4

Assuming that both players do the best move, I want to know the minimum number of moves needed in the worst case scenario when checkmating a lone king using king and rook.

Edit: The worst case does not include "stalemate" or "king able to capture rook" positions, as it will be clearly draw in that cases.

7

According to this site, the worst case for King + Rook vs. King is the following position, requiring 16 moves to mate (White to move):

[FEN "8/8/8/8/8/2k5/1R6/K7 w - - 0 1"]

There are other positions which require 16 moves, e.g. with the White King on a1, Rook on e2, and the Black King on d3.

You can play these endgames with an online database viewer, e.g. Shredder.

The worst case scenario (for White) with Black to move is when Black is stalemated or can capture the rook, when it is a draw. With White to move, all positions are won.

  • 1
    So that means we can deliver checkmate under 16 moves from any position? – berserk Nov 22 '16 at 13:50
  • @berserk yes, that's correct. – Glorfindel Nov 22 '16 at 13:58
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    except for positions where the rook is immediately captured of course. – user1583209 Nov 22 '16 at 14:36
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    @user1583209 And positions where the lone king is stalemated (e.g., switch the positions of the two kings in the diagram in this answer). – David Richerby Nov 22 '16 at 17:35
  • I'm confused. Is the image depicting the "starting" positions for the 3 pieces, or the "ending" (checkmate) positions? If this is the "checkmate" position, then shouldn't the Rook be Black instead of White (or exchange the two Kings)? – Kevin Fegan Nov 22 '16 at 23:04

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