Take the definition of day to be sunrise to sunset, that is all the time that any part of the star is visible from the point on the planet.

Given that the diameter of the star is greater than the planet, there is slightly more day than night. (Draw the two lines that are tangent to 2 circles, a larger circle and a smaller circle exterior to each other.) The closer the planet is to the star the bigger the effect.

If the star was smaller than the planet, like a planet orbiting a neutron star (diameter of only 20 km), then geometrically night would be more than day. So a very large planet orbiting very close to a very compact star would maximize night.

Take the definition of day to be sunrise to sunset, that is all the time that any part of the star is visible from the point on the planet.

Given that the diameter of the star is greater than the planet, there is slightly more day than night. (Draw the two lines that are tangent to 2 circles, a larger circle and a smaller circle exterior to each other.) The closer the planet is to the star the bigger the effect.

If the star was smaller than the planet, like a planet orbiting a neutron star (diameter of only 20 km), then geometrically night would be more than day. So a very large planet orbiting very close to a very compact star would maximize night. PSR J1719-1438 b is about 1000 times the radius of its neutron star and orbits at a distance of less than 1 solar radius.