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One interesting Chess variant which tries to solve White's first-move advantage is Pie Rule Chess, which works as follows:

• White makes a move.
• Black then decides whether he wants to play with the white or black pieces.
• The came then continues as normal (with the possibility of the players swapping seats).

Now, in terms of what side to play based on the 20 possible opening moves of FIDE chess, here is the choices I would make:

First move	Side to play
a3	Black
a4	Black
Na3	Black
b3	???
b4	???
c3	Black
c4	White
Nc3	White
d3	???
d4	White
e3	???
e4	White
f3	Black
f4	???
Nf3	White
g3	???
g4	???
h3	Black
h4	Black
Ng3	Black

Any other opinions on using the pie rule in FIDE Chess?

Edit: I note that the Pie Rule does nothing to discourage Black from playing to draw. My answer to the draw problem is to make it so both players get 0 points (instead of half a point) in a drawn game; both players lose. Or have it so that the player with more material on the board wins .75 points after a three-fold repetition/50 moves without capture/insufficient mating material position. We can also consider the Ko rule for chess: You can not repeat a position on the board that has been already played.