I haven't bred them, so I can't speak from experience. That said ...

I believe that the amount of white has genetic influences. That is to say, I believe that if you were to breed low-white to low-white or high-white to high-white for many generations, you would start to get snakes that would "breed true" and produce primarily low- or high-whites, respectively.

I base this belief on several factors. For one, it makes sense to me that there would be other genetic factors that influence the amount of white that could be selected for. We know that other known, single-gene mutations (spider, sable, etc.) influence the amount of white -- generally increasing the percentage. Why shouldn't there be other genes that influence the expression of the pied gene which simply aren't expressed visually in its absence?

Now, obviously it would take quite a few generations to "fix" those other genes in a bloodline. Without trying to select for anything, and just randomly breeding high and low whites, I do believe that the amount of white is going to be random, AND that a highly outcrossed high or low white could easily produce animals with the opposite distribution of white. This is why I think many people see the amount of white as being random -- because in their animals, it is!

Two, I *think* that the empirical evidence seems to suggest that is can be selected for. I have seen and heard of individuals who claim to have done just that, and to have lines that produce high whites fairly consistently. Maybe this is just a marketing ploy, but then again ... Maybe not.

Also, it seems to me that, when looking at a bunch of pieds for sale from the same clutch, they very frequently look to have similar amounts of white. There is obviously variation, but I often find the similarity between clutchmates to be striking.

Tl;dr version is, I believe that the degree of white is influenced by genetic factors and can be selected for, but that in the absence of active selection, in an out-crossed animal the degree of white will be random.

I currently own a no-white pied female; my plan is to pick up a high-white female and high-white male. My hypothesis is that the no-white gal will produce a mix of whites, while the high-whites will produce all high whites. Tiny sample size, but I'm curious as to the outcome (many years down the road, since my high-whites probably haven't even been born yet ) ...