White wins
The only move to win is 1. Qh1!!
This position was found with the help of SEE using the following commands:
[Tablebase "KQPkrr"]
[Output "out.pgn"]
[Position "1"]
[Eval "win"]
[SideToMove "white"]
[Piece2 "a8"]
[Piece5 "rank1"]
[Piece6 "fileH"]
[OnlyMove "yes"]
[Move "Qa8h1"]
[Capture "no"]
[Check "no"]
[Position "2"]
[AttackedByBlack "h1"]
[NotAttackedByWhite "h1"]
I was searching for a position where the only winning move for white is Qa8-h1, a silent move without capture or check. Two black rooks should protect h1, so the queen move should be a sacrifice on a double protected corner square! It turned out that I was lucky: there exists a position like that!
I have succeeded to turn this position into a nice study which will be published soon.
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