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I have a Russian translation of Bobby Fischer's My 60 Memorable Games. In the Game 1 (http://www.chessgames.com/perl/chessgame?gid=1008366) in the annotations given after Black's 4. ...Ng8-f6 the author writes that 4...d5 5. Nbd2 Bd6 6. Bg2 Nge7 7. 0-0 0-0 8. Nh4!

[fen ""]
1. e4 c5 2. Nf3 e6 3. d3 Nc6 4. g3 d5 5. Nbd2 Bd6 6. Bg2 Nge7 7. O-O O-O 8. Nh4

results in White's initiative. I think that initiative means creating direct threats to which the opponent must respond immediately. But where is initiative after Nh4? White doesn't seem to create any direct threats at all

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You are correct; there is no initiative. The author is overstating the idea behind Nh4 which is to throw pieces and pawns toward the black king, who is at this point in no danger.

If you put this in a modern chess program it would probably show the position as completely equal.

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