
How to draw, and when they are not a draw
Endgame type 1: KPVK, weak king not blocking the pawn
Key concept: the rule of the square
The simplest type of KPVK endgame is one where the pawn-less, or weak, king has not yet arrived in front of the pawn. In these types of positions, the first thing to do is calculate if the king can even reach the pawn before, or immediately after, it promotes. The best-known way of quickly calculating who will win the race to the queening square is called the rule of the square:
If the king is within a square of side length equal to the distance between the pawn and the queening square, he will be able to capture the pawn before it promotes.
Note 1: The side length of the square is one less than expected if the pawn is on its starting square.
Note 2: The rule is applied on the pawn's turn
Example 1: Intro to the square
This first visualization uses bishops to outline the region that the king must be within to stop the pawn.
The square in action:
Example 2: The 2nd rank pawn square
This example is a good illustration of the first of two secondary rules that apply to the rule of the square: When a pawn has not been moved yet, the square's sides are one less than the distance between the pawn and the queening square. The black king is within a square of side length 7, but ends up short due to the pawn moving two squares on its first move.
Example 3: Weaker king move in hand
By using the same board setup and swapping the starting turn we can see the second clause to the rule of the square: it is applied on the pawn's turn to move. Although black's king is outside of the square in our starting position he is able to enter it before white's turn, securing a draw. Even if white brings his king in first, king and rooks pawn can never force the opposing king out of the corner, as we will see later.
Key concept: Shouldering
A king cannot enter the 3x3 box centred around the other king, and thus can be repelled from a goal by the opposing king.
Unfortunately for the player with the weak king, the rule of the square is only applicable if the strong player's king is not in a position to interfere. In many cases the concept of shouldering is more important than the rule of the square.
In the following position we can see that the weak king is well within the pawn's square, yet is unable to capture it before it promotes.
Endgame type 2: KPVK, weak king blocking the pawn
Endgames where the weak king has already lodged himself in-front of the advancing pawn are significantly trickier than those where he has not. The stronger side is often winning in these positions, but only if he plays the correct patterns.
Key concept: opposition
When two kings are standing on the same file with one square between them they are said to be in opposition. Opposition is almost always dis-advantageous for the player who has to move their king next.
Example: Using opposition to secure the pawn's path
Opposition exception: Limited movement
The critical exception to opposition being an advantage for the player who enters it, is in situations when that player's king has limited mobility, either because of a board edge or an opponent's piece. While it appears black has managed to secure opposition in the following position, the white pawn blocks black’s king from maintaining opposition after 1.kf5 and forces black to give way to white.
Example: Pawn shouldering
Key concept: The 6th rank key squares
With the concept of opposition under our belt we can move on to the simplest of the king blocking endgames: those where the pawn has already advanced to the 5th rank. In these positions there are three key squares that both sides are vying for: the three 6th rank squares directly in front of the pawn. Should the strong player manage to plant his king on one of these squares, they will have a forced win. However, should they fail to land the king on one of these squares the weaker side can force a draw.
Should the strong king arrive on any of the squares marked with a queen, the pawn will promote:
Example: Winning from the key squares; strong side secures opposition
Despite being put in opposition, white is able to win the above position by pushing the pawn, and passing the turn back to black. From these examples we can derive a rule for when to push a pawn to the 6th rank:
If the kings are in opposition on the 6th rank, push the 5th rank pawn, else make a king move to secure the path for the 5th rank pawn.
This pawn push is an example of a reserve move. As we discussed earlier opposition is almost always dis-advantageous for the player who has to move their King next. Thus if you have a non-king move held in reserve, you can play it to pass the turn back to the other player. By pushing the 6th rank pawn we force black to make the next king move, giving ground, and allowing the promotion of the pawn.
Key concepts: non-6th rank key squares
Now that we know the key squares for the 5th rank pawn it seems logical to assume that the key squares for your king always lie directly in front of your pawn. But in actuality, getting opposition on one of these squares in any non-6th rank position will result in a draw.
Example: drawing with the 4th rank pawn
This example demonstrates the problem with the squares one rank in front of the pawn: that using the pawn as a reserve move restricts the movement of your king, allowing the weak king to maintain his position and secure opposition on the 6th rank. Thus to avoid this problem we need to have the king 2 squares in front of the pawn, allowing for a reserve move that does not inhibit our movement.
Diagram: the key squares for non-5th rank positions are marked with Queens
Example: winning from non-5th rank key squares
Distant opposition:
The odd thing about opposition is that it is not only applicable when the kings are 1 square apart, but rather any time they are an odd number of squares apart. These cases are like an old west shootout, if one king flinches and moves forward, the other king will as well; securing the opposition and forcing the king that struck first aside.
Example: securing opposition from distant opposition
This concept of the distant opposition is particularly relevant for KPVK where the pawn is not yet on the 6th rank, and thus the weak king needs to protect the three squares two ranks ahead of it. The best way to protect these squares is by entering opposition with the strong king, with the key squares as the middle row, and the easiest way to secure this draw is to place an overzealous strong king in distant opposition.
Example: forcing a draw through distant opposition
For the strong side, preventing the weak side from securing the distant opposition (or securing it yourself) is crucial for landing the king on one of the key squares.
Endgame type 3: KPVK, The Rook's pawn loves to draw
Most of the prior endgames we've talked about thus far have been winning for the strong side, assuming precise play. Unfortunately (or fortunately if you're on the losing side), that trend turns on its head when talking about the Rook’s pawn. The rook (or flank) pawns are by far the hardest pawns to promote, as the normal strategy of forcing the king out from the front of the pawn leads to a stalemate as the board edge prevents the existence of an escape square for the weak king! Thus, to win a rook's pawn endgame you must prevent the weak king from arriving in front of the pawn
Example: rook's pawn forced draw
In this example the white player does everything right, controlling the key squares and advancing the pawn to the 6th rank when the kings are in opposition, while the black king just moves back and forth. Despite this, there is no way to force the black king from the corner, and the game ends in a draw.
Key concept: creating a prison
Even in situations where the weak king has not yet reached the corner, rooks pawn endgames can still be forced into a drawing position if he is able to secure the bishop’s home, or the square directly in front of it. Securing one of these squares forces the stronger king to the edge of the board, and makes it impossible for him to push the pawn without ceding the corner to the weaker king.
Example: Imprisoning the white king in the corner
Conclusion
I guess in conclusion the key takeaways from all this endgame nonsense are:
1) if you have extra material, don't enter king+rook's pawn endgames if you don't have to.
2) Always push your king ahead of your pawn in endgames where the opposing side is standing in the pawn's way
3) In knights/bishops pawn endgames be aware of sneaky stalemate tricks
4) opposition and distant opposition are useful for both side sides. However, they are superseded by movement limiting factors like pieces or the edge of the board, and by reserve moves.
If you were insane enough to read this whole thing, let me know what you thought.
