King & Pawn Endgames
Chess with the physics exposed
Every pawn endgame is an exact science: with so little material, every position is a forced win or a forced draw, and one tempo separates the two. Master four ideas (the opposition, key squares, the square rule, and zugzwang) and these endings become arithmetic.
Play this ending (free)King and pawn vs king: the atom
The single most important endgame in chess: it is where simplified games end, and its evaluation drives every pawn trade decision earlier. The rules of thumb: the pawn promotes if the attacking king is in front of its pawn and can take the opposition; it draws if the defending king reaches the squares in front of the pawn in time and defends with the opposition.
One giant exception: the rook pawn. With an a- or h-pawn, the defender only needs to reach the corner: there is no room to outflank, and even king-in-front positions are drawn. Countless endgames are saved (and thrown away) on this exception alone.
The four tools
The opposition: kings facing each other with one square between; whoever does not have to move wins the standoff and forces the other king aside. Key squares: for each pawn there are specific squares (for an e4-pawn: d6, e6, f6) such that if the attacking king reaches one, the win is forced regardless of tempo. Fights about opposition are really fights about reaching key squares.
The square of the pawn: the instant test for whether a king catches a running pawn. Draw the diagonal from the pawn to the promotion rank and complete the square; the defending king catches the pawn if and only if it stands in (or can enter) that square on its move. Zugzwang: the engine underneath all of it; most pawn-ending wins are delivered by handing the opponent the obligation to move.
Beyond the atom
Multi-pawn endings run on the same four tools plus two strategic trumps. The outside passed pawn: a passer far from the main pawn mass wins by decoy; the defending king must leave its pawns to stop it, and your king eats the abandoned side. The protected passed pawn: a passer guarded by its neighbor is a permanent hostage-taker; the enemy king can never leave its square.
And when the kings deadlock, triangulation (losing a move with the king to recreate the same position with the opponent to move) converts mutual zugzwangs into wins. Every one of these has a playable drill: pawn endings, more than any other, must be played against perfect defense, because they punish single-tempo errors with reversed results.
Questions
When is king and pawn vs king a win?
Broadly: when the attacking king is in front of its pawn and can take the opposition, or when it reaches one of the pawn's key squares. With a rook pawn it is a draw whenever the defending king reaches the corner in front of the pawn.
What are key squares in pawn endgames?
Squares whose occupation by the attacking king guarantees the pawn's promotion regardless of whose move it is. For a pawn on e4 they are d6, e6 and f6 (and they move up as the pawn advances). Opposition battles are the method; key squares are the goal.
Why are pawn endgames considered the most important to study?
Because they are the currency every other endgame converts into: evaluating any piece trade in any endgame requires knowing whether the resulting pawn ending wins or draws. They are also exactly calculable, so studying them trains calculation itself.
Don't just read it, play it
Every position below is playable right now, free, no signup, against a tablebase-perfect opponent that never gives up and explains every mistake.
Opposition: King Before Pawn
White to play and win
Defending King & Pawn vs King
Black to play and draw
The Square of the Pawn
Black to play and draw
Winning the Pawn Race
White to play and win
Follow the full curriculum (free)or sharpen these endings in the Gym