Is this KBPP vs. KR position a draw or a win with perfect play?

Question

I played a game on Lichess today as white, and me and my opponent reached this interesting endgame position.

[Title "Rewan Demontay-NN, Lichess, 5/14/19"]
[StartFlipped "0"]
[FEN "8/8/3r1kP1/5B2/4PK2/8/8/8 b - - 0 1"]

With Black to play, is this KBPP vs. KR position a draw or a win, with perfect play by both sides?

It looks like a draw to me. White can make no progress here. Black cannot exchange his rook for the bishop and a pawn at any point, or else the other white pawn will advance ahead and promote. Therefore, each side will effectively end up making infinite waiting moves. That is what happened in our game, and it was drawn by the 50 move rule.

Although I could use a computer, I wish to know how I can tell it is a draw without one.

Answer 1

You're right, Black's dominance on the dark squares makes sure White cannot make any progress, and he only needs to sacrifice his rook for two pawns to ensure the draw. If he occupies the key squares for the last pawn, sacrificing the rook for the bishop and a pawn works too. (Of course, there's the immediate threat of e5+ winning the rook you need to protect against.)

Black shouldn't even be thinking of winning; the endgame KR vs. KB is a draw (unless the KB are badly placed) and as you can see in the position, it'll be very hard to force a pawn move from White, which would be necessary to win a pawn. Right now, everything is just too well protected.

Answer 2

IF White wanted to have any winning chances, the pawns should either be connected or, at least, staying in dark squares for quite some time. In the presented position, even if the central pawn pushes, Black will be able to blockade in the second rank

Answer 3

Yes it's a draw. It's hard enough for White to win these endgames with 2 split pawns if he had a rook instead of a bishop.