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Sometimes I have a queen against an opponent rook, or I have a rook against a minor piece, but all the pawns are traded off(so I can't force the trade of the remaining piece for an about-to-promote pawn) and I have no idea how to win. The rook/minor piece gets in the way of usual queen or rook checkmates.
No, I meant R vs B OR N. As in, I'm the exchange up.
you can find the winning techniques in any endgame book although Q v. R is very tricky in practice, while in the R v. B you have to make sure the king is driven into the corner of the bishop's diagonal colour in order to win (eg. KB means the king must be driven to a1 or h8); whilst the knight generally has to be forced away from the king.
Normally Q v. R is a win but R v. B or N tends to be a draw.
Queen vs. Rook is an extremely hard win; even GMs have had trouble winning with the queen. For practice, you would have to try against a computer that is making optimal moves as well as reading up on the basic idea. A good endgame book that covers it is Dvoretsky's manual, which is just a great endgame book overall (but it is not intended for players below 1800 ELO or so).
These wins are discussed in almost every endgame book.
WIM Energia has some interesting articles on this subject, I believe.
I always pray I can mate my opponent in the middlegame, rather than embarass myself trying to win with a R vs B or Q vs R. In fact I recently spent some time mastering mating with B+N vs K. This ending has never come up in a single game of mine, and probably never will, but I was haunted by the prospect of failing to mate in the required 50 moves!
I've always considered going into a B+N v. K endgame a superb practical, last ditch attempt to save a draw because with today's time controls players have less time to play endgames and an amazing number of people don't know how to mate with the bishop and knight. Not everyone can pull off a feat Judit Polgar once did: mating with the B+N with 2 minutes left and at the Amber Blindfold event too!
Roman Dzindzichashvili has a video on QvR, check the endgame videos.
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