I'll give an example of what I'm talking about. In a game like
1. e4 e5 2. Nf3 Nc6 3. Bb5 d6 4. Bxc6+ bxc6 5. d3 Rb8
Are the doubled pawns worth it if you're going to open up their rook to some extent? The moves around it aren't really relevant or when exactly the rook takes the file, but in general am I making a mistake if I'm allowing this for my opponent? I do it relatively often.
Some food for thought:
- Doubled pawns are not always bad. They might be very strong.
- You don't want to exchange pieces for no good reason.
- Don't exchange your active pieces for their passive ones.
- A bishop is generally a bit better than a knight.
- Doubled pawns give open lines for their pieces.
TLDR: It very much depends on the concrete position, and doing the right exchanges is difficult to master.
(In the given line, taking the knight wouldn't be great.)
Before that, why would you play a move like 5. d3? It closes up the position and your rooks are dead while the opponent has the newly-opened b-file. Instead, play 5. d4, where you are opening up the d-file for your rooks and your opponent is stuck with a not-so-important b-file.
It is not yet in black's interests to suddenly play 5...Rb8, which he can do after developing and bringing his kind to safety. We usually play Rb8 in the middlegame.
To answer the question, even though they open files for the rook, doubled pawns are usually a weakness - it's even worse if they're isolated - but sometimes they show some strength. In the given line, the doubled pawns control a few important central squares, and they are not isolated. Rb8 was premature and d3 did not suit the position, but otherwise it is a common (though not the most common) line among chess players with chances for both sides.
