why 2 minor > rook and how to execute

one of the hardest puzzles i ever managed to solve. truth be told i was handwaving some of the last parts.

https://lichess.org/training/WwnEm

what is it that makes trading a rook for 2 pieces so good? i always find it extremely hard to coordinate those extra pieces in a game if the enemy king is safe (and in fact after the puzzle the computer just shuffles around for like 30 moves until it is able to convert an advantage of -5).

are there some easy steps to follow or general things to be mindful of after such an exchange that help you poke this advantage (and not hang too many important pawns in the process)?

appreciate your thoughts!

I must admit I did not solve it on the first attempt although I have not done many puzzles recently. I was looking at Ne4 instead of Nxd5 thinking that the knight at e4 prevents any defense of the bishop and after say Qe1 Bxe5 Qxe4 Qxd4 but then I underestimated the continuation Qxd4 Bxd4 Rc7! and technical difficulties. After Nxd5 I missed that after f6 the Bishop cannot defend the knight leaving black a clean 2 bishops for a rook.

In response to the main question winning 2 pieces for a rook is probably the next hardest conversion to make after the advantage of the exchange. Converting 2B vs a rook is much easier than converting BN or 2N vs a rook I have seen titled players fail to convert the latter.

When playing 2 pieces up one tempting idea is to trade pieces. This is one of the few cases when you do not want to do this. In the endgame the rook comes alive while in the midgame it usually takes a more distant role. In contrast the 2 minor pieces are more nimble and mobile in the middle game than the rooks so usually aim for a middle game unless you are totally confident that you can win the endgame otherwise just play chess as usual and create pressure and attack which wing you are attacking and the rest is just playing chess with an extra boost. This is especially helpful when the opponent has pawns in addition to the rook for 2 pieces since the effect of the pawns are minimized in the middle game.

Just note that there is a lot more to say in the endgame where the pawn structure has a very significant impact on the game but for now just be content to not rush into endgames just because you are up material and just play a strong middle game. 8 times out of 10 the extra piece is definitely felt.

The two minor pieces need an additional coordinator, often a heavy piece and then they are fine. In the endgame lone R vs. BN is almost equal.

thanks for the answers! i def got into trouble before when i got trapped and was forced to trade the last rook, especially when there were 2 pawn islands in different locations it felt impossible to avoid horizontal forks later on.

@Rookitiki said in #5:

thanks for the answers! i def got into trouble before when i got trapped and was forced to trade the last rook, especially when there were 2 pawn islands in different locations it felt impossible to avoid horizontal forks later on.

Sounds like the textbook example. Trading the rooks boosts the remaining rook, never do this owning B+N.

2 pieces vs rook is the most difficult common situation to evaluate.

https://ibb.co/tJw3RhS

Even more notorious when the minor pieces are both bishops.

That answers the first part. Its just about the amount of squares they control and the ease of access to most places of the board with the least amount of tempos.

The second question i cant answer.

I usually make sure both of the minor pieces are sufficiently defended and try to push the pawns to promotion, if possible.

Here is an example:

Magnus once said, lemme paraphrase, "a defended bishop is almost as powerful as a Rook".
Now, if you add another minor piece, vs the rook, we're almost looking at a won position.