Single Comment

I feel I need to ask again whether you are arguing about the SIZE of the
first-turn advantage, or the EXISTENCE of the first-turn advantage? 
Because you said earlier you were arguing over its existence, but all of
your arguments seem to be about its size.

You could be a thousand moves away from mounting a credible attack, but
that doesn't mean the value of a move is zero.  After you move, you will
only be 999 moves away from a credible attack, which surely must be at
least a tiny bit better than 1000?

Your typical player probably won't notice that advantage.  But then, a lot
of players probably don't notice the first-turn advantage in FIDE, either.
 Small is not the same as zero, and what counts as "small" depends on how
good you are and how many times you're playing.

And zero first-turn advantage isn't even necessarily desirable.  Suppose
we have a game where players are allowed to pass on their turn, the initial
array is symmetrical, and the players know that there is no first-turn
advantage.  Since there is no first-turn advantage, passing is (by
definition) at least as good as anything else you can do on your first
turn, so you might as well pass.  Then the second player is in exactly the
same position as the first player on his first turn, so he might as well
pass.  So not only is the perfect strategy obvious, it's also incredibly
boring.

But even if passing isn't allowed, the first player either has a move that
is EXACTLY AS GOOD as passing--which I'm not sure is possible, and I
don't think it changes the outcome compared to allowing passing--or else
the best possible move is WORSE than no move at all, which means we've
simply traded a first-turn advantage for a SECOND-turn advantage.

All else being equal, I think we want the first-turn advantage to be
"small".  We might even want people to be uncertain whether the advantage
lies with the first player or the second player, perhaps by using an
asymmetric starting array or placing special restrictions on the first move
(such as moving half as many pieces as normal).  But if you could somehow
prove that the first-turn advantage was exactly zero, I think that would
probably end up being bad (not so much because the advantage was zero, but
because you were able to prove it).