user9192: I came across this interesting position:
[Title "Black to move (with full castling rights)"]
[FEN "r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1 b kq - 0 1"]

On first glance, it seems like Black ought to have a little bit of advantage, as White is down a rook for a pawn. But due to the significant danger for Black (under a pin and unable to castle safely), it is quite unclear, and even after looking at a couple of lines using Lichess analysis I am unable to decide which side is better off. Is there any broad-brushed strategy for either side that would gradually but decisively achieve victory?
Based on Stockfish evaluation, it seems that both sides can maintain a dead draw for 10+ moves, but I think the outcome under perfect play is unlikely to be a draw. So who is most likely winning here?

user4418: 
Is there any broad-brushed strategy for either side that would gradually but decisively achieve victory?

Sounds like what you are really asking here is "Can black survive long enough, without giving back too much material, to take advantage of the extra material to win." That's because white's winning strategy would have to be to checkmate black quickly and that's not a gradual process and in any case, as you say, the engines evaluate the position as close to equal out to move 10.
If there were such a strategy for black it would be something like:

Avoid checkmate
Avoid giving back too much material
Get the queens off

1 is achievable, 2 is achievable for a while but white can easily sidestep 3.
Although a rook for a pawn up, black is facing an immediate checkmate threat, Nd6#, plus Qe6 looks really nasty, plus the white squares around the black king are very weak.
The most obvious move, Qb6, protects against both the checkmate and Qe6 but is one of many second favourites of the engine. As some of the comments point out, Nb6 is the first choice of the silicon-based players.
This carbon-based player likes the look of Nc5 which also protects against both the mate and Qe6 and aims to return some material to get to a more comfortable, albeit more materially balanced position, with a sequence like 1...Nc5 2. cxd4 Qd7 3. Nxe7 Bxe7 4. dxc5. Then black can choose between Rd8 threatening mate (albeit easy for white to parry) and O-O.
It could go something like this:
[FEN "r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1 b kq - 0 1"]

1...Nc5 2. cxd4 Qd7 3. Nxe7 Bxe7 4. dxc5 Rd8 (4...O-O 5. Qc4+ Kh8 6. Be3 Bf6) 5. Be3 O-O 6. Rc1

Of course the engines don't go for any of this cowardly stuff. They prefer, as black, to hang on to the extra material as long as possible, even at the expense of having to make a number of "only moves":
[FEN "r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1 b kq - 0 1"]

1...Nb6 2. Bf4 d3 {only move} 3. Qe6 Nc8 {only move unless you want to allow white a draw by repetition} (3...Qd5 4. Nd6+ Kd8 5. Nf7+ Ke8 6.Nd6+) 4. Ne5 Qd5 {only move} 5. Nd6+ Qxd6 {only move} 6. Qf7+ Kd8 7. Rd1 Qf6 8. Rxd3+ Nd6 {only move} 9. Qxf6 gxf6 10. Nf7+ Kd7 11. Nxh8 Nec8

At the end of the day the computer has given back material, black is up a piece for two pawns, but in return white has allowed the exchange of queens. White's more active pieces means that the evaluation in black's favour is less than 0.5.

I think the outcome under perfect play is unlikely to be a draw. So who is most likely winning here?

I think the outcome in such a double-edged position with human play is unlikely to be a draw. More scope for mistakes means humans are more likely to make them and lose, but the computer suggests that with perfect play it is a draw.

user18809: This is a quite complicated position. It's not about "following a strategy" but rather about concrete calculation of different lines that could arise. Any "tiny" mistake by either side can lead to a huge change in evaluation (for example, White is threatening checkmate right now).
Most players would prefer to have White here, since playing with the initiative is often easier than finding defensive moves. For instance, after Black defends d6 with ...Nf6 or ...Nb6, White could follow with Bf4, insisting on Nd6+ and perhaps later Re1 to add pressure on the pinned knight. Qe6 is an option too with many chances for a perpetual (see for instance 1...Nf6 2.Qe6 Qd5 3.Nd6+). Finding natural moves for Black is not easy at all though.

9192: <p>I came across <a href="https://lichess.org/analysis/r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1_b_kq_-_0_1" rel="nofollow noreferrer">this interesting position</a>:</p>
<pre><code>[Title &quot;Black to move (with full castling rights)&quot;]
[FEN &quot;r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1 b kq - 0 1&quot;]
</code></pre>
<p>On first glance, it seems like Black ought to have a little bit of advantage, as White is down a rook for a pawn. But due to the significant danger for Black (under a pin and unable to castle safely), it is quite unclear, and even after looking at a couple of lines using Lichess analysis I am unable to decide which side is better off. Is there any broad-brushed strategy for either side that would gradually but decisively achieve victory?</p>
<p>Based on Stockfish evaluation, it seems that both sides can maintain a dead draw for 10+ moves, but I think the outcome under perfect play is <em>unlikely</em> to be a draw. So who is most likely winning here?</p>
 4418: <blockquote>
<p>Is there any broad-brushed strategy for either side that would gradually but decisively achieve victory?</p>
</blockquote>
<p>Sounds like what you are really asking here is &quot;Can black survive long enough, without giving back too much material, to take advantage of the extra material to win.&quot; That's because white's winning strategy would have to be to checkmate black quickly and that's not a gradual process and in any case, as you say, the engines evaluate the position as close to equal out to move 10.</p>
<p>If there were such a strategy for black it would be something like:</p>
<ol>
<li>Avoid checkmate</li>
<li>Avoid giving back too much material</li>
<li>Get the queens off</li>
</ol>
<p>1 is achievable, 2 is achievable for a while but white can easily sidestep 3.</p>
<p>Although a rook for a pawn up, black is facing an immediate checkmate threat, Nd6#, plus Qe6 looks really nasty, plus the white squares around the black king are very weak.</p>
<p>The most obvious move, Qb6, protects against both the checkmate and Qe6 but is one of many second favourites of the engine. As some of the comments point out, Nb6 is the first choice of the silicon-based players.</p>
<p>This carbon-based player likes the look of Nc5 which also protects against both the mate and Qe6 and aims to return some material to get to a more comfortable, albeit more materially balanced position, with a sequence like 1...Nc5 2. cxd4 Qd7 3. Nxe7 Bxe7 4. dxc5. Then black can choose between Rd8 threatening mate (albeit easy for white to parry) and O-O.</p>
<p>It could go something like this:</p>
<pre><code>[FEN &quot;r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1 b kq - 0 1&quot;]

1...Nc5 2. cxd4 Qd7 3. Nxe7 Bxe7 4. dxc5 Rd8 (4...O-O 5. Qc4+ Kh8 6. Be3 Bf6) 5. Be3 O-O 6. Rc1
</code></pre>
<p>Of course the engines don't go for any of this cowardly stuff. They prefer, as black, to hang on to the extra material as long as possible, even at the expense of having to make a number of &quot;only moves&quot;:</p>
<pre><code>[FEN &quot;r2qkb1r/pp1nn1p1/7p/5N2/3p4/2P2N2/PP2QPPP/R1B3K1 b kq - 0 1&quot;]

1...Nb6 2. Bf4 d3 {only move} 3. Qe6 Nc8 {only move unless you want to allow white a draw by repetition} (3...Qd5 4. Nd6+ Kd8 5. Nf7+ Ke8 6.Nd6+) 4. Ne5 Qd5 {only move} 5. Nd6+ Qxd6 {only move} 6. Qf7+ Kd8 7. Rd1 Qf6 8. Rxd3+ Nd6 {only move} 9. Qxf6 gxf6 10. Nf7+ Kd7 11. Nxh8 Nec8
</code></pre>
<p>At the end of the day the computer has given back material, black is up a piece for two pawns, but in return white has allowed the exchange of queens. White's more active pieces means that the evaluation in black's favour is less than 0.5.</p>
<blockquote>
<p>I think the outcome under perfect play is unlikely to be a draw. So who is most likely winning here?</p>
</blockquote>
<p>I think the outcome in such a double-edged position with <em>human play</em> is unlikely to be a draw. More scope for mistakes means humans are more likely to make them and lose, but the computer suggests that with perfect play it <em>is</em> a draw.</p>
 18809: <p>This is a quite complicated position. It's not about &quot;following a strategy&quot; but rather about concrete calculation of different lines that could arise. Any &quot;tiny&quot; mistake by either side can lead to a huge change in evaluation (for example, White is threatening checkmate right now).</p>
<p>Most players would prefer to have White here, since playing with the initiative is often easier than finding defensive moves. For instance, after Black defends d6 with ...Nf6 or ...Nb6, White could follow with Bf4, insisting on Nd6+ and perhaps later Re1 to add pressure on the pinned knight. Qe6 is an option too with many chances for a perpetual (see for instance <strong>1...Nf6 2.Qe6 Qd5 3.Nd6+</strong>). Finding natural moves for Black is not easy at all though.</p>
