user9192: [White "White (to move)"]
[Black "Black"]
[FEN "rnq1kb1r/ppp3pp/4pn2/4N3/2QP4/2N2P2/PPP3PP/R1B1K2R w KQ - 0 13"]

In this position, White can still castle, but Black cannot (having moved the king twice). Stockfish 10+ (depth 18) assures me that White has an advantage of +6.1, but I am unable to really see why the advantage is so great. I tried some continuing lines of play but Black can hold on to roughly equal material for a long time, so I do not even know how much of the advantage is due to a future tactical threat or merely a superior position.
I am hoping that there is some simple reasoning that is humanly understandable and does not require looking at all possible lines of play for the next 10 moves. Anyone can help?

user17476: I checked the position on Lichess' analysis and looked at the source code on Github. On Lichess' engine, the evaluation is +5.8 (Stockfish 10+ depth 22). 

If we give castling rights to the black king, the evaluation drops to +3.4.  
If we then take out the pawn on f3 (restore material balance), the evaluation drops to +3.1.
If it's black's move (one tempo given to Black and taken away from white), the evaluation drops further to +1.6
If we now put the black Queen back to d1, the evaluation drops to +0.8
If we put the center pawn back on d2, the evaluation is now +0.3, which is more or less the starting evaluation for a chess game.

From this we can infer that the main factors in this evaluation are:

King safety
Development/mobility and initiative 
Material imbalance (one extra pawn)
space (defined by Stockfish as the number of safe squares on your side - the area behind your pawns counts double) 


user20721: The advantage is positional.  It is not material nor tactics that are about to happen.
It is harder for many players to understand positional advantages.  But the computer understands is quite well.
Most average players see material advantages but only see positional when it is a looming mate or other drastic advantage.
Looking at every line of play would not make it clearer if you are not able to grok the positional advantage.  
What may make it clearer is more experience.  Some people never reach that level.  Some like Fischer get their quickly.  
The big thing here is that black cannot castle and his king is in the middle. Black has an isolated pawn that needs defending.  White owns the centre.  White is better developed. And white is a pawn up.  
Yes,  black can defend quite well here, and with club players might even draw.  But between GMs or computers it is just a matter of technique and white should win without any problems. 
Technique is that magic ingredient GMs use to convert a positional advantage to a win.  Although often in the end a positional advantage will result in tactics that win material too and sometimes mate. 

user12629: If you look at the static evaluation of the position in Stockfish, White gets an advantage of 4.17. The top factors in this position are are:
+1.23: King danger. This measures various things, like whether the king has a pawn shelter, how many checks are available, and how many pieces are threatening the area around the king.
+0.77: Piece value bonus. This is the extra pawn.
+0.76: Piece square table bonus. A bonus (or penalty) is given to each piece based simply on what square it's currently on. The knight on e5 is getting a bonus while the knight on b8 is getting a penalty.
+0.48: Mobility. A measure of how many squares are available for each piece. Squares defended by enemy pawns are not counted, and for the queen squares defended by a weaker enemy piece are not counted.
+0.38: Outpost bonus. The White knight on e5 gets a bonus for being on an outpost, and there's also a bonus for the other knight because it can reach the outpost on e4 in one move.
There are also various smaller factors, like Black's isolated pawn, but these are the main factors in the static evaluation of this position.

user8300: So, the simple way to reason out that white is winning is to look at the safety of black's king. White has a very simple plan of developing their bishop to g5, castling and then breaking open the center (either with d5 or with f4-f5, the latter seeming a bit stronger since it forces the a2-g8 diagonal open for white's queen to cause mayhem). After this, white's rooks will be placed on the central files, leaving black's king in mortal danger.
If we try to find moves that hold on for the moment for black, then it's possible to play the bishop out to either e7 or d6, or it's possible to move pawns. Note that no matter what black tries to do, they cannot prevent white from realizing their plan. Black is simply too passive and tied down (due to their obligation to defend e6)
A major problem for black is of course that they cannot castle to put their king to safety, but it's worth noting that even if black still had the option of castling, the kingside wouldn't be a very safe haven due to the f4-f5 break, since the e6 pawn would then be pinned and lost immediately with the black king on g8.

user19877: It really is about king position, but also about how it affects the evaluation when it programmatically adds up the and compares the differences in mobility for each side's pieces. This is where you get the huge difference, and I think this is what you are looking for.
In each of the following lines, deemed best by Stockfish 11, you can see how little the black pieces can move. in particular, it is of note that in each case, the Ra8 and the Qc8 hardly move, and when the Qc8 finally does, it is just to sacrifice itself, or loses material on the move. The same for the Ra8 in the main line that follows. By comparison, look at the mobility of every white piece. The difference is enormous.
For example:
 [FEN "rnq1kb1r/ppp3pp/4pn2/4N3/2QP4/2N2P2/PPP3PP/R1B1K2R w KQ - 0 1"]

 1. Bg5 Be7 2. f4 Nbd7 (2... c6 3. O-O Nbd7 4. Rae1 Rf8 5. Nd3 Nb6 6. Qb3 Nbd5 7. f5 exf5 8. Nxd5 cxd5 9. Nf4 Rf7 10. Bxf6 gxf6 11. Rf3 Kf8 12. Rg3 Bd6 13. Ne6+ Qxe6 14. Rxe6 Bxg3 15. Qa3+ Kg8 16. Qxg3+ Rg7 17. Qd6) (2... Rf8 3. O-O Nbd7 4. Rae1 Nb6 5. Qd3 c6 6. f5 exf5 7. Rxf5 Kd8 8. Rff1 Qe6 9. Ng6 Qc4 10. Nxf8 Bxf8 (10... Qxd3 11. Ne6+ Kd7 12. cxd3) 11. Rxf6 gxf6 (11... Qxd3 12. Rxf8+ Kc7 13. Bf4+ Kd7 14. Rf7+ Kd8 15. Bg5+ Kc8 16. Re8#) 12. Bxf6+ Kc7 13. Be5+ Kd8 14. Qxh7 Nd7 15. Rf1 Qb4 16. Qh4+ Kc8 17. Qg4 Kd8 18. Qh4+ Be7 19. Qh8+ Nf8 20. a3 Qxb2 21. Rxf8+ Bxf8 22. Qxf8+ Kd7 23. Qf7+ Kd8 24. Bf6+ Kc8 25. Qe8+ Kc7 26. Qe7+ Kb6 27. Na4+) (2... Nc6 3. O-O Nxe5 4. fxe5 Nd5 5. Nxd5 exd5 6. Qxd5 Bxg5 7. Qf7+ Kd8 8. Qxg7 Be3+ 9. Kh1 Re8 10. Qf6+ Re7 11. d5 Bd4 12. Qg5 Ke8 13. Qh5+ Kd7 14. Qg4+ Ke8 15. Qxd4) 3. O-O Nb6 4. Qd3 Nfd7 5. Bxe7 Nxe5 6. dxe5 Kxe7 7. f5 Qd7 8. Qg3 Ke8 9. Rad1 Qf7 10. fxe6 Qe7 11. Ne4 Rd8 12. Nd6+ cxd6 13. exd6


9192: <pre><code>[White "White (to move)"]
[Black "Black"]
[FEN "rnq1kb1r/ppp3pp/4pn2/4N3/2QP4/2N2P2/PPP3PP/R1B1K2R w KQ - 0 13"]
</code></pre>

<p>In this position, White can still castle, but Black cannot (having moved the king twice). Stockfish 10+ (depth 18) assures me that White has an advantage of +6.1, but I am unable to really see why the advantage is so great. I tried some continuing lines of play but Black can hold on to roughly equal material for a long time, so I do not even know how much of the advantage is due to a future tactical threat or merely a superior position.</p>

<p>I am hoping that there is some simple reasoning that is humanly understandable and does not require looking at all possible lines of play for the next 10 moves. Anyone can help?</p>
 17476: <p>I checked the position on Lichess' analysis and looked at the source code on Github. On Lichess' engine, the evaluation is <strong>+5.8</strong> (Stockfish 10+ depth 22). </p>

<ul>
<li>If we give castling rights to the black king, the evaluation drops to <strong>+3.4</strong>.  </li>
<li>If we then take out the pawn on f3 (restore material balance), the evaluation drops to <strong>+3.1</strong>.</li>
<li>If it's black's move (one tempo given to Black and taken away from white), the evaluation drops further to <strong>+1.6</strong></li>
<li>If we now put the black Queen back to d1, the evaluation drops to <strong>+0.8</strong></li>
<li>If we put the center pawn back on d2, the evaluation is now <strong>+0.3</strong>, which is more or less the starting evaluation for a chess game.</li>
</ul>

<p>From this we can infer that the main factors in this evaluation are:</p>

<ol>
<li>King safety</li>
<li>Development/mobility and initiative </li>
<li>Material imbalance (one extra pawn)</li>
<li>space (defined by Stockfish as the number of safe squares on your side - the area behind your pawns counts double) </li>
</ol>
 20721: <p>The advantage is positional.  It is not material nor tactics that are about to happen.</p>

<p>It is harder for many players to understand positional advantages.  But the computer understands is quite well.</p>

<p>Most average players see material advantages but only see positional when it is a looming mate or other drastic advantage.</p>

<p>Looking at every line of play would not make it clearer if you are not able to grok the positional advantage.  </p>

<p>What may make it clearer is more experience.  Some people never reach that level.  Some like Fischer get their quickly.  </p>

<p>The big thing here is that black cannot castle and his king is in the middle. Black has an isolated pawn that needs defending.  White owns the centre.  White is better developed. And white is a pawn up.  </p>

<p>Yes,  black can defend quite well here, and with club players might even draw.  But between GMs or computers it is just a matter of technique and white should win without any problems. </p>

<p>Technique is that magic ingredient GMs use to convert a positional advantage to a win.  Although often in the end a positional advantage will result in tactics that win material too and sometimes mate. </p>
 12629: <p>If you look at the <em>static</em> evaluation of the position in Stockfish, White gets an advantage of 4.17. The top factors in this position are are:</p>
<p>+1.23: King danger. This measures various things, like whether the king has a pawn shelter, how many checks are available, and how many pieces are threatening the area around the king.</p>
<p>+0.77: Piece value bonus. This is the extra pawn.</p>
<p>+0.76: Piece square table bonus. A bonus (or penalty) is given to each piece based simply on what square it's currently on. The knight on e5 is getting a bonus while the knight on b8 is getting a penalty.</p>
<p>+0.48: Mobility. A measure of how many squares are available for each piece. Squares defended by enemy pawns are not counted, and for the queen squares defended by a weaker enemy piece are not counted.</p>
<p>+0.38: Outpost bonus. The White knight on e5 gets a bonus for being on an outpost, and there's also a bonus for the other knight because it can reach the outpost on e4 in one move.</p>
<p>There are also various smaller factors, like Black's isolated pawn, but these are the main factors in the static evaluation of this position.</p>
 8300: <p>So, the simple way to reason out that white is winning is to look at the safety of black's king. White has a very simple plan of developing their bishop to g5, castling and then breaking open the center (either with d5 or with f4-f5, the latter seeming a bit stronger since it forces the a2-g8 diagonal open for white's queen to cause mayhem). After this, white's rooks will be placed on the central files, leaving black's king in mortal danger.</p>

<p>If we try to find moves that hold on for the moment for black, then it's possible to play the bishop out to either e7 or d6, or it's possible to move pawns. Note that no matter what black tries to do, they cannot prevent white from realizing their plan. Black is simply too passive and tied down (due to their obligation to defend e6)</p>

<p>A major problem for black is of course that they cannot castle to put their king to safety, but it's worth noting that even if black still had the option of castling, the kingside wouldn't be a very safe haven due to the f4-f5 break, since the e6 pawn would then be pinned and lost immediately with the black king on g8.</p>
 19877: <p>It really is about king position, but also about how it affects the evaluation <strong>when it programmatically adds up the and compares the differences in mobility for each side's pieces. This is where you get the huge difference</strong>, and I think this is what you are looking for.</p>

<p>In each of the following lines, deemed best by Stockfish 11, you can see how little the black pieces can move. in particular, it is of note that in each case, the Ra8 and the Qc8 hardly move, and when the Qc8 finally does, it is just to sacrifice itself, or loses material on the move. The same for the Ra8 in the main line that follows. By comparison, look at the mobility of every white piece. The difference is enormous.</p>

<p>For example:</p>

<pre><code> [FEN "rnq1kb1r/ppp3pp/4pn2/4N3/2QP4/2N2P2/PPP3PP/R1B1K2R w KQ - 0 1"]

 1. Bg5 Be7 2. f4 Nbd7 (2... c6 3. O-O Nbd7 4. Rae1 Rf8 5. Nd3 Nb6 6. Qb3 Nbd5 7. f5 exf5 8. Nxd5 cxd5 9. Nf4 Rf7 10. Bxf6 gxf6 11. Rf3 Kf8 12. Rg3 Bd6 13. Ne6+ Qxe6 14. Rxe6 Bxg3 15. Qa3+ Kg8 16. Qxg3+ Rg7 17. Qd6) (2... Rf8 3. O-O Nbd7 4. Rae1 Nb6 5. Qd3 c6 6. f5 exf5 7. Rxf5 Kd8 8. Rff1 Qe6 9. Ng6 Qc4 10. Nxf8 Bxf8 (10... Qxd3 11. Ne6+ Kd7 12. cxd3) 11. Rxf6 gxf6 (11... Qxd3 12. Rxf8+ Kc7 13. Bf4+ Kd7 14. Rf7+ Kd8 15. Bg5+ Kc8 16. Re8#) 12. Bxf6+ Kc7 13. Be5+ Kd8 14. Qxh7 Nd7 15. Rf1 Qb4 16. Qh4+ Kc8 17. Qg4 Kd8 18. Qh4+ Be7 19. Qh8+ Nf8 20. a3 Qxb2 21. Rxf8+ Bxf8 22. Qxf8+ Kd7 23. Qf7+ Kd8 24. Bf6+ Kc8 25. Qe8+ Kc7 26. Qe7+ Kb6 27. Na4+) (2... Nc6 3. O-O Nxe5 4. fxe5 Nd5 5. Nxd5 exd5 6. Qxd5 Bxg5 7. Qf7+ Kd8 8. Qxg7 Be3+ 9. Kh1 Re8 10. Qf6+ Re7 11. d5 Bd4 12. Qg5 Ke8 13. Qh5+ Kd7 14. Qg4+ Ke8 15. Qxd4) 3. O-O Nb6 4. Qd3 Nfd7 5. Bxe7 Nxe5 6. dxe5 Kxe7 7. f5 Qd7 8. Qg3 Ke8 9. Rad1 Qf7 10. fxe6 Qe7 11. Ne4 Rd8 12. Nd6+ cxd6 13. exd6
</code></pre>
