user9192: This line of play leads to this position:
[White "White"]
[Black "Black to move"]
[FEN "8/rp4p1/1N1nkb2/3n4/6R1/1R6/8/2K5 b - - 1 38"]

StockFish 10+ assures me that Black has a big advantage, but I am interested to know whether it is possible to humanly analyze it and be completely certain of a winning strategy. Although SF suggests keeping my pieces, my instinct is to exchange as many pieces as possible except the pawns, while pushing the pawns to queen, which includes taking the knight immediately. However, is there any hope of proving a winning strategy here, rather than relying on intuition? I think this is somewhat plausible because Black has enough minor pieces for the king to hide behind (even after exchanging 2 of them), and so White cannot make sustained checks. The question is whether there is a systematic way for Black to push the pawns that is guaranteed to work.
I do not see any convincing reason that there cannot be a proof of a winning strategy, because there are numerous examples of endgames with human analysis of the optimal strategy (e.g. a,b,c,d,e). If the position was not so imbalanced, I know it would be much harder to prove a win. But here, Black has sufficiently many pieces that I feel there should be a proof that we can force some trades to get to a certain winning position. That is also why I would choose to take the knight immediately to hopefully make a full analysis humanly tractable.

user12873: The position looks clearly winning for Black, and I don't think it makes much of a difference whether you exchange knights or not. It might make your task simpler, but Black's knight could be a bit stronger than White's.
To win all you really have to do is push one of your pawns, with the support of the king. Your other pieces can be used to block checks, and the minor pieces can also chase any blockading rooks out of the pawn's way. Eventually things will get to the point where you win a White rook for the pawn and a minor piece (in the worst case scenario), which will result in an easily won position.
I'm not sure how to give a certain proof that guarantees a win, as there's no forced mate yet. It's just a position where Black is up 4 points, so a winning edge should be taken for granted at this point.

user11749: @SmallChess is right. This position is absolutely hopeless for White, and there is a very human strategy for Black, which consists here in not exchanging pieces, but hunting the white king. This strategy will force White to exchange pieces unfavorably or White will lose material to avoid being mate.
The principle behind this strategy is simple "with three or more pieces in the attack the enemy king will not be able to escape."
Here is an example where nothing is forced but it's very difficult to suggest good ideas for White. White is completely squeezed.
[White "White"]
[Black "Black to move"]
[FEN "8/rp4p1/1N1nkb2/3n4/6R1/1R6/8/2K5 b - - 1 38"]

1...Nc3! {Black chases the king and cuts off the two rooks. They can't easily coordinate.} 2.Nc4 Nde4! {same strategy: coordinating the pieces to go against the White king} 3.Kc2 (3.Ra3 {is probably better but now Black is happy to exchange and push the g pawn} 3...Rxa3 4. Nxa3 Kf5 5.Rg2 g5-+) b5 4.Ne3 (4.Rxb5 Nxb5 5.Rxe4 Kf5-+ {does not help White}) Rc7 {here with get our principle of three or more pieces in the attack and the White king feels unsafe} 5.Rg2 (5.Kd3 Nf2-+) Na2! 6.Kb1? (6. Kd1 {is better but the King does not escape} Rc1+ 7. Ke2 Nac3+ 8. Kf3 Rh1-+) Rc1 7.Kxa2 Ra1#


9192: <p><a href="https://chess.stackexchange.com/posts/comments/46636">This line of play</a> leads to this position:</p>

<pre><code>[White "White"]
[Black "Black to move"]
[FEN "8/rp4p1/1N1nkb2/3n4/6R1/1R6/8/2K5 b - - 1 38"]
</code></pre>

<p>StockFish 10+ assures me that Black has a big advantage, but I am interested to know whether it is possible to humanly analyze it and be completely certain of a winning strategy. Although SF suggests keeping my pieces, my instinct is to exchange as many pieces as possible except the pawns, while pushing the pawns to queen, which includes taking the knight immediately. However, is there any hope of <strong>proving</strong> a winning strategy here, rather than relying on intuition? I think this is somewhat plausible because Black has enough minor pieces for the king to hide behind (even after exchanging 2 of them), and so White cannot make sustained checks. The question is whether there is a systematic way for Black to push the pawns that is guaranteed to work.</p>

<p>I do not see any convincing reason that there cannot be a proof of a winning strategy, because there are numerous examples of endgames with human analysis of the optimal strategy (e.g. <a href="https://chess.stackexchange.com/q/9003">a</a>,<a href="https://chess.stackexchange.com/q/28225">b</a>,<a href="https://chess.stackexchange.com/q/12220">c</a>,<a href="https://chess.stackexchange.com/q/18601">d</a>,<a href="https://chess.stackexchange.com/a/1725">e</a>). If the position was not so imbalanced, I know it would be much harder to prove a win. But here, Black has sufficiently many pieces that I feel there should be a proof that we can force some trades to get to a certain winning position. That is also why I would choose to take the knight immediately to hopefully make a full analysis humanly tractable.</p>
 12873: <p>The position looks clearly winning for Black, and I don't think it makes much of a difference whether you exchange knights or not. It might make your task simpler, but Black's knight could be a bit stronger than White's.</p>

<p>To win all you really have to do is push one of your pawns, with the support of the king. Your other pieces can be used to block checks, and the minor pieces can also chase any blockading rooks out of the pawn's way. Eventually things will get to the point where you win a White rook for the pawn and a minor piece (in the worst case scenario), which will result in an easily won position.</p>

<p>I'm not sure how to give a certain proof that guarantees a win, as there's no forced mate yet. It's just a position where Black is up 4 points, so a winning edge should be taken for granted at this point.</p>
 11749: <p>@SmallChess is right. This position is absolutely hopeless for White, and there is a very human strategy for Black, which consists here in not exchanging pieces, but <strong>hunting the white king</strong>. This strategy will force White to exchange pieces unfavorably or White will lose material to avoid being mate.</p>

<p>The principle behind this strategy is simple <strong><em>"with three or more pieces in the attack the enemy king will not be able to escape."</em></strong></p>

<p>Here is an example where nothing is forced but it's very difficult to suggest good ideas for White. White is completely squeezed.</p>

<pre><code>[White "White"]
[Black "Black to move"]
[FEN "8/rp4p1/1N1nkb2/3n4/6R1/1R6/8/2K5 b - - 1 38"]

1...Nc3! {Black chases the king and cuts off the two rooks. They can't easily coordinate.} 2.Nc4 Nde4! {same strategy: coordinating the pieces to go against the White king} 3.Kc2 (3.Ra3 {is probably better but now Black is happy to exchange and push the g pawn} 3...Rxa3 4. Nxa3 Kf5 5.Rg2 g5-+) b5 4.Ne3 (4.Rxb5 Nxb5 5.Rxe4 Kf5-+ {does not help White}) Rc7 {here with get our principle of three or more pieces in the attack and the White king feels unsafe} 5.Rg2 (5.Kd3 Nf2-+) Na2! 6.Kb1? (6. Kd1 {is better but the King does not escape} Rc1+ 7. Ke2 Nac3+ 8. Kf3 Rh1-+) Rc1 7.Kxa2 Ra1#
</code></pre>
