King on the 6th, pawn on the 5th always wins
Collection of thinking shortcuts in chess

By the Bishop dominated Knight position, do you mean that position where the Bishop is three tiles away from the opposing Knight, restricting its movements, or is that something else?
If 20 points of material is infront of the king(For example 2 rooks and a queen)there is a heavy attack on the king which needs to to be defended
Hope that helps

Place a piece two diagonal squares from the enemy knight (see diag), and the piece is safe from the knight's attack for at least two moves (e.g., a king can be checked on Move 3.)

Some good inputs! Thanks guys, I am already feeling more efficient by pondering about these. Forgot about the two connected pawns vs rook bit.
Something a bit more advanced, maybe?

"Draw a diagonal from the pawn to the eighth rank. Now imagine a square that encloses the pawn, the queening square and the diagonal like below.

And here comes the Rule of the square: if the king can enter this square of the passed pawn, then it can capture the pawn before (or as soon as) it promotes."

There is a ver instructive endgame puzzle position by Richard Reti which is a good one to solve and shows up the geometry of the chessboard (Diagonals are the same length as straight lines)
As well as a rather nice stalemate trick where the q cannot take the c pawn
https://www.youtube.com/watch?v=upQ4RKHMQGg

I'll be dog. Thanks Ivan. Sure didn't know that one. Beats having to count it
down with your finger like a patzer.

Another one; in case of double check, the king under the attack always has to move. This rule is also a time saver, no need to be paranoid about any piece attacking you for that one move, besides the fleeing king, obviously.
Hello!
Just recently, I have been thinking about all the mental shortcuts and rules of thumb one can follow in order to lessen the burden of calculation, especially while playing blitz games.
You know, things like:
: the square of the pawn rule (no need for calculation, one can instantly see whether the pawn is making the promotion or not)
: The Bishop dominates Knight position ( saves time sometimes, make trapping tactics easier to spot too)
I am not referring to principles like opposition - these, however simple, need to be studied thoroughly (even though there are a few neat instantly know whether you have the distant opposition or not rules there as well...). I am interested specifically in this kind of easy to spot, time saving principles within the game. I bet there must be some more besides these two? I was trying to google it, but I was not able to formulate the question properly.
So if you'd be interested to help me compile a small list of these, that would be awesome!