Is there a science to figure that out?
Is brown always dominant over green or could I get a darker green egg?
There are two colors for eggshells, white or blue. Blue is dominant over white. Brown eggs are the result of a coating that is applied on top of white eggshells. Green is the result of that same brown coating, but applied on a blue eggshell. There are over nine different genes for that brown coating, and a bird can have a combination of several of those genes.
Now, since the hen already had a brown coating gene, and may only have one blue eggshell gene instead of two; you might get a variety shades of green or brown from the resulting chicks.