Can a rook and king expertly played capture a king expertly guarded by a knight, if so how?
------------------- Hi Sam,
The pawnless endgame king and rook versus king and knight is a draw if the king and knight are placed in the center. Then the opponent who has the rook will not be able to chase the king to the edge of the board.
Only if the knight or king are badly placed then a win is possible.
For example if the king and knight are far apart or if the king or knight are placed at the edge of the board then this can lead to a loss of the game by losing the knight.
White is winning by cutting off the knight and capturing it later on. He has three good moves to cut off the knight and after that he will attack the knight with the king and capture it. 1. Kf3 or 1. Ra3 or 1. Rg4
White plays 1.Ra6 pinning and winning the knight.
White plays 1.Rg4 and if Black plays 1...Kh6 then 2.Rh4++ checkmate. Or Black plays 1...Nf7 and loses the knight.
Don't spend too much time on that because these endings occur extremely seldom. Better invest your time learning chess strategies and positional play, which is extemely important.