I'm with Hissin - Amsoil would likely tell you to change the filter every 3-4K, and to pull a sample and send it in for analysis to determine when the oil needs to be changed. My brother routinely gets 15-25K on Amsoil in a Powerstroke diesel before analysis indicates it should be changed. Of course, those have a much better filtration system, and they hold a boat-load of oil. Color of the oil or mileage has no predictive value at all on a synthetic's ability to protect/lubricate.
Me - I buy the least expensive synthetic I can find (Shell Rotella T for diesels) and run it in my wife's Bimmer as BMW specs synth for that engine. We change the filter every 3K, and the oil every 6k. Her oil change indicator (looks at temps, miles, revs, etc.) recommends a change every 10-12K depending on how it's driven. In mine I use a quality dino oil, or an inexpensive synth BLEND (on sale) and change oil and filter every 3K.