Lesson
White to move. Main line: 1. Rd1+ Ke7 2. Rd4 Ra1 3. Kc7 Rc1+ 4. Kb6 Rb1+ 5. Kc6 Rc1+ 6. Kb5 Rb1+ 7. Rb4
1.Rd1+ drives the king away, and 2.Rd4 prepares the bridge before White exposes the king to checks. The order matters: place the rook first, then walk.
Black checks from the side as the king zigzags toward the rook. On 7.Rb4, White interposes the rook and the checks end; exchanging rooks allows the pawn to queen.
Lucena is the fundamental winning rook ending. If your king is in front of a non-rook pawn on the seventh rank and the enemy king is cut off, this is the technique to recall.
The most useful position in chess
Rook endgames are the most common endgames in serious play, and this is the position that tells you when a rook endgame with an extra pawn is actually won. If you learn one endgame position, learn this one.
The setup: the pawn is one step from promoting, your king is in front of it and cut off from shelter by the enemy rook’s checks. The win exists, but only with a specific method.
Building the bridge
The technique is to place the rook on the fourth rank, walk the king out towards the checking rook, and then interpose that rook to block the final check. That interposition is the “bridge”.
What matters is the plan, not one exact move order. Stockfish rates several first moves as winning here — the check on d1 in the recorded line, and also the quieter rook moves — because the bridge can be built with more than one sequence. Memorizing the idea generalizes; memorizing the moves does not.
The move that throws it away
There is one instructive trap in the line. At the point where White’s king is walking out, the natural-looking rook move to c4 evaluates as exactly 0.00 — Black plays ...Rxc4+ and after the recapture the pawn cannot be escorted home.
Every other continuation there is winning by a wide margin. The difference between +14 and a draw is one careless rook move, which is a fair description of rook endgames in general.
Rd1+ (the line shown): Winning, around +6.8 — the standard teaching move order.
Rf1 / Re3: Also winning, marginally higher at about +7.2. Several move orders reach the bridge.
Rc4 (later in the line): 0.00 — a draw. Black takes on c4 with check and the pawn falls.
Learn the bridge as a plan: rook to the fourth rank, king out, rook interposes.
Cutting the enemy king off along a file is worth more than a pawn in rook endgames.
In a winning rook endgame, check every rook move for a capture-with-check reply before you play it.
Source: The Lucena position — https://en.wikipedia.org/wiki/Lucena_position