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endgame technique and alternative checkmates

hydraslayer10
| 0
     In the game, heading towards endgame, I relive it with a stronger continuation for the opposition, in a variation to the mainline.
It's not over until I mate...
     
Stair case mate, where the two rook-like pieces walk the king to the edge of the board, is best here... unless there is a better move -and I find 63...Rc2, to effectively cut down the king mobility.
It makes sense that the stair case mate sets the standard for length of mate from the diagrammed position. It is four moves in length. So all checkmates are four moves in length (if both sides play theoritical best). Of course this is something that could be made certain (a chess engine would be applicable here) (but I wouldn't waste funds on it as a matter of preference). In the variation 63...Rc2, it follows 64 Ke3 gets white mated on 65, and all of white other responses get mated on move 66, as does the main variation. 63...Rc2! for one.
    Also good is 63...Qc1, which technically has fewer responses by white, despite looking like stalem or too many moves.
I have been doing some reading, from which I get this exercise...