|Black to move|
8/pp2R1k1/2pp2P1/7p/2PP3P/P5p1/KPQ2r2/5q2 b - - 3 2
This position is halfway the solution of this problem
How to answer the check?
I'm going to think this over.
Feel free to comment already. That was of great help the previous post. I will update this post whenever I have found an adhesive plaster.
What I'm looking for, is a way to avoid as much calculation as possible, and guide my attention to the right plan. What is going on? At first there is the promotion motif. On both sides. I see promotion as the same as gaining wood. There is not much difference between capturing a hostile queen, or getting a friendly one yourself. Reaching the promotion square is the same as capturing a queen. There are a few differences. The rim of the board can't move, while the enemy queen can. On the other hand, the queen is usually attacked with one move at most, while the pawn becomes more dangerous with every move closer to the rim. This difference is due to the volatility of the queen versus the fixed position of the rim. This makes the path to promotion an asset in itself.
Another element is the (counter) assault motif. We already saw that the assault motif is not about B.A.D. (Barely Adequate Defended) pieces but about B.A.D. squares and cages.
Shielding the check by 1.... Rf7 doesn't seem to be a happy move. So the king must flea. There are two potential functions to perform. Preventing promotion and attacking the rook. We are already attacking the white queen, so if we can alleviate the check with tempo, we are good. The only way to potentially gain a tempo is by attacking the rook. This can be done in two ways: Kf6 or Kf8. This means that we don't have to look at Kh6, Kh8 and Kg8. Only when both attacks of the rook go wrong, we need to look at these alternatives. We don't need to worry about the promotion, as long as we can gain the white queen in exchange. I played 1. ... Kf6 since I didn't like the check 1. ... Kf8 2. g7+. If I knew then what I know now, viz that the promotion is exchangeable for the capture of the white queen, I wouldn't have been so worried about that check.
What is the difference between 1. ... Kf6 and 1. ... Kf8? Essentially it is the loss of a tempo. After 1. ... Kf6 2. Rf7+ the black king must move out of the way. While after 1. ... Kf8 2. Rf7+ the rooks can be exchanged immediately. After such exchange, black is left with a pawn that can promote, while the white pawn can't, due to the position of the black king.
In order to avoid redundancy in your thinking, you should not think of the kings safety as a first. You look at the most active continuation first. Only once you found that, you start to think of your king safety. Since the black king can flea to a safe haven after the white queen invades, there is no reason to not play the most active line. It all boils down to precision.