user-1: rn1qkb1r/1p3pnp/p1p1p1p1/3pP3/3P2P1/2NBBQ1P/PPP2P2/2KR3R w kq - 0 13

Stockfish (depth 30) says the best move is Kb1 with +1.5 evaluation.
I'm having trouble to understand why.
The a2 pawn is not getting threatened soon,
and that the c1-h6 diagonal is well guarded against checks.
Furthermore, it is early game and white has an advantage,
building pressure on black's kingside. Kb1 looks like a tempo wasting move
that just doesn't accomplish much.
The engine also likes Qg3, Ne2 and Bh6, which I deem more active ones.
But can you help me understanding reasons why Kb1 is a good move?

user7657: Typieclly Kb1 (or Kb8) is played after queenside castling to add protection to the "a" pawn. The likely necessity of doing this at some point at the expense of time is one of the reasons queenside castling is not as  popular as kingside castling.  Whether the pawn is attacked immediaely or not is irrelevant.  It's best to do this when not under duress.  In a later critical position, it may be a compromising, time-losing move even though necessary.

user8300: It's difficult to know exactly why the engine makes Kb1 in particular its top move here, and I wouldn't get too hung up on it since it's such a close tie in evaluations between the engine's top moves. But it's really not a bad move at all, so I'm not surprised that the engine recommends it.
The dreadful knight on g7 is a clear indication that something has gone terribly wrong for black, and this together with the fact that white is seriously ahead in development indicates that white should be the one to push in this position. But here black doesn't really have any good way to create any active counterplay at the moment, so white has some time to prepare before going for the kill. When there is time to prepare it is often a good idea to prepare one's position for the attack by placing all the pieces optimally in order to facilitate a concrete winning plan.
So, what does a concrete winning plan look like in this position? I think a sound idea is to go for a pawn break, say f2-f4-f5 since the pawns on e6 and g6 create a nice hook for white to use in order to break black's position. But white could also go for another potential break with c2-c4 if black's king decides to run to the queenside, and for this particular break the white king would be better on b1 than on c1. More generally, the king is going to be safer and less in the way on b1 than on c1, so investing a move in improving its position is not a bad idea when there is no rush.

user12629: Just because Stockfish thinks a move is best doesn't mean it is best. But let's see why Stockfish might like it.
When I look at Stockfish's static evaluation of that position, and move the king from  c1 to b1, I see four sub-evaluations change. In order of the size of the change, those sub-evaluations are:

Psqt bonus. This gives a bonus to each piece based on what square it's on. The king gets a bigger bonus simply by being on b1 instead of c1.

Shelter weakness. The king gets a penalty on c1 because the adjacent d-pawn has moved, and gets no penalty on b1 because none of its adjacent pawns have moved.

Mobility bonus. On b1, the White pieces are slightly more mobile (the rooks can now move to c1 - yes, it counts the square for both rooks) and that gives a bonus.

Shelter storm. Black gets a bonus for the d5 pawn beginning to "storm" the White king if the king is on c1. With the king on b1, the d-pawn does not count as "storming" since it's no longer on an adjacent file to the king, and Black doesn't get this bonus.


All told, it adds up to about 0.5 evaluation points.
It seems that Stockfish is simply having a hard time coming up with a good plan here. At depth 27 it gives Rhf1 as the second-best move, but the line it gives starts with this.
rn1qkb1r/1p3pnp/p1p1p1p1/3pP3/3P2P1/2NBBQ1P/PPP2P2/2KR3R w kq - 0 13

1. Rhf1 Nd7 2. Kb1 a5 3. Rg1

But it doesn't exactly seem like the best sequence for making progress.

-1: <pre><code>rn1qkb1r/1p3pnp/p1p1p1p1/3pP3/3P2P1/2NBBQ1P/PPP2P2/2KR3R w kq - 0 13
</code></pre>
<p>Stockfish (depth 30) says the best move is <code>Kb1</code> with +1.5 evaluation.
I'm having trouble to understand why.
The <code>a2</code> pawn is not getting threatened soon,
and that the <code>c1-h6</code> diagonal is well guarded against checks.</p>
<p>Furthermore, it is early game and white has an advantage,
building pressure on black's kingside. <code>Kb1</code> looks like a tempo wasting move
that just doesn't accomplish much.</p>
<p>The engine also likes <code>Qg3</code>, <code>Ne2</code> and <code>Bh6</code>, which I deem more active ones.
But can you help me understanding reasons why <code>Kb1</code> is a good move?</p>
 7657: <p>Typieclly Kb1 (or Kb8) is played after queenside castling to add protection to the &quot;a&quot; pawn. The likely necessity of doing this at some point at the expense of time is one of the reasons queenside castling is not as  popular as kingside castling.  Whether the pawn is attacked immediaely or not is irrelevant.  It's best to do this when not under duress.  In a later critical position, it may be a compromising, time-losing move even though necessary.</p>
 8300: <p>It's difficult to know exactly why the engine makes Kb1 in particular its top move here, and I wouldn't get too hung up on it since it's such a close tie in evaluations between the engine's top moves. But it's really not a bad move at all, so I'm not surprised that the engine recommends it.</p>
<p>The dreadful knight on g7 is a clear indication that something has gone terribly wrong for black, and this together with the fact that white is seriously ahead in development indicates that white should be the one to push in this position. But here black doesn't really have any good way to create any active counterplay at the moment, so white has some time to prepare before going for the kill. When there is time to prepare it is often a good idea to prepare one's position for the attack by placing all the pieces optimally in order to facilitate a concrete winning plan.</p>
<p>So, what does a concrete winning plan look like in this position? I think a sound idea is to go for a pawn break, say f2-f4-f5 since the pawns on e6 and g6 create a nice hook for white to use in order to break black's position. But white could also go for another potential break with c2-c4 if black's king decides to run to the queenside, and for this particular break the white king would be better on b1 than on c1. More generally, the king is going to be safer and less in the way on b1 than on c1, so investing a move in improving its position is not a bad idea when there is no rush.</p>
 12629: <p>Just because Stockfish thinks a move is best doesn't mean it is best. But let's see why Stockfish might like it.</p>
<p>When I look at Stockfish's static evaluation of that position, and move the king from  c1 to b1, I see four sub-evaluations change. In order of the size of the change, those sub-evaluations are:</p>
<ul>
<li><p>Psqt bonus. This gives a bonus to each piece based on what square it's on. The king gets a bigger bonus simply by being on b1 instead of c1.</p>
</li>
<li><p>Shelter weakness. The king gets a penalty on c1 because the adjacent d-pawn has moved, and gets no penalty on b1 because none of its adjacent pawns have moved.</p>
</li>
<li><p>Mobility bonus. On b1, the White pieces are slightly more mobile (the rooks can now move to c1 - yes, it counts the square for <em>both</em> rooks) and that gives a bonus.</p>
</li>
<li><p>Shelter storm. Black gets a bonus for the d5 pawn beginning to &quot;storm&quot; the White king if the king is on c1. With the king on b1, the d-pawn does not count as &quot;storming&quot; since it's no longer on an adjacent file to the king, and Black doesn't get this bonus.</p>
</li>
</ul>
<p>All told, it adds up to about 0.5 evaluation points.</p>
<p>It seems that Stockfish is simply having a hard time coming up with a good plan here. At depth 27 it gives Rhf1 as the second-best move, but the line it gives starts with this.</p>
<pre><code>rn1qkb1r/1p3pnp/p1p1p1p1/3pP3/3P2P1/2NBBQ1P/PPP2P2/2KR3R w kq - 0 13

1. Rhf1 Nd7 2. Kb1 a5 3. Rg1
</code></pre>
<p>But it doesn't exactly seem like the best sequence for making progress.</p>
