user15234: For the position after 10...Kc4:
    [Title "White to move; castling is considered a blunder"]
    [FEN ""]
    [Startply "20"]

    1. e4 e5 2. Nc3 Nf6 3. Nf3 Bb4 4. Bc4 Bxc3 5. Bxf7+ Kxf7 6. bxc3 Nxe4 7. Nxe5+ Kf6 8. Qf3+ Kxe5 9. d4+ Kd5 10. Qf5+ Kc4 11. O-O? d5 12. f3 Bxf5 13. fxe4 Bxe4

The position from a blitz game I just played; I was Black.
I'm up 5 points of material, but obviously my King is horrifically exposed.
Stockfish rates the position after 10...Kc4 as drawn, which seems surprising given the lack of any immediately obvious threats.
But if White castles with 11.0-0, then the position immediately drops to -5.67. I can only assume that Stockfish believes it can see a series of forced attacks by White which ultimately end in a draw, but dropping tempo at any point allows Black to "escape."
But a) I'm not sure that I've got that right.
And b) I can't really tell how it's supposed to work if that is right.

user8300: This is a classic case of king safety vs. material balance. Black's king is obviously way less safe than white's, BUT black has a lot more material. So if black manages to survive and consolidate their position, then black will win.
Castling is not a very direct move in this position, and the simplest explanation why it's bad is that it's too slow, allowing black to bring their king to safety by means of playing ...d5 followed by ...Kb5 and then letting the black king slowly creep towards a safe haven surrounded by friendly pieces. This shouldn't come as a great surprise; after all, you gotta strike while the iron is still hot!
The thing that genuninely surprised me about your post was your comment that Stockfish rates the position as drawn. I get different results when running SF on my machine, as it's convinced that white is just winning after trying to immediately kill the black king with Rb1 (threatening Qb5+, with mate soon to follow).
The winning line goes as follows, and I don't see any flaw in it: 11. Rb1! (cutting off black's king's escape route via b5) 11...c5 12. Qf7+ (forcing black to block its king's mobility further) 12...d5 13.Qf3 (threatening checkmate in 1) 13...cxd4 14.Ba3! (cutting off black's king's escape route via c5) 14...Nxf2 15.0-0 (here castling is actually a good move, as it moves white's king out of the way of some annoying knight checks) 15...Rf8 (if black starts giving back material, then black might as well resign on the spot as nothing in the position speaks in black's favour then) 16.Qe2+ d3 17.cxd3 Nxd3 (here we see the point of castling more clearly; if white's king were still on e1, ...Nxd3 would be check, which could give black some time to consolidate) 18. Rfd1! (threatening checkmate in 1) 18...Bf5 19. Qc2! (threatening checkmate in 1; here black is finally forced to give up massive amounts of material just to delay the inevitable), and white is completely winning.
Go through this line carefully (it's quite a good example of how to conduct a proper king hunt), and note how at every move white harasses the black king trying to checkmate it. This leads to black not having time to coordinate their pieces properly, and their king gets caught in an inescapable mating net at the end. This is why in this position (and many, many others as well) king safety trumps material count.

15234: <p>For the position after 10...Kc4:</p>
<pre><code>    [Title &quot;White to move; castling is considered a blunder&quot;]
    [FEN &quot;&quot;]
    [Startply &quot;20&quot;]

    1. e4 e5 2. Nc3 Nf6 3. Nf3 Bb4 4. Bc4 Bxc3 5. Bxf7+ Kxf7 6. bxc3 Nxe4 7. Nxe5+ Kf6 8. Qf3+ Kxe5 9. d4+ Kd5 10. Qf5+ Kc4 11. O-O? d5 12. f3 Bxf5 13. fxe4 Bxe4
</code></pre>
<p>The position from a blitz game I just played; I was Black.</p>
<p>I'm up 5 points of material, but obviously my King is horrifically exposed.</p>
<p><a href="https://en.wikipedia.org/wiki/Stockfish_%28chess%29" rel="nofollow noreferrer">Stockfish</a> rates the position after 10...Kc4 as drawn, which seems surprising given the lack of any immediately obvious threats.</p>
<p>But if White castles with 11.0-0, then the position immediately drops to -5.67. I can only assume that Stockfish believes it can see a series of forced attacks by White which ultimately end in a draw, but dropping tempo at any point allows Black to &quot;escape.&quot;</p>
<p>But a) I'm not sure that I've got that right.
And b) I can't really tell how it's supposed to work if that is right.</p>
 8300: <p>This is a classic case of king safety vs. material balance. Black's king is obviously way less safe than white's, BUT black has a lot more material. So if black manages to survive and consolidate their position, then black will win.</p>
<p>Castling is not a very direct move in this position, and the simplest explanation why it's bad is that it's too slow, allowing black to bring their king to safety by means of playing ...d5 followed by ...Kb5 and then letting the black king slowly creep towards a safe haven surrounded by friendly pieces. This shouldn't come as a great surprise; after all, you gotta strike while the iron is still hot!</p>
<p>The thing that genuninely surprised me about your post was your comment that Stockfish rates the position as drawn. I get different results when running SF on my machine, as it's convinced that white is just winning after trying to immediately kill the black king with Rb1 (threatening Qb5+, with mate soon to follow).</p>
<p>The winning line goes as follows, and I don't see any flaw in it: <strong>11. Rb1!</strong> (cutting off black's king's escape route via b5) <strong>11...c5 12. Qf7+</strong> (forcing black to block its king's mobility further) <strong>12...d5 13.Qf3</strong> (threatening checkmate in 1) <strong>13...cxd4 14.Ba3!</strong> (cutting off black's king's escape route via c5) <strong>14...Nxf2 15.0-0</strong> (here castling is actually a good move, as it moves white's king out of the way of some annoying knight checks) <strong>15...Rf8</strong> (if black starts giving back material, then black might as well resign on the spot as nothing in the position speaks in black's favour then) <strong>16.Qe2+ d3 17.cxd3 Nxd3</strong> (here we see the point of castling more clearly; if white's king were still on e1, ...Nxd3 would be check, which could give black some time to consolidate) <strong>18. Rfd1!</strong> (threatening checkmate in 1) <strong>18...Bf5 19. Qc2!</strong> (threatening checkmate in 1; here black is finally forced to give up massive amounts of material just to delay the inevitable), and white is completely winning.
Go through this line carefully (it's quite a good example of how to conduct a proper king hunt), and note how at every move white harasses the black king trying to checkmate it. This leads to black not having time to coordinate their pieces properly, and their king gets caught in an inescapable mating net at the end. This is why in this position (and many, many others as well) king safety trumps material count.</p>
