I had Armadillos and swapped them for Gatorskins. So far no flats, but I do carry CO2 or a pump (Topeak Road Morph G), levers, and a tube and patches. I did have a presta valve fail on me before a ride before I left home and swapped out the tube. Just because you have a puncture resistant doesn't mean the tube still can't fail.

Two is one, one is none.