I don't mean rules like "rooks behind passed pawns" that work a lot but also have a huge number of exceptions. Rather, I mean endgame rules that either have no exceptions, or else a sufficiently small number of exceptions that it's easy to memorise those exceptions.
For example, the rule that "in K+N vs K+P the knight can draw so long as it reaches the square in front of the pawn and can’t be immediately captured by the enemy king" has exactly one exception. The exception relates to the situation in which the pawn is on the seventh rank.
Here White is winning despite Black's knight being immediately in front of the pawn.
[FEN "n7/P7/2K5/8/8/8/8/7k w - - 0 1"]
Are there other useful rules with a similarly small number of exceptions?