King-and-pawn vs. King: The ‘O’ Word

_{Click or tap on a move in the game text for a popout display board.}

The game of king vs. king — White wins by reaching the 8th rank, Black wins by preventing such — is designed to teach the principle of kings in “opposition”.
When the kings occupy the same file with an odd number of squares between them, the side not on the move “has the opposition”. Black to move in the diagram means White has the opposition, and Black must give way:
1…Kd82.Kf7+−

With White to move, Black has the opposition:
1.Kd6Kd82.Kc6Kc83.Kd5Kd7=

White should always win these games, as long as he “takes the opposition” and keeps it:
1.Ke6!
1. Ke4 would keep the opposition (and preserve the winning condition), but the task is to reach the 8th rank. Not1.Kf5??1.Kd6??Kd8=1…Kf7!=.
1…Kd82.Kf7+−

From the b-file to the g-file, this is always a win for White. With Black to move:1…Kd82.Kf7+−
Guarding each square on the pawn’s path to promotion, and White wins.

If it’s White on the move, then Black starts with the opposition:
1.Kd6Kd8
1…Kf8makes it too easy for White2.Kd7+−. Following 1…Kd8, White’s pawn advance returns the move to Black, and the opposition goes to White.
2.e6Ke83.e7Kf74.Kd7+−

The king vs. king exercise is usually the first thing I share with an unfamiliar student, and the know-everything-already kids say: “I know about opposition.” I ask them to omit the jargon until demonstrating their command of the idea (and you see that I delay using the term in my writing, too). Shifting the kings to the a-file sometimes reveals that they know the fancy words, but not the moves.

1.Ka2Kb82.Kb2!+−

If the king is already on the 6th rank ahead of the pawn, White can advance the pawn without thinking about it:
1…Kd82.e4
2. e3 will also reach the winning position, but there could be a nervous moment on2.Kf7Kd73.e4Kd6, when suddenly the pawn is in peril, and must halt while White restores order:4.Kf6Kd75.e5Ke86.Ke6+−.
2…Ke83.e5+−

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