user3405: Take a look at this position:
 [FEN "4k3/pppppppp/8/8/8/8/PPPPPPPP/4K3 w - - 0 1"]

This is a popular chess "tabiya" at our club. The young students play it quite often actually. I placed this position in Deep Fritz 14 for 10 minutes or so, and it told me the game was a draw. A computer isn't needed to figure this out anyhow. Then an idea struck me.
Since pawn moves are the only ones you cannot turn back, shouldn't this position be with the addition of pieces a draw? I am inclined to think so, encouraged by the popular "Chess is a draw" theory.

user3890: If your assumption is:

If a position is a draw and I add new pieces, then the position is still a draw.

Then this is certainly false. As a proof, you may have a look at the position:
      [FEN "r4b1k/2R3np/3p2p1/3Qp1N1/qrb1P2P/P5N1/1B4P1/K1R5 w - - 10 35"]
      [Title "White to move and draw"]

Which is a draw by perpetual check. Notice how black is threatening mate and attacking white's queen at the same time. Now, add a white pawn on e3, a white rook on e2, a black pawn on e6 and a black rook on e7:
      [FEN "r4b1k/2R1r1np/3pp1p1/3Qp1N1/qrb1P2P/P3P1N1/1B2R1P1/K1R5 w - - 10 35"]
      [Title "White to move and fail to draw"]

Which is no longer a draw, since the added pawn blocks the discovered check and the rook controls the f7 square, allowing black to either checkmate white or to win enough material to convert without problems. Note that this also works without adding the extra pawn.
A more tranquil position that also proves the assumption wrong is the next one:
      [FEN "k7/1p6/pP6/P2K4/8/8/5B2/8 w - - 0 1"]
      [Title "An effortless draw"]

Despite being a piece down, black has achieved a drawn position. By simply moving the king back and forth from a8 to b8 black has secured the half point. Note how the position is still a draw without the extra bishop for white. Now, add a white pawn on h2 and a black pawn on h7.
      [FEN "k7/1p5p/pP6/P2K4/8/8/5B1P/8 w - - 0 1"]
      [Title "An effortless win"]

The position is no longer a draw since white can chase off that extra pawn and queen his. If black leaves the protection of his pawns, white can choose to either win by the fox in the chicken coop principle or by securing a safe route to h8 to his pawn. Note that the position arising from the one without the extra bishop is also a win for white.

3405: <p>Take a look at this position:</p>

<pre><code> [FEN "4k3/pppppppp/8/8/8/8/PPPPPPPP/4K3 w - - 0 1"]
</code></pre>

<p>This is a popular chess "tabiya" at our club. The young students play it quite often actually. I placed this position in Deep Fritz 14 for 10 minutes or so, and it told me the game was a draw. A computer isn't needed to figure this out anyhow. Then an idea struck me.</p>

<p>Since pawn moves are the only ones you cannot turn back, shouldn't this position be with the addition of pieces a draw? I am inclined to think so, encouraged by the popular "Chess is a draw" theory.</p>
 3890: <p>If your assumption is:</p>

<blockquote>
  <p>If a position is a draw and I add new pieces, then the position is still a draw.</p>
</blockquote>

<p>Then this is certainly false. As a proof, you may have a look at the position:</p>

<pre><code>      [FEN "r4b1k/2R3np/3p2p1/3Qp1N1/qrb1P2P/P5N1/1B4P1/K1R5 w - - 10 35"]
      [Title "White to move and draw"]
</code></pre>

<p>Which is a draw by perpetual check. Notice how black is threatening mate and attacking white's queen at the same time. Now, add a white pawn on <code>e3</code>, a white rook on <code>e2</code>, a black pawn on <code>e6</code> and a black rook on <code>e7</code>:</p>

<pre><code>      [FEN "r4b1k/2R1r1np/3pp1p1/3Qp1N1/qrb1P2P/P3P1N1/1B2R1P1/K1R5 w - - 10 35"]
      [Title "White to move and fail to draw"]
</code></pre>

<p>Which is no longer a draw, since the added pawn blocks the discovered check and the rook controls the <code>f7</code> square, allowing black to either checkmate white or to win enough material to convert without problems. Note that this also works without adding the extra pawn.</p>

<p>A more tranquil position that also proves the assumption wrong is the next one:</p>

<pre><code>      [FEN "k7/1p6/pP6/P2K4/8/8/5B2/8 w - - 0 1"]
      [Title "An effortless draw"]
</code></pre>

<p>Despite being a piece down, black has achieved a drawn position. By simply moving the king back and forth from <code>a8</code> to <code>b8</code> black has secured the half point. Note how the position is still a draw without the extra bishop for white. Now, add a white pawn on <code>h2</code> and a black pawn on <code>h7</code>.</p>

<pre><code>      [FEN "k7/1p5p/pP6/P2K4/8/8/5B1P/8 w - - 0 1"]
      [Title "An effortless win"]
</code></pre>

<p>The position is no longer a draw since white can chase off that extra pawn and queen his. If black leaves the protection of his pawns, white can choose to either win by the <em>fox in the chicken coop</em> principle or by securing a safe route to <code>h8</code> to his pawn. Note that the position arising from the one without the extra bishop is also a win for white.</p>
