Endgame: If you have 3 pawns for a knight, should you trade 1 set of rooks?

In the above game, I did not know how to evaluate if I would be better with 1 or 2 rooks in the endgame, having 3 pawns against an opponent's knight.

I would love to know what the rule of thumb is in this situation, and if there are any additional aspects of this position that would change the rule of thumb.

Many thanks to anyone who responds!

"Exchanging pieces increases the value of pawns" is a rule of thumb, but a rather unreliable one.

In the current situation White's pawns are safely blockaded, and the black king is much closer to the weak c5-pawn than the white one. Therefore exchanging rooks was a mistake that made it easier for Black to convert their advantage, which would have been achieved by 39...Nd8 and 40...Kc6, after which the pawn drops.

It depends on the position. Ever heard this before?

When looking at the position three rules of thumb comes to mind:

1. "Pieces that have more space or ways to engage are more valuable"
2. "the player with less space/flexiblity usually gets relief from trading"
3. "Pawns need to roll forward"
4. "It is easier to convert an attack/advantage without double rooks on the board

If you look at 1: The black rooks are a bit stuck, it is not killing but you can imagine black would be happy to trade them off.

If you look at 2: In general white has the space advantage and is pushing, so in general trades here could be favorable for white

If you looka 3: If a trade allowed you a better pawn push, it could well be worth it. Now looking at the position with either all rooks at the board, or with one pair traded off I don't think there is much difference.

4. If you look at 4: This is a tricky one, on the one hand if you felt that you already had a winning position, then generally trading off a pair of rooks would help you convert that advantage more. However the rule works both ways so if you think about it that black is also attacking (e.g. wanting to eat your pawn), it is easier for them to approach this with less rooks on the board.

In short: You asked 'what is the rule of thumb for the situation' but in these nuanced situations there may be a rule of thumb, but even if you cannot see a clear refusal of it it is still a matter of evaluating other rules of thumb that can also apply to the postion.

----

Now, a real evaluation of the actual position and move:
I did not calculate any lines, but it feels like there is no immediate threat. And I do feel that it may be easier for white to keep improving than for black. If so, then it would be good to do this instead of (or before) simplifying.
Some possibilities that come to mind are pushing the a-b pawns to make your pawn advantage more relevant, or perhaps walking up the king and kingside pawns to capture some more space and let the king join in as soon as the simplification does happen.

@Testrider said in #4:
> When looking at the position three rules of thumb comes to mind:
>
> 1. "Pieces that have more space or ways to engage are more valuable"
> 2. "the player with less space/flexiblity usually gets relief from trading"
> 3. "Pawns need to roll forward"
> 4. "It is easier to convert an attack/advantage without double rooks on the board
>
> If you look at 1: The black rooks are a bit stuck, it is not killing but you can imagine black would be happy to trade them off.
>
> If you look at 2: In general white has the space advantage and is pushing, so in general trades here could be favorable for white
>
> If you looka 3: If a trade allowed you a better pawn push, it could well be worth it. Now looking at the position with either all rooks at the board, or with one pair traded off I don't think there is much difference.
>
> 4. If you look at 4: This is a tricky one, on the one hand if you felt that you already had a winning position, then generally trading off a pair of rooks would help you convert that advantage more. However the rule works both ways so if you think about it that black is also attacking (e.g. wanting to eat your pawn), it is easier for them to approach this with less rooks on the board.
>
> In short: You asked 'what is the rule of thumb for the situation' but in these nuanced situations there may be a rule of thumb, but even if you cannot see a clear refusal of it it is still a matter of evaluating other rules of thumb that can also apply to the postion.
>
> ----
>
> Now, a real evaluation of the actual position and move:
> I did not calculate any lines, but it feels like there is no immediate threat. And I do feel that it may be easier for white to keep improving than for black. If so, then it would be good to do this instead of (or before) simplifying.
> Some possibilities that come to mind are pushing the a-b pawns to make your pawn advantage more relevant, or perhaps walking up the king and kingside pawns to capture some more space and let the king join in as soon as the simplification does happen.

Your detailed response is very helpful and much appreciated! Thanks!

here he could blcok all promoting with knight rook and king, stopping them from move, but You did a Great Work stimulating him to go for fast advance , his knight attack on roook opened a window to promote, so he didn't calculated that sacrifice, so if You see that chance, then why not?

Trading one set of rooks when you have three pawns for a knight in the endgame can be advantageous. With fewer pieces on the board, your pawns have more way to advance and potentially promote

No engine here, only an amateur's eye.
Rule of thumb that comes to mind.
If the rooks are of similar activity and there are no apparent attacks the side who is better should trade one pair of rooks. And the side who is worse should avoid it.
Here I think white pushes. I also think that 3 good pawns are usually better than a knight in the endgame.
Concretely I don't want to allow ... a4 though. I want to start with b3, then maybe g3, f4 and then Re1.