- x or more (at least x) of the color must be in the upper/bottom half
- x or more must be in the left/right half
- x or less must be connected at the very start, which would probably be the largest indicator of fairness
- x or less connected groups of one color exist at the start (or reverse, x or less isolated, depending on the approach)
I have for a very long time played with two colors each player anyway, once to mitigate the advantage in the occasional one-sided starting position, but especially because it's naturally much more interesting to me. And still every now and then you will hit just the two colors that seemingly are least favorable at the start.