user24659: In a recent game, I forked a queen and rook with a knight. After seeing no immediate threats from 8. Qf4 I immediately captured with 8. ...Nxb3. Apparently this was quite a mistake (a 213 centipawn evaluation drop), but it's not clear to me why the material advantage from Nxb3 is inferior to Stockfish's recommendation of Nxc2, let alone far superior.
[White "White"]
[Black "Black"]

[fen ""]

1. e4 c5 2. Bc4 { B20 Sicilian Defense: Bowdler Attack } b6 3. a4 Bb7 4. Qf3 e6 5. Ra3? { (-0.77 → -2.15) Mistake. d3 was best. } a6 6. Rb3 Nc6 7. Nh3? { (-2.78 → -5.30) Mistake. Re3 was best. } Nd4 8. Qf4 Nxb3? { (-5.02 → -2.89) Mistake. Nxc2 was best. } 9. Ng5?? { (-2.89 → -6.87) Blunder. Bxb3 was best. } f6 10. Nxe6 dxe6 11. Bxe6?! { (-5.59 → -10.58) Inaccuracy. Bxb3 was best. } Nd4 12. Bg4 Nxc2+ 0-1

What am I missing here? Why shouldn't Nxb3 be played (or maybe, why is Nxc2 far superior)?

user18809: A 213 "centipawn" loss can be critical in an equal position. If you still have a +9 position, it's irrelevant. In this case, I think the engine dislikes to take the rook right now because 8...b5 looks like a stronger move. If White removes the bishop, you can still take the rook, while 9.axb5 axb5 would make your ...Ra1 threat unstoppable

user1296: Note, also, that Nxc2 is +1 on material while Nxb3 is +2 as the knight should be captured--I do not see why your opponent launched that futile attack and let the knight escape.
However, along with that +1 material the king has to move, costing him several moves to get the rook out and the king to safety.

user14767: The key point is that taking the rook reduces your positional advantage.

Your knight is active but the rook is passive;
With your knight on d4 the squares the rook can move to are extremely limited. After 8. ... Nxc2+ 9. Kf1 h6, only f3 and g3 are better squares for the rook. However, with the advancement of pawns on the king side, the queen will be chased away and the development of Nf6 will trap the rook. This will gain both the material advantage and the increasing positional advantage.

This is reflected in the Stockfish evaluation as Nxb3 yields -2.3, with the -2 coming from the material whereas Nxc2+ yields -3.8.

24659: <p>In a recent game, I forked a queen and rook with a knight. After seeing no immediate threats from 8. Qf4 I immediately captured with 8. ...Nxb3. Apparently this was quite a mistake (a 213 centipawn evaluation drop), but it's not clear to me why the material advantage from Nxb3 is inferior to Stockfish's recommendation of Nxc2, let alone <em>far</em> superior.</p>
<pre><code>[White &quot;White&quot;]
[Black &quot;Black&quot;]

[fen &quot;&quot;]

1. e4 c5 2. Bc4 { B20 Sicilian Defense: Bowdler Attack } b6 3. a4 Bb7 4. Qf3 e6 5. Ra3? { (-0.77 → -2.15) Mistake. d3 was best. } a6 6. Rb3 Nc6 7. Nh3? { (-2.78 → -5.30) Mistake. Re3 was best. } Nd4 8. Qf4 Nxb3? { (-5.02 → -2.89) Mistake. Nxc2 was best. } 9. Ng5?? { (-2.89 → -6.87) Blunder. Bxb3 was best. } f6 10. Nxe6 dxe6 11. Bxe6?! { (-5.59 → -10.58) Inaccuracy. Bxb3 was best. } Nd4 12. Bg4 Nxc2+ 0-1
</code></pre>
<p>What am I missing here? Why shouldn't Nxb3 be played (or maybe, why is Nxc2 far superior)?</p>
 18809: <p>A 213 &quot;centipawn&quot; loss can be critical in an equal position. If you still have a +9 position, it's irrelevant. In this case, I think the engine dislikes to take the rook right now because 8...b5 looks like a stronger move. If White removes the bishop, you can still take the rook, while 9.axb5 axb5 would make your ...Ra1 threat unstoppable</p>
 1296: <p>Note, also, that Nxc2 is +1 on material while Nxb3 is +2 as the knight should be captured--I do not see why your opponent launched that futile attack and let the knight escape.</p>
<p>However, along with that +1 material the king has to move, costing him several moves to get the rook out and the king to safety.</p>
 14767: <p>The key point is that taking the rook reduces your positional advantage.</p>
<ul>
<li>Your knight is active but the rook is passive;</li>
<li>With your knight on <code>d4</code> the squares the rook can move to are extremely limited. After <code>8. ... Nxc2+ 9. Kf1 h6</code>, only <code>f3</code> and <code>g3</code> are better squares for the rook. However, with the advancement of pawns on the king side, the queen will be chased away and the development of <code>Nf6</code> will trap the rook. This will gain both the material advantage and the increasing positional advantage.</li>
</ul>
<p>This is reflected in the Stockfish evaluation as <code>Nxb3</code> yields -2.3, with the -2 coming from the material whereas <code>Nxc2+</code> yields -3.8.</p>
