The Reti maneuver is the endgame idea of marching the king along a diagonal so it pursues two goals at once, made famous by Richard Reti's 1921 study where a hopeless king catches an uncatchable pawn.
On a chessboard the shortest path is not unique: a king travels from h8 to h1 in seven moves whether it walks straight down the file or zigzags through the center. Reti's insight was that the diagonal route can carry threats the straight route does not, so the king should walk where it fights for two things at once.
His 1921 study shows it in purest form. White's king on h8 looks absurdly far from Black's h-pawn, and White's own c-pawn seems doomed. But after 1.Kg7! h4 2.Kf6 Kb6 3.Ke5! the king suddenly has two roads: 3...h3 4.Kd6 lets White promote alongside Black, while 3...Kxc6 4.Kf4 catches the h-pawn cold. Black cannot prevent both, so the position is a draw.
The maneuver is not museum chess. Any time your king seems out of the game, look for the diagonal path that combines defense with attack: supporting your own passer while stepping into the square of the enemy pawn. Kings that multitask save and win endgames that raw counting calls lost.
By making every step do double duty. The diagonal march costs no time compared with the direct route, but each move also creates a threat with White's own pawn, and the moves Black spends answering that threat let the king re-enter the square.
Never write off an active king, and prefer diagonal king routes that combine two ideas. In pawn races especially, check whether a shouldering or two-purpose king move changes the count before you concede that a pawn cannot be caught.
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