Black to play, draw
That one's slightly more interesting.
According to Syzygy 3.5% of KQKR positions are drawn.
Queen v Rook Position
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May 10, 2022
0
#43
this is the draw i had in mind:
black simply toggles Rf7+/Rg7+/Rh7+...
white king to e-file runs into the pin Re7;
K to h6 runs into Rh7+! Kxh6 stalemate;
K to f6 runs into Rg6+! Kxg6 stalemate;
knowing & avoiding tricks is important.
Queen advantage really
fortress = no way to make progress.
wrong. sorry (kinda). i just read where they say that a fortress (in puzzle) is one where the strong side moves first and/or the weak side king is protected (why theyre calling it a 4tress duh) by its own pieces. i feel summa u are confuzing a fortress w/ stalemate tricks.
go back to #36 (2nd board ex.). White to Move. this should learn ya.
no dopey. White to MOVE in #42. got it ? lol !
to me this is a pseudo-fortress at best. only cuz it needsa stalemate trick at the end to make it hold up. feeling unconvinced.
May 10, 2022
0
#50
no way for white to make progress:
with best play the game will end in a 3-fold rep, 50-move, stalemate or insufficient material draw. 🙂
May 10, 2022
0
#51
Wikipaedia is not an authoritative source, but I think many people would agree with their definition:
In endgame theory, a fortress is an impenetrable position which, if obtained by the side with a material disadvantage, may result in a draw due to the stronger side's inability to make progress.
Seems to fit the bill. What would your definition be?
Lots of positions described as fortresses in endgame manuals where the side with a material advantage can stalemate.
May 10, 2022
0
#52
i'd replace may with will with best play:
otherwise it isn't truly a fortress to begin with. 🙂
May 10, 2022
0
#53
Yes. But then it's difficult to distinguish between a fortress and a draw.
White to play and win 
May 10, 2022
0
#57
It seems chess.com calls this a fortress, too.
https://www.chess.com/terms/chess-fortress
A lonely king = fortress? Sounds strange.
May 10, 2022
0
#59
technical_knockout wrote:
no way for white to make progress:
with best play the game will end in a 3-fold rep, 50-move, stalemate or insufficient material draw. 🙂
Don't believe it can end in a 50 move rule draw with best play. Both #42 and #48 are set up with a ply count 0 FEN.
Best play by Black would be to claim a triple repetition first.
fortress = no way to make progress.