Giving up a Rook for a minor piece(a Knight or Bishop) is one of the most fascinating and challenging decisions in chess.
SyntaxError, playing out of France at the internet chess club, is quite fond of winning the exchange. He is firmly convinced that his “material advantage” will last to the endgame. His 1400 rating is reflective of a solid chess player who will probably never understand the difficult concept of material or force in chess.
In the diagrammed position, SyntaxError(no doubt a computer programmer) attacks the Black Horse pinned to the d8 Rook by the g5 Bishop prior to castling. Now if the Black Rook were the Queen, then capturing the d5 Knight would be tantamount to chess suicide.
However in this case, there are two ways for the second player,who essayed the Leningrad Dutch Defense to get a pawn and minor piece for the sacrificed Rook. I think Jonathan Rowson, who ingeniously and instructively questions the concept of material in his famous deadly chess sins book, would consider using this position to illustrate the difficult questions associated with material imbalances.
Jeremy Silman’s magnum opus, of course, is the seminal work on sizing up and dealing with imbalances in general. Silman, who is not nearly as visible in the chess world these days, simply defined an imbalance as a difference in the White and Black armies. He has been charged with oversimplifying chess, but his simple approach got me to USCF expert after many years of frustration trying to improve.