Rook vs lone pawn on the 7th rank. The position you'll see 50 times in your life. Here's how to actually win it.
Few endgames embarrass amateurs more than rook-vs-pawn. You're up the exchange. You've ground them down. They have a single passed pawn one square from promotion. You assume it's an easy win. You think for 2 minutes. Then they queen and you resign. What happened?
You skipped the technique. The rook-vs-pawn endgame has a specific algorithm. It's been known for 200 years. Capablanca could have written this article. Tarrasch did write a version. The technique is exact, mechanical, and unforgiving — if you know it, you win 100% of the won versions and draw 100% of the drawn versions. If you don't know it, you guess. Guessing fails.
There are only two named positions you absolutely need: the Lucena (the winning technique with rook AND pawn against a lone king) and the Philidor (the drawing technique with king and rook defending against king and pawn). Everything else in this endgame is a variation on these two.
Lucena position — this is the ONE you need. White king on e8, white pawn on e7, white rook on a1. Black king on c7, black rook on b2. White to move and win. The win technique is called 'building the bridge' — and it works in 4 moves.
The bridge: 1.Rc1+ Kd6 (or any king move) 2.Rc4 (the bridge square — fourth rank, far from the pawn) 2...Re2 (rook starts checking) 3.Kd8 (pawn one move from queening) ...Rd2+ 4.Ke8 Re2+ 5.Re4 (the bridge!) — the rook on c4 swings to e4, blocking the check, and the pawn promotes next move. White wins.
If you don't know this position, you'll lose half the won rook endgames you ever play. If you know it cold, you win them all. There's no third option.
The other half of the endgame: you have a king and rook defending against a king, pawn, and rook. You can hold this if you set up the Philidor correctly.
Philidor: white king on e8, white rook on a6 (or any square on the 6th rank). Black king on e6, black pawn on e5, black rook on a1. White to move. The technique: keep your rook on the 6th rank as long as the pawn hasn't crossed it. When the pawn pushes to e5, switch your rook to attack the pawn from behind: Ra1+! Black king must move forward or lose the pawn. If black king moves forward, you check from behind. If black blocks with the rook, you take the pawn.
This is one of the most elegant draws in chess. The rook acts as a wall on the 6th rank, then becomes a perpetual checker on the back rank when the wall breaks. Practice this position 5 times in a row and you'll never lose a holdable rook endgame again.
Sounds simple? It is. But under time pressure, with adrenaline going, players forget step 1 and start chasing the king with the rook. The pawn promotes. The game flips. Don't be that player.
Your rook is in front of the pawn (blocking). The enemy king is supporting the pawn. Your king is far away. This is often LOST — the enemy king and pawn cooperate to push your rook off the file, and the pawn queens. Don't get into this position. Get behind the pawn.
Quigley's law of pawn endings: the rook belongs behind the passed pawn. Yours or theirs. Same rule. Behind your own pawn: the rook supports promotion. Behind your opponent's: the rook restrains the pawn while leaving your king free to roam. Tarrasch said this 130 years ago and it's still the most reliable rule of thumb in chess endgames.
Set up a board (or use the analysis board on Lichess). Position 1: White king on e1, white rook on a1. Black king on e8, black pawn on h2. Your move. You should win this 100 times out of 100 in under 30 seconds once you've drilled it.
Position 2: Lucena. White king on e8, white pawn on e7, white rook on a1. Black king on c7, black rook on b2. Your move. Win in 5 moves with the bridge technique.
Position 3: Philidor. White king on e8, white rook on a6. Black king on e6, black pawn on e5, black rook on a1. Your move. Hold the draw with the rank-switching technique.
Drill these three positions until they're automatic. The investment is one weekend afternoon. The return is a 50-100 ELO bump because you stop blowing winning rook endgames.
You'll play roughly 3-5 rook endgames per 100 games. Most of them are decided by whether you know the basic Lucena/Philidor/rook-behind-pawn technique. Each game where the technique flips a draw to a win or a loss to a draw is worth 0.5-1.0 rating points on average. Over 100 games, that's 5-10 ELO from one weekend of endgame study.
Compare to opening study: memorizing 10 more moves of your favorite opening might gain you 0.05 pawns on average — a tiny fraction of a position improvement that gets washed out by middlegame mistakes. Endgame technique is permanent and exact. Opening theory is approximate and forgettable.
"Rooks belong behind passed pawns."
— Siegbert Tarrasch