What's the strategy for winning this?

Trexler3241

DaniilKalabukhov

The strategy is to force your opponent in zugzwang. Force your opponent's king to the corner, then bring your own king close to the opponent's one, and finally try to fork the rook or deliver checkmate.

blueemu

You'll want to force Black to release your King from the a-file. This can be accomplished by advancing your King to threaten his Rook in cooperation with your Queen. Make sure you don't fall for any stalemate cheapos such as 

Once you've got your King off the a-file, the winning method breaks down into three stages.

1) Force Black to adopt the "third rank defense" with his Rook, in order to prevent you from taking the sixth rank with your own King.

2) Break down the "third rank defense" and force him to set up his defenses on the second rank instead.

3) force him into Zugzwang so that he must split his Rook away from his King, then check / check / and fork his King and Rook.

You can find a simple example by googling "Queen vs Rook endgame".

n9531l1

Trexler, I just came across this thread. I've studied this ending, so I can give you some detail on what will happen at the end. If you follow blueemu's procedure (the trickiest part is breaking down the third-rank defense) you will reach the Philidor position (see diagram). There are eight versions, one with the black king and white queen reflected across the long diagonal, and those two positions in each of the other corners. You want it to be Black's move, so you may have to triangulate with your queen to lose a move (Qe5+, a1+, a5).

With Black to move, you can mate in 7 moves or less. If the black king moves, you'll pin and capture the rook. If the rook moves to a black square, it will be forked or captured at once. So the rook only has four safe destinations. Winning it is fairly easy, but it helps to know which queen move to make first, so it's worth the effort to memorize the fastest win against each of the four rook moves.

Once you've mastered the technique, your only problem will be waiting for an endgame to come up where you can use it.

White to play and mate in 10