When is a bishop and knight stronger than the rook?

Question

Often times, players will trade their rook for the opponent's knight and bishop.

This seems to have a slight advantage materialistically as a rook is worth 5 and a knight and bishop are worth 6 total. But from a strategic view, this seems quite unnecessary as it is very hard to coordinate the knight and bishop together (it takes 33+ moves to checkmate by themselves versus a King) let alone deal with a rook at the same time.

Midgame though, they might have an advantage as with all (or most) of the pieces all over the board, the rook may have trouble navigating through the board. The bishop-knight pair though should be sound since the knight should just jump all over the board. Endgame though, I just don't see how a knight and bishop can overpower a rook.

So my question is, when is a bishop-knight pair generally stronger than a rook?

Answer 1

N+B is generally considered to be superior to R+P, because of their greater coverage of squares and the ability to attack the same point twice rather than once. N+B is drastically better than a lone rook in a normal position.

Except for positions with immediate tactics, the only time I can think of that a rook might be superior is in an endgame with passed pawns for both sides. Rooks excel in such circumstances.

Answer 2

In an ending it will often come down to who has the weak pawns and if BN can cooperate. If the R-side has a weak pawn that can be attacked by both B and N, it will be lost. Coordinating BN to do that is a lot easier than chasing a lone K all over the board. If the BN-side has a weak pawn, just one piece is enough to defend it. This is the sort of reasoning that favors the BN.

On the other hand, Mihail Marin, in "Learn from the Legends" shows a number of instances where Tal was successful with a very active R, and that chapter discusses the question nicely.To be effective, the R also needs partners to collaborate with.