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I was always wondering how to win an endgame queen vs. rook. Luckily it never appeared in any of my games yet.
What I know is, that there is a position from which you can reach a forced win (see below). What I also know is there are endgame databases for all positions with 5 pieces (maybe already 6 by now?) so it should be possible to force a win from any position. Or are some draw?
This is a position from where Black to move (first move will be Re7) White can force win. Euwe did the analysis on this. First the Black king will be forced to the g-file with all pieces remaining in the same constellation and then White can win the rook (Qe8-e4!).