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It seems that most of you already know this, but maybe it's still helpful
to note that there is a definite answer for who wins chess given perfect
play on both sides (white, black, or neither [draw]).  This is true of any
chess variant that involves a fixed turn structure, perfect information
(& no randomization), and finite length (here's where we need something
like the 50 turn rule).

So, in the mathematical sense, any such chess variant either has a perfect
1st turn, perfect 2nd turn, or absolutely no advantage.

Joe keeps referring to "noise", which is how we can manage to talk about
a 1st turn advantage without the mathematics making it boring.  So far no
one has actually defined the framework of the question, but it seems
generally to be accepted as referring to people's current thoughts on
optimum strategies, and how those interact.  I suppose to make this
rigorous we would want to define the fuzzy value of positions (it's
unclear how to do this, though current chess programs are probably a good
starting idea), then allow for some randomness in the players' moves that
biases toward high value positions.  Then I think we should say there's
"no" advantage if the probability distribution of wins-draws-losses given
this framework has no advantage with statistical significance.  So we say
there's no advantage if the noise drowns out whatever perfect mathematical
advantage actually exists.  (I think this is essentially what Joe has been
saying?)