In the following position which arose from a Budapest Defense (Sometimes a gambit opening) , Black has just played the speculative and risky g5. One has to be quite circumspect when playing a move that weakens two squares in the proximity of his King.
Chess GM Patrick Wolff , who dropped out of sight way too early , once stated in some excellent game analysis that a chess player has to have a very good reason for decentralizing a Knight. Wolff tried to make a living at chess with his Grand Master Analysis service which he advertised via Seirawan’s now dissolved Inside Chess magazine. Wolff wanted 50 dollars per game and requested that you send him a game you played as Black and White. I don’t think his chess analysis service ever really took off. Patrick, like many other genius chess players, must have figured out other ways to use the overdeveloped organ between his ears in a more profitable fashion.
In the chess position that follows, White has to move his f4 Knight somewhere as it is being attacked by the g5 pawn. The natural move is , of course, the centralizing Nd5. However, I believe even GM Wolff would agree that the decentralizing Nh5 is concretely the correct location for the harried steed. Nh5 prevents Black from developing his bishop to it fianchettoed g7 square and also eyes the potentially weak f6 square. Moreover, if the g5 pawn advance then f4 could become a super positional/tactical square for the only chess piece that can hop over pieces and pawns.
While we are talking about centralized pieces, the work of Dan Heisman can not go unmentioned. In one of Heisman’s books, the talented chess author devised a concept he referred to as a centralization ratio. The Knight has a centralization number of 4 since 8 divided by 2 equals 4. Where do the values 8 and 2 come from? A Knight in the center of the board attacks 8 squares whereas a Horse in the corner strikes at only 2 squares.
Contrast a Knight’s centralization number of 4 with a rook’s centralization quotient of 1. A rook always attacks 13 squares on an open chess board, so 13 divided by 13 is 1 which indicates a Rook does not benefit from centralization nearly at much as a Knight!
Heisman, a frequent commentator at ICC , is an excellent chess teacher and should be commended for his metric which numerically establishes the extent to which a chess piece benefits from centralization. Miles Ardaman, a medical doctor who did figure out a better way to use the overdeveloped organ between his ears , strongly espoused the pedagogical value of Heisman’s Elements of Positional Chess Evaluation.
Pop quiz: What is the Queen’s centralization number?
In a related side note, Bobby Fischer got away with putting his Knight on the rim in his legendary World Championship match with Boris Spassky. Fischer’s Nh5 on the Black side of a Benoni startled Spassky and swung the match in the Jew hating American’s way.