Thank God this endgame is rare, because it really fucking sucks to pull off a win.
Botvinnik faced a Q+Q&P ending twice--in 1944 and 1954, winning both of them. The first game was analyzed by Paul Keres for 26 pages (not like there was a lot else to do in the Soviet Union back then).
Today though, there's no need for endgame books like Keres's Practical Chess Endings since computer engines do a far superior job to any human.
If the weaker side's king gets behind the pawn, the game is a dead draw. It's also far easier to win with a bishop, queen, or king pawn than it is a knight or rook pawn due to having more space to work with. Both of those Botvinnik games did involve a knight pawn. Beware if keeping the king next to the queen, especially around the edge of the board, because the king could get stuck in a corner and mated.
>>53480918
>If the weaker side's king gets behind the pawn, the game is a dead draw.
Anon, that's just wrong. Unless the pawn's on a, b, g or h, the side with the pawn can pretty much always win. The trick is to get your own king ahead of the advancing pawn. Your opponent can only move in two directions then, to the side or back, and you can use your king to control the fields your pawn must move to.
>>53481266
http://www.chessgames.com/perl/chessgame?gid=1149858
In this example, the Black king gets in front of the White pawn and the game ended finally in a stalemate.
>>53481266
>Unless the pawn's on a, b, g or h, the side with the pawn can pretty much always win
Both Botvinnik games had a g pawn, which makes it all the more remarkable that he pulled it off, especially the first one when he admitted to being inexperienced with this endgame.
Queen endgames are a terrible headache, I hate getting those.
>>53481511
Yeah, but white was unable to get their king ahead of the pawn. In OP's case, that's not a problem whatsoever.
There was a Kasparov game early in his career (I forget the opponent) where he won a queen ending almost brilliantly.
Queen vs rook is also a bastard, even GMs have a hard time with it.
http://www.chessgames.com/perl/chessgame?gid=1062748
Here, young Korchnoi wins a QvR ending.
>>53482069
I don't know if there's a general guideline to winning queen vs rook other than attempting to fork the enemy king and rook. It's even harder to pull it off without running into the 50 move rule.
>>53482122
Slowly force the king and rook into a corner then fork them.
>>53482122
>>53482069
It's hard to beat computer-perfect defense, but a human player, even a master/grandmaster, will make mistakes. But I've never encountered a Q v R ending in 20 years of playing chess, so I wouldn't worry too much about it.