What is the Lucena position?
The Lucena position is a rook ending with one pawn on the board. One side has a king, a rook and a pawn on the seventh rank. The other side has a king and a rook.
Two things have to be true. The pawn's own king stands on the queening square in front of it. The enemy king is cut off, which means the rook keeps it at least one file away from the pawn.
When both are true, the side with the pawn wins. The win is not automatic, though. There is an order of moves, and this page teaches it.
Step one: check the king one file further away
White plays 1.Rd1+. The rook gives check along the d-file, and the black king must step off it.
After 1...Ke7 the black king is two files from the pawn instead of one. That extra file is what gives the white rook room to work.
Do not rush the king out yet. If White plays 1.Kc7 straight away, Black checks from the side and never has to stop.
Step two: put your rook on the fourth rank
White plays 2.Rd4. This is the move players call building a bridge.
The rook is not attacking anything on d4. It is standing on the rank where the white king will end up, ready to step in front of the last check.
Count the ranks. The pawn is on the seventh, the king is on the eighth, and the king will walk down to the fifth. The rook waits one rank below that, on the fourth.
Step three: walk your king out of the checks
Now the white king leaves the queening square and walks down the board. Black checks from the side every time.
1. 3.Kc7 Rc1+
2. 4.Kb6 Rb1+
3. 5.Kc6 Rc1+
4. 6.Kb5 Rb1+
The king has reached b5, which is on the fifth rank. The rook on d4 is one rank below, on the same side as the checks.
Now 7.Rb4 blocks the check. The white king on b5 protects the rook. Black can take it, but then White takes back and the pawn queens.
What happens if you skip the bridge?
The second chapter of the study shows it. White walks the king out with the rook still on the first rank.
The black rook checks from the side, the white king runs, and there is nothing to block with. The king never gets a quiet move, so White has to come back and build the bridge after all.
The rook on the fourth rank is not a decoration. It is the only piece that can stand between the checking rook and the king.
The mistake we see most often
Learners play the right moves in the wrong order. They start with the king walk and only then think about the rook.
By that point the rook cannot get to the fourth rank in time, because it has to keep the enemy king cut off as well.
Say the order out loud before you touch a piece. Check the king further away. Rook to the fourth rank. King out. Block the last check.