Cutting off the king
Cutting off the king means placing a rook on a file or rank so that the enemy king cannot cross it, which keeps the king away from the pawns and often makes a rook ending easy to win.
Cutting off the king is one of the first skills of rook endings. The rook controls a whole file or rank, and because the enemy king may not step onto a square the rook attacks, it is shut out of everything on the far side of the line. If your passed pawn and king stand on the far side, they can advance with no interference from the defender's king. This is the reason the Lucena position is winning: the defender's king is cut off along a file and cannot get back. To cut a king off well, place the rook a safe distance away, not next to the king, where it could be attacked and driven off. Choose the line that blocks the king's most useful route, usually the file between it and the pawn. A common mistake is cutting off along the wrong line, so the king can still walk around to the pawn. Another is forgetting that the defending rook may attack yours, so make sure the cutting rook is protected by the king or the pawn. When you are the defender, bring the king toward the pawn before the cut is in place, because once it is, the defense becomes much harder.
A neighboring idea is Rook versus pawn. Rook versus pawn is an ending in which a rook faces a single pawn, usually a win for the rook, although an advanced pawn supported by its king can save the game.
It sits close to Second rank defense. Second rank defense is a rook-ending method in which the defender keeps the rook on its own second rank to stop the enemy king stepping up and to keep checking options open.
It sits close to Shouldering. Shouldering is a king maneuver in which one king steps into a square that cuts the opposing king off from a pawn or from the route toward it, so the opponent cannot approach.
If "Cutting off the king" has cost you half a point, a first lesson is a good place to find the pattern behind it: George Li goes through your games and builds a plan.
Related terms
A rook endgame is an ending in which each side has a rook and some pawns and no other pieces, and it is the most common type of endgame, so its main ideas are worth learning early.
The Lucena position is the key winning setup in rook and pawn against rook: the pawn stands on the seventh rank, its king sits on the promotion square, the enemy king is cut off, and building a bridge with the rook wins.
King activity describes how freely a king can take part in the endgame, by centralizing, attacking enemy pawns and supporting its own, and the more active king frequently decides otherwise equal positions.
Rook and pawn versus rook is the ending where one side has a rook and a single pawn against a lone rook, a common practical ending whose result usually turns on where the defending king stands.
Key squares are the target squares for the attacking king in a pawn ending: once it reaches one while its pawn is safe, the pawn promotes by force, no matter whose move it is.
Guides that go further
What to decide first, the questions to ask, what a first lesson should show and the red flags to avoid.
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A game review, a read on your level and a written study plan from George Li.
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A first lesson starts with your games: George reviews them and builds a study plan around what he finds.