The mystery rook move

"To require from the pieces only direct attacking actions-this is the thinking of the average player. The more flexible understanding of the game would also require profilaxical influence from the pieces." This is how the great thinker of chess Aaron Nimzovitsch explains the ideas behind the mystery rook moves. And here is a demonstarion:
Von Gottschall,Hermann - Nimzowitsch,Aaron
Hannover Hannover (2), 1926

28...Rh8! Black wants to improve his king-Kf7-g6-f5. However, if he tries this idea immediately, White has the g4 resource, for instance: [28...Kg6 29.g4 hxg4 30.hxg4 Rh8 31.Kg3= Thus, the mystery rook move. Profilaxis!] 29.Rd1?! For Von Gottschall black's move remained mystery. Otherwise, he could have ruined his opponent's plans if he had thought also profilactically. The move: [29.Rd6 (Dvoretsky) hitting the pawn on d6 would prevent Black's activisation.] 29...Kg6 30.Rd4 Kf5 31.Bd2

31...Rf8! Yet another mystery rook move. The reason for it is seen in the line- [31...e5 32.fxe5 fxe5 33.g4+ hxg4 34.hxg4+ Ke6 35.Rd6+=] 32.Be1?! White had to find instead the mystery king move- [32.Kg1!? taking away the king from the discovered attack, for example- 32...e5 33.fxe5 fxe5 34.g4+ hxg4 35.hxg4+= (Dvoretsky)] 32...e5 [32...g5 is more subtle.] 33.fxe5 fxe5 34.Rh4? g5 35.Rb4 [35.Rxh5 Kg6+ is one possible result of he mystery.] 35...Ke6+ 36.Ke2 e4 37.Bf2 Rf3 38.Rb6

Nimtzovitsch succeeded in his plans. Now the subtle maneuver- 38...Ke5! 39.Rb4 Kd5 created a zugzwang position, and later he won convincingly. 40.h4 gxh4 41.gxh4 Rh3 42.Rd4+ Ke5 43.Rd8 Bd5 44.Re8+ Be6 45.Rd8 46.Rf8+ Bf5 47.Rf7 Rh2 48.Re7 Bg4+ 49.Ke1 50.Rf7 Kg2 51.Kd2 52.Ke3 Bf3 54.Bd6 Rb3+ 55.Kd4 Kf2 56.Rg7 e3 57.Bg3+ Kf1 58.Rf7 e2 59.Re7 Bc6 'This game, which I count amongst the best I have played, is also significant for its treatment of the isolani as an endgame weakness. 0–1

This strong method is nowadays not a secret for any young player. Especially, if his name is Carlsen:
Carlsen,M (2714) - Adams,Mi (2729)
World Cup Khanty-Mansiysk RUS (4.1), 03.12.2007

33.Rb1!! "This was my plan. Due to the weakness of the b6 pawn, White wins the needed time for regrouping."-Carlsen. 33...Kf8?! [better was- 33...Bg6 34.Rd1 Bc2 35.Rxd5 Rxd5 36.Ne3 Bb3 37.Nxd5 Bxd5 the position is unpleasant, but Black play on, states the young GM.] 34.Be1! Ke7 35.Kg1! The king moves away from the center, but this is temporarily. He frees at the moment the f2 square for the bishop, and White's position becomes obviously better after that. 35...Nb8 36.Bf2 Nd7 37.Re1+ Kf8 38.Rd1 Ke7 39.Re1+ Kf8 40.Nd6±

We see the results of Carlsen's deep strategy. He kept both his bishops on the board, and now exchanges the black one, thus achieving comfortable edge. Adams could not resist the growing pressure. 40...Ne5 [40...Bg8 41.Bb5] 41.Nxf7 Kxf7 42.Rd1 Ke7 43.f4 Ng4 44.Re1+ Kf8 45.Bd4 Rd6 46.h3 Nh6 47.Rd1 Nf5 48.Bf2 Ke7 49.g4 Nh6 [49...Nfe3 50.Re1 Re6 51.f5 Re5 52.Bg3 Re4 53.Bg2 nets a piece for White.] 50.f5 Nf7 51.Bg2 Nf4 52.Rxd6 Nxd6 53.Bxb6 Nc4 54.Bc5+ Kd7 55.Bf1 [55.b3 wins faster. Anyway, Carlsen was in full control till the very end-] 55...Nxb2 56.Bb5+ Kd8 57.Bb6+ Ke7 58.Kh2 Nd5 59.Bxa5 Kd6 60.Bd2 Kc5 61.Kg3 Nc7 62.Be3+ Kb4 63.Bd2+ Kc5 64.Bc1 Nc4 65.Bxc4 Kxc4 66.Bd2 Na6 67.a5 Kb5 68.Kf3 Nc5 69.Bc3 h6 70.Ke3 Kc4 71.Bd4 Na6 72.Ke4 Nb4 73.h4 Kb5 74.Bc3 Na6 75.Kd5 Nc5 76.Bd4 Nd3 77.Ke6 1–0

However, even experienced players may pass through the idea, like in the game:
Najer,Evgeniy (2608) - Landa,Konstantin (2614)
EU-Cup 19th Rethymnon (3), 30.09.2003

24...Rd5 Landa could have used the mystery rook move instead- [24...Rb8і (Hellsten) aiming Rb8-b5-a5, with better prospects. In the game he allowed the freeing a2-a3, which relieved White's game.] 25.a3 bxa3 26.bxa3 Rb5 27.Rb3 Ke6 28.Ke2 Rxb3 1/2