A Rook or Two Minor Pieces?

I cannot even tell you how many times I had to discuss the subject of ' A Rook vs. Two Minor Pieces' with my students.  Usually it starts in a position like this:

And I face the same problem again: how do I explain that the trade of a Bishop and a Knight for a Rook and a pawn is not that good in this position? 

I know the arguments that I will face very well:

1) Two minor pieces are worth about 6 pawns and so are a Rook and a pawn, so White doesn't lose any material.

2) Black's King gets exposed, so it gives White additional benefits. 

Indeed, what should I tell my students? There is no 'rule of thumb' to follow and besides I remember very well, how I was attracted to this 'combination' in my childhood until my own experience taught me that it is not such a great idea.

I was looking for help from the great chess players, but all I found was:

" I saw it so many times that after one opponent wins two minor pieces for a Rook and a pawn (usually on the 'f7' square), then he either loses a game or makes a draw with great difficulties in an endgame.  The experience shows that in endgames, especially if a passed pawn exists, the player who has a Rook has a better position.  It is a different situation in the complicated middle game. Here it is much easier to create an attack having two minor pieces."  GM Alexander Zaitsev

" In the endgame a Rook is frequently stronger than two minor pieces. It happens when the Rook penetrates into the opponent's camp and wins some material or when there is an opportunity to create a passed pawn." Famous Russian coach IM Mark Dvoretsky

At first sight, it looks like the case is very simple: In the opening and middle game two minor pieces are better and a Rook can be better in the endgame, especially if we use the classical examples that prove the rule:

Black was completely helpless at the end against a well coordinated attack by the White pieces.  His Rook was practically useless there.

It is funny that nine years later, the same opponents played a game where three minor pieces were fighting two Rooks.  The minor pieces won again:

And here is another game from the same epoch:

So, indeed the two minor pieces are better in the middle game and the Rook   can be better in the endgame.  The case is closed, right?

But this is what the great Mikhail Tal says: "I have to confess that it is my favorite sacrifice to give up two minor pieces for a Rook. If an exchange sacrifice can be treated as an admission that a Rook can be weaker than a minor piece, then in this case we have a statement that a Rook is frequently stronger than two minor pieces. This paradox is valid in an endgame too, especially when the Rook fights against a Bishop and a Knight and they are not cooperating very well in that particular situation. This paradox stays true in a middle game, providing that a Rook has an open file (or better yet, files!)."

 And here is the proof from the Magician:

to be continued...