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richardgee2001 23 ( +1 | -1 )
Q+K vs R+K Sorry, I know this must be quite a common question so has almost certainly been asked before, but is it a win or a draw? I ask because I recently won a game like this, but my opponent made a mistake and I could not see any way to force the win.
brunetti 18 ( +1 | -1 )
This is a certain win except for a very few special positions where the strong side's King is under perpetual check, or where there's an immediate 1-move draw (or loss).

brunetti 27 ( +1 | -1 )
Check these docs too:

philaretus 12 ( +1 | -1 )
The technique..... for the Queen to manoeuvre the enemy King onto a square where the enemy Rook can be captured by a forking check.
macheide 73 ( +1 | -1 )
brunetti is right This important endgame is draw with a few obvious exceptions. If you want to learn the definitive theory about this ending, read the corresponding chapter in "Secrets of Pawnless Endings" by Dr. John Nunn. One thing!, this is a winning endgame (with the exceptions mentioned), but, you need to know exactly how to play it!, it's tricky and sometimes very long. If you know well the theory of this endgame, your posibilities of a draw in the inferior side are pretty good, because in many positions, even with perfect play, the winning is dangerously close to the 50 moves. Even a player of the caliber and experience of GM Walter Browne failed to win this ending against a computer, twice!

macheide 9 ( +1 | -1 )
Errata! I must said: "This important endgame is a win..."

Excuseme: "Lapsus digitalis"

zdrak 21 ( +1 | -1 )
Gelfand - Svidler game in the FIDE world championship reached this endgame. Svidler, rated 2680 or something like that, failed to win having the K+Q.

So this endgame is "theoretically won", but very difficult to win in practice !
fiancaro 14 ( +1 | -1 )
impossible sometimes in practice check out the endgame some cases it is impossible in less than 50 moves. walter browne failed to do it v. a computer in the 70s i believe
atrifix 17 ( +1 | -1 )
GM Browne drew the first game, but he won the second--barely. He captured the opposing rook on move 50.