Due to advances in opening book theory and the introduction of chess
supercomputers in recent times, I regard the most recent estimates of the
first-move-of-the-game advantage (by white) in Chess as the most reliable
and accurate available.  These fall generally in the 54%-56% range as wins
for white.  Specifically, I find the "chessgames.com" results of 55.06%
and CEGT results of 55.40% wins for white the most compelling.  Also, it is
noteworthy that the CEGT results (involving computer AI players
exclusively) eliminated what a few fuzzy thinkers once considered a
legitimate possibility that "psychological factors" were solely,
artificially responsible for white's first move advantage.

I was intrigued by Joe Joyce's assessment that white's first move
advantage, as established statistically, is higher than one would
intuitively expect.  So, I devised a method to define and quantify it
mathematically based upon what is dictated by the white-black turn order
itself to discover what is actually predicted.  The amount of the 
all-but-proven first move advantage by white now seems quite appropriate to
me.

Note:  The following table can be adapted to any chess variant with a
white-black turn order.  Its use is not restricted only to Chess.

first move advantage (white)

white-black turn order

http://www.symmetryperfect.com/shots/wb/wb.pdf

2 pages

I've read that the average game of Chess runs appr. 40 moves.  So, I
completed series calculations for 40 moves.  However, anyone is free to
extend the series calculations as far as desired using a straightforward
formula.

Of course, white's first move advantage is greatest at the start of the
game, gradually reduces and is least at the end of the game.

The "specific move ratios" simply compare how many moves each player has
taken up to every increment in the game.  [The ratio is optionally
presented at par 10,000 for white.]

The "average move ratios" average all of the specific move ratios that
have occurred up to every increment in the game.  [The ratio is always
presented at par 10,000 for white.]  

In the example provided, a simple (unweighted) average is used whereby no 
attempt is made to unequally weight the value of the first move of the 
average-length game (white's move #1) compared to the value of the last
move of the average-length game (black's move #40) in accordance with
their relative importance.

At par, the "chessgames.com" results can optionally be expressed as
10000:08162.  

At par, the CEGT results can optionally be expressed as 10000:08051.

The table results are 10000:09465 (at black's move #40).

This accounts for only 27.45%-29.59% of the observed statistical advantage

(for white) which brings us to the crossroads:

Those who support the theory that the last move of the game (the checkmate
move) is the most important and valuable should employ a steep weighted
average defining this linear function.  Unfortunately, doing so will cause
the table results which are already too low for Chess to become
significantly lower, rendering the irrefutably-existant first move
advantage utterly inexplicable.

Those who support the theory that the very first move of the game is the
most important and valuable should employ a steep weighted average defining
this linear function.  Fortunately, doing so by the appropriate amount will
cause the table results which are too low for Chess to become significantly
higher, roughly in agreement with the observed statistical advantage (for
white).