Trade two for one and see what happens
There are two wings on a regular airplane, right? What if I tell you there is only one wing? You can call me insane, out of my mind or just ignorant. This would be the first thought you might initially have. Then I tell you that I did my undergraduate study in Aerospace/Mechanical Engineering. Hmm, maybe she is not completely out of her mind, maybe they learn something about airplanes that only engineers have the right to know. I am now in an authority position, since you have respect for that education, lets say; but still convincing someone that there is only one wing on a plane when there are obviously two wouldn’t be an easy job.
Soon I will reveal the mystery of one wing but let’s transfer this discussion into something more familiar – chess. Lets just say that if one wing was as efficient as two wings, we would have planes flying with one or two wings. In chess two minor pieces (equal to 6 pawns) are better than a rook (equal to 5 pawns), since having a quantity of two is better than having one. Sometimes this holds true, sometimes not. Like with airplanes if two wings are as good as one then having one wouldn’t be a problem. Thus, having a rook against two pieces if the rook is as efficient as two minor pieces would not be a disadvantage. The rook can even be better than two pieces. In endgames when there are open files and a lot of operational space for a rook, with an extra pawn it can do much better against a knight and a bishop. In middlegames usually two minor pieces are better than a rook, since there are not many open files and if the pieces are well coordinated then they will be stronger than the rook. Also, in the middle of the game a side usually gives away two minor pieces for a rook and a pawn to open the opponent’s king and generate an attack. Every situation is unique and sometimes two pieces are the same as a rook. As with an airplane in engineering we look at two wings as one: in drawing we extend two wings inside the plane so they eventually merge into one. We get the shape of a boomerang and call it a wing. We say aspect ratio of a wing, shear stress across a wing, cross section of a wing but never use wings as plural. This was the secret.
Lets go to the first example. This example will feature a game that was most of the time equal. A rook fought successfully against minor pieces in the middlegame due to an open file it controlled. Also, white's two minor pieces couldn’t find good squares, thus had to be relatively passive. Overall, the position looks like just from an opening. Black has a strong knight on e4. N:c3 is a threat already. White finds a small combination that solves their problems.
As you could see from the first example, having this type of material balance is complex. You have to take a lot of things into consideration when deciding to go for two pieces for a rook, such as: position of king, who owns open files, are there any good central squares for minor pieces, passed pawns etc. The next example shows how priorities in a position changed. At first white’s passed pawn looked very dangerous, but then black managed to put his pieces in the center and suddenly white’s king turned out to be undefended. It looks like a Semi-Slav, Shirov-Shabalov line of opening. Black did not commit to castle yet. White controls white squares on the queenside, since black’s bishop on b7 cannot defend them.
Now it is time to get a huge mug of tea and relax since the next example is really long. It shows how white, getting the advantage never let it slip. It requires unbelievable patience to play for so long and never allow a chance for your opponent. The first thing that pops into one's eyes is that black’s king is open and two monstrous bishops look at him. There is always a Nh5 sacrifice in the air. Nc6 is loose, d6 is weak. White is obviously better and found a nice combination here.
The next example shows how sometimes less pieces but well coordinated can dominate more with poor coordination. Black has some problems with the queenside: if he develops his bishop then b7 would be vulnerable. On the other hand Bf4 does not have good squares for retreat after Nh5 or g5. White decided that there is no time for castling.
One article cannot drain such a big topic. I tried to look at the situation from both sides – the one with two pieces and the one with a rook. The positions are complex and as you can see from the examples, top players of the modern day like to play them for either side. It is a question of a wing(s), or of a personal preference. As long as you think that your positional plusses (center, passed pawns, material) will outnumber your opponent’s pluses you can play these type of positions for either side. I would say that coordination of pieces is mostly the major factor when making such a decision. Overall, try to think about this type of exchange with an open mind, do not stick to just a material evaluation; at the end it might turn out that one piece is better than two.