user3237: After making my engines evaluate the starting position for more than 10 hours each, here is what I got:
.
Fritz 12:
Depth = 25/65
Time = 10 hours and 30 minutes

1.f3 : -0.90 
1.g4 : -0.77
1.Nh3 : -0.56
1.Na3 : -0.52
1.h4 : -0.47
1.b4 : -0.47
1.a4 : -0.42

All 13 other moves are -0.25 or more.
.
Houdini 3 Pro x64
Depth = 29/76
Time = 11 hours and 45 minutes

1.g4 : -0.51
1.f3 : -0.50
1.Nh3 : -0.38
1.Na3 : -0.37
1.h4 : -0.25
1.b4 : -0.20
1.a4 : -0.17

All 13 other moves are -0.12 or more.
.
One thing seems very probable: the worst possible first move is either 1.f3 or 1.g4.
So between these two moves: which is the number #1 worst possible move?

user9030: It's terribly wrong to dump an engine output as an opening analysis! Engines are weaker in strategy comparing to humans. An opening analysis should be done by a computer-aided human, not by an engine itself. 

user3688: I have probably the largest high quality database in private hands on the planet, including human and engine games.  Tens of millions of games.  A proper assessment of a move's merit has to include both a deep evaluation of the strongest engine available (right now that's Stockfish) combined with comprehensive empirical data.
Empirically, f3 is definitely the worst.  Nh3 and g4 challenge it but cannot match it in terms of chess malpractice.  As for the defenders of the Grob (g4), sorry, it's a bad move, no question, and this opinion is double-reinforced by how often it has been seen, which is about 4-5x more often than f3.  Its principal advantage is that it doesn't lose material right away by force.

user2042: 
What is the worst possible first move for White: 1.f3 or 1.g4?

f3 doesn't contribute to the piece development ( it actually hinders it by taking away the best square for the Ng1 ), it doesn't fight for the center ( it only strengthens the e4 square that White can claim anyway with 1.Nc3 or 1.e4 ) and above all it exposes the king. 
g4 vacates g2 for the Bf1 ( fianchettoed bishop is usually good ), it helps in the fight for the center indirectly ( you can weaken Black's control of d5 and e4 if Black plays ...Nf6 at some point, by simply playing g5 ) and pawn at g4 can be useful in kingside attack if Black castles short. It does weaken f4 and h4, so it is somewhat dubious, but it is playable ( although I doubt White can reach full equality...).
Therefore, when we compare the above facts, we can see that 1.f3 is clearly the worst first move, based on the opening theory ( since only one move is played it is to early to make final conclusions, since White may transpose into decent position with his next moves ).

3237: <p>After making my engines evaluate the starting position for more than 10 hours each, here is what I got:</p>

<p>.</p>

<p>Fritz 12:</p>

<p>Depth = 25/65</p>

<p>Time = 10 hours and 30 minutes</p>

<ul>
<li>1.f3 : -0.90 </li>
<li>1.g4 : -0.77</li>
<li>1.Nh3 : -0.56</li>
<li>1.Na3 : -0.52</li>
<li>1.h4 : -0.47</li>
<li>1.b4 : -0.47</li>
<li>1.a4 : -0.42</li>
</ul>

<p>All 13 other moves are -0.25 or more.</p>

<p>.</p>

<p>Houdini 3 Pro x64</p>

<p>Depth = 29/76</p>

<p>Time = 11 hours and 45 minutes</p>

<ul>
<li>1.g4 : -0.51</li>
<li>1.f3 : -0.50</li>
<li>1.Nh3 : -0.38</li>
<li>1.Na3 : -0.37</li>
<li>1.h4 : -0.25</li>
<li>1.b4 : -0.20</li>
<li>1.a4 : -0.17</li>
</ul>

<p>All 13 other moves are -0.12 or more.</p>

<p>.</p>

<p>One thing seems very probable: the worst possible first move is either 1.f3 or 1.g4.</p>

<p>So between these two moves: which is the number #1 worst possible move?</p>
 9030: <p><strong>It's terribly wrong to dump an engine output as an opening analysis!</strong> Engines are weaker in strategy comparing to humans. An opening analysis should be done by a computer-aided human, not by an engine itself. </p>
 3688: <p>I have probably the largest high quality database in private hands on the planet, including human and engine games.  Tens of millions of games.  A proper assessment of a move's merit has to include both a deep evaluation of the strongest engine available (right now that's Stockfish) combined with comprehensive empirical data.</p>

<p>Empirically, f3 is definitely the worst.  Nh3 and g4 challenge it but cannot match it in terms of chess malpractice.  As for the defenders of the Grob (g4), sorry, it's a bad move, no question, and this opinion is double-reinforced by how often it has been seen, which is about 4-5x more often than f3.  Its principal advantage is that it doesn't lose material right away by force.</p>
 2042: <blockquote>
  <p>What is the worst possible first move for White: 1.f3 or 1.g4?</p>
</blockquote>

<p><code>f3</code> doesn't contribute to the piece development ( it actually hinders it by taking away <strong>the best</strong> square for the <code>Ng1</code> ), it doesn't fight for the center ( it only <strong>strengthens</strong> the <code>e4</code> square that White can claim <strong>anyway</strong> with <code>1.Nc3</code> or <code>1.e4</code> ) and above all it exposes the king. </p>

<p><code>g4</code> vacates <code>g2</code> for the <code>Bf1</code> ( fianchettoed bishop is usually good ), it helps in the fight for the center indirectly ( you can weaken Black's control of <code>d5</code> and <code>e4</code> if Black plays <code>...Nf6</code> at some point, by simply playing <code>g5</code> ) and pawn at <code>g4</code> can be useful in kingside attack if Black castles short. It does weaken <code>f4</code> and <code>h4</code>, so it is somewhat dubious, but it is playable ( although I doubt White can reach full equality...).</p>

<p>Therefore, when we compare the above facts, we can see that <code>1.f3</code> is clearly the worst first move, <strong>based on the opening theory</strong> ( since only one move is played it is to early to make <strong>final</strong> conclusions, since White may transpose into decent position with his next moves ).</p>
