That is true. White doesn't have to play Rxb4 after Bb4 either.
Once white stops the discovered check with Ng2, black can either capture the rook at b7 or try for mate. White can't move to the king to g1 or h1 because the new queen is covering that row.
In either case, you are moving the bishop out of the way for a discovered check. My question is wouldn't it be better to get a pawn out of it?
That is true. White doesn’t have to play Rxb4 after Bb4 either.
It doesn't matter whether white takes the bishop or not, in any case black can promote without being taken by white's rook, for example 1...Bb4 2. Ng2 b1=Q, and white can0t take the new queen.
Once white stops the discovered check with Ng2, black can either capture the rook at b7 or try for mate.
I don't think I follow you. Do you mean after 1...Bxf4 2. Ng2? How can black capture the rook? If the pawn promotes, the rook simply takes the new queen (1...Bxf4 2. Ng2 b1=Q 3. Rxb1). And trying for mate without promoting the b2 pawn seems unnecessarily complicated to me (I mean, the position is -5 in favour of black according to the engine, so probably there is some path to mate, but it isn't obvious)
White can’t move to the king to g1 or h1 because the new queen is covering that row.
White moves the king before the pawn promotes: 1...Bxf4 2. Kh1. And again, if you promote, the white rook simply takes the new queen 1...Bxf4 2. Kh1 b1=Q+ 3. Rxb1
I see. You are planning on moving the king before the discovered check. That was not mentioned in the original solution, and also changes the play for:
... Bb4
If we use your solution we can't use discovered check for the same reason, because:
My question was: what would happen if black did not move his bishop to b4, but rather took the pawn at f4. So far, the answers I keep getting begin with b4
which in all cases stop the threat of 2... b1=Q because now 3. Rxb1 is available
The move Bb4 has two functions: clearing the way for a possible discovered check in the second rank, and shielding the promotion square from white rook. On the other hand, the move Bxf4 only clears the way for the discovered check, but doesn't protect b1, so promotion is no longer possible.
Black could always move the rook to a1 before promoting the pawn. It forces a trade, but still leaves black with an advantage.
This is too slow. After 1... Bxf4 2. Ng2/Kh1/Kg1 Ra1, white can simply take the pawn for free with 3. Rxb2, and black loses all the advantage.
If white moves his knight to g2, check with the bishop at g3 also gets him another pawn and opens up the king’s defenses a little.
Trading a bishop for a pawn (one pawn that wasn't passed and only in the third rank) is not a very good deal, and black makes no progress towards promoting. Also, in endgames, king activity tends to be more important that king safety.