When is it a good idea to trade pieces in the endgame?

Question

Per title, I'm wondering when it's a good idea when defending an inferior endgame to seek to trade pieces, and when not to do it.

For example, take this endgame with Black to play:

[FEN "1k2q3/1pp1r3/p2p2p1/P2P3p/5P1P/1PQ3P1/2P5/1K1R4 w - - 3 30"]

With the extra pawn White's position is clearly preferable, but it's not obvious how to make progress, so Black has realistic chances of holding. As Black, is it a good idea to:

• Trade queens?
• Trade rooks?
• Neither, keep all the pieces on the board?

The pure pawn ending is lost, so Black clearly has to keep some pieces on the board to threaten counterplay with. However, which pieces? If Black wants to trade rooks then 1...Re3 forcing 2. Rd3 achieves the trade, but is it a good idea?

Answer 1

General rule: If losing, trade pawns. If winning, trade officers.

Specific rules, as always in chess:

• Black controls the only open line - big time. One argument more for not trading.
• Both kings are relative safe, but as White, after e.g. 1...Re3 2.Rd3 Re1+ 3.Kb2 Qe2 with the idea of doubling on the first, I already would have a certain Halloween feeling :-) (You can't scare an engine, though: +1) Still an argument against trading. White can't produce any mating scare at all.
• A sketchy analysis confirms that +1 increases to +1.5 after trading either rooks or queens. If queens remain, White must safeguard against a perpetual to bring home the bacon. If rooks remain, White must activate the rook (by bringing the king into the center and offering a trade). None of this is a trivial win, rooks might be a bit easier.
• Trading both officers, even by ruining the pawn structure with cxd3, increases the white advantage to +2.