user25876: (Inspired by this cool problem)
Let’s say it’s White to move. Let A = the number of squares currently attacked by White, and B = the number of squares attacked by White after White’s next move.

What is the maximum possible value of B - A?

A “attacked” square’s definition is just as you’d expect. More rigorously, a square is attacked by White if, after Black skips the next move, a White piece can legally capture anything on that square. Specifically, if it were empty, then after teleporting a dummy black piece onto that square, a White piece must be able to legally capture that dummy piece. (A dummy piece does not attack). If it were occupied by a white piece, then it must be legally defended by another white piece (the sequence “black captures the white piece with a dummy black piece, and white recaptures the dummy piece with some white piece” must be legal). If it were occupied by a black piece, it must be able to be legally captured by a white piece.
For example, in the linked problem above, we have A = 26 and B = 58. This means B - A = 32, which is really high. But is this the best we can do?
Another example: after opening moves 1. e4 c5 2. Bc4 a6 3. Nf3 we note that Black’s c-pawn attacks b4 and d4, but he does not attack f7, because the King cannot move into check. Furthermore, after a random move (say 3. … h6), f5 is attacked by White’s e-pawn.
In the solution, preferably, the “current position” should be legal, but if there’s a really nice illegal solution we should see it too.

user10380: [Title "White to move"]
[StartFlipped "0"]
[fen "1q4Q1/P7/8/8/4B3/8/5k1K/R7 w - - 0 1"]

1.axb8=Q

In the diagram position, WTM controls 4 squares: b8, g3, h3, h1. After 1 axb8=Q, White controls 48: a8-h8 (8), a7, b7, c7, f7, g7, h7, a6-e6 (5), g6, a5, b5, d5, e5, f5, g5, a4, b4, c4, f4, g4, a3, b3, d3, f3, g3, h3, a2, b2, c2, g2, b1-h1 (7).
A=4. B=48. B-A=48-4=44.

user4572: The original problem may be reduced to
[Title "White to move"]
[FEN "5nRB/6PR/8/8/8/8/8/k2K4 w - - 0 1"]

White controls f8, h8, g7, h6 to h1 (6 squares) and 5 squares around the king, for a total of 14 squares.
[Title "After gxf8=Q"]
[FEN "5QRB/7R/8/8/8/8/8/k2K4 w - - 0 1"]

White now controls row 8 (8 squares), row 7 but h7 (7 squares), 4 squares on row 6, 5 on each of the three next rows, 7 squares on second row, 6 squares on first row, for a total of 47 squares.
Thus B - A = 47 - 14 = 33.
In the example given in the original post, I count A = 26 and B = 58, thus B - A = 32. Or, if you do not count squares c2, d2, f2 in your problem as attacked by white, then you would have A = 23 and B = 55, thus B - A = 32 still.

25876: <p>(Inspired by <a href="https://chess.stackexchange.com/q/32845/25876">this cool problem</a>)</p>
<p>Let’s say it’s White to move. Let A = the number of squares currently attacked by White, and B = the number of squares attacked by White after White’s next move.</p>
<blockquote>
<p>What is the maximum possible value of B - A?</p>
</blockquote>
<p><strong>A “attacked” square’s definition is just as you’d expect.</strong> More rigorously, a square is attacked by White if, after Black skips the next move, a White piece can legally capture anything on that square. Specifically, if it were empty, then after teleporting a dummy black piece onto that square, a White piece must be able to legally capture that dummy piece. (A dummy piece does not attack). If it were occupied by a white piece, then it must be legally defended by another white piece (the sequence “black captures the white piece with a dummy black piece, and white recaptures the dummy piece with some white piece” must be legal). If it were occupied by a black piece, it must be able to be legally captured by a white piece.</p>
<p>For example, in the <a href="https://chess.stackexchange.com/q/32845/25876">linked problem</a> above, we have A = 26 and B = 58. This means B - A = 32, which is really high. But is this the best we can do?</p>
<p>Another example: after opening moves <code>1. e4 c5 2. Bc4 a6 3. Nf3</code> we note that Black’s c-pawn attacks <code>b4</code> and <code>d4</code>, but he does not attack <code>f7</code>, because the King cannot move into check. Furthermore, after a random move (say <code>3. … h6</code>), <code>f5</code> is attacked by White’s e-pawn.</p>
<p>In the solution, preferably, the “current position” should be legal, but if there’s a really nice illegal solution we should see it too.</p>
 10380: <pre><code>[Title &quot;White to move&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;1q4Q1/P7/8/8/4B3/8/5k1K/R7 w - - 0 1&quot;]

1.axb8=Q
</code></pre>
<p>In the diagram position, WTM controls 4 squares: b8, g3, h3, h1. After 1 axb8=Q, White controls 48: a8-h8 (8), a7, b7, c7, f7, g7, h7, a6-e6 (5), g6, a5, b5, d5, e5, f5, g5, a4, b4, c4, f4, g4, a3, b3, d3, f3, g3, h3, a2, b2, c2, g2, b1-h1 (7).</p>
<p>A=4. B=48. B-A=48-4=44.</p>
 4572: <p>The original problem may be reduced to</p>
<pre><code>[Title &quot;White to move&quot;]
[FEN &quot;5nRB/6PR/8/8/8/8/8/k2K4 w - - 0 1&quot;]
</code></pre>
<p>White controls f8, h8, g7, h6 to h1 (6 squares) and 5 squares around the king, for a total of 14 squares.</p>
<pre><code>[Title &quot;After gxf8=Q&quot;]
[FEN &quot;5QRB/7R/8/8/8/8/8/k2K4 w - - 0 1&quot;]
</code></pre>
<p>White now controls row 8 (8 squares), row 7 but h7 (7 squares), 4 squares on row 6, 5 on each of the three next rows, 7 squares on second row, 6 squares on first row, for a total of 47 squares.</p>
<p>Thus B - A = 47 - 14 = 33.</p>
<p>In the example given in the original post, I count A = 26 and B = 58, thus B - A = 32. Or, if you do not count squares c2, d2, f2 in your problem as attacked by white, then you would have A = 23 and B = 55, thus B - A = 32 still.</p>
