Consider all configurations where the White Queens are located in the following two pengagons
inside the unit square [0,1]x[0,1]
[[0, 0], [a, a], [a, a+b-e], [a-e, a+b-e], [0, b], [0, 0]]
[[0, 0], [a, a], [a, a+b-e], [a-e, a+b-e], [0, b], [0, 0]]
and
[[v0, 0], [v0+c, 0], [v0+c, c-2*f+d], [v0+c-f, c-f+d], [v0, d], [v0, 0]]
then the Black Queens are located in the two pentagons
[[v0, 1], [a, 1], [a, v0+2*c-2*f+d-a], [1/2*v0+1/2*d-1/2*b+c-f, 1/2*v0+1/2*d+1/
2*b+c-f], [v0, v0+b], [v0, 1]]
and
[[1, 1], [v0+c, v0+c], [v0+c, a+b-e], [a+b-e+v0-d, a+b-e], [1, 1+d-v0], [1, 1]]
The area of the White Queens region is
a*b-1/2*e^2+c*d+1/2*c^2-f^2
and the area of the Black Queens region is
-d+2*v0-a-a*b-c*d-3/2*c^2+2*c*f-7/4*v0^2-1/2*v0*b+a*v0-a^2+2*a*d+3*a*c-2*a*f+3/
2*b*d-3/4*b^2+2*b*c-b*f+1/2*v0*d-2*v0*c+v0*f+f*d-3/4*d^2+a*e+b*e-e*d-e*c-1/2*e^
2-f^2
Optimally, these should be the same. Maximizing them under this constaint sh\
ows that
the maximal area (for each of them) is
7/48
and it is achieved with the following configuration for White followed by Bl\
ack
[[[[0, 0], [1/4, 1/4], [1/4, 1/2], [1/6, 1/2], [0, 1/3], [0, 0]], [[1/2, 0], [3
/4, 0], [3/4, 1/4], [2/3, 1/3], [1/2, 1/6], [1/2, 0]]], [[[1/2, 1], [1/4, 1], [
1/4, 3/4], [1/3, 2/3], [1/2, 5/6], [1/2, 1]], [[1, 1], [3/4, 3/4], [3/4, 1/2],
[5/6, 1/2], [1, 2/3], [1, 1]]]]