How do you win a Queen and king vs king and rook endgame?

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The first step is to learn the Philidor position (see below), which is a win with either side to move.

Following learning that, there is a series of videos by Derek Grimmell which is probably the best resource to learn Q v R endings.

The third rank defense is considered the best option for the defender, as the ideas to hold this are surprisingly simple for the defender. There is a key move to break this defense down which is not easy to find for the attacker.

In practice defenders will often play sub optimally and make life easier for the side with the queen.

A chess.com King and Queen vs King and Rook video. I hope this helps.

https://www.chess.com/video/player/mating-with-queen-vs-rook-i

Here are 75 interactive K+Q vs K+R positions you can play against stockfish

https://chess-endgame-trainer.mooo.com/list/7/0

Forum member many_hanging_pieces is quite correct. The Philidor position is one of the keys to this endgame. If Black is to move, then the win is straightforward. If White is to move, then he must deliberately lose a tempo in order to put Black on the move.

that was winning anyway

Just keep checking and don't fall for skewers.

No.

Try to check the king into isolation from the rook, and then attempt to force a double attack or something.

There isn't any way to check the King into isolation from the Rook.

Why would he seperate them in reply to a check?

You win by ZUGZWANG. By putting Black in a position where he is NOT in check, but must move the Rook away from the King.

See my post #24 above.

#22 is absolutely correct. Philidor position is basic. And there’s theme exhausting series from Derek Grimmel. But if you are under 2000 dońt try to study it. You will dońt understand it. This endgame you will get so rarely in your life that studying it is just a waste of time.

Try this:

What I did was: Get the rook out, then just keep moving until you can get a checkmate, or knock the king with the queen.

Yeah so maybe you can use pins an win it with that

There’s a chess.com course and a drill on this endgame

menu--> learn--> endgames--> checkmates--> queen vs rook is another option, but 'derek grimmell' on youtube is the best resource if you really want to understand the nuances of this one.

There is a systematic way to win, but it is tricky and takes a while.

first, you have to drive the enemy king to the edge of the board. This requires that you use your king and queen together. You have to be careful to avoid having the rook pin and win the queen. You also have to be careful to avoid so many repetitions that you run up against the 50-move draw rule. During this process, the rook has to stay near its king; when the rook is far away from its king, there may be ways to win the rook through a double attack.

when the enemy king is on the edge, the stronger side can eventually use zugzwang to force the rook to move away from its king. Then, a double attack will win the rook.

The ending is tricky. I have never had it come up in an OTB game, but I have won it several times in blitz games.

A few years ago, in a speed tourney when he was playing on the increment, Nepomniatchi was unable to win the ending against Carlsen. That shows hard hard it can be.

Good