For me, the most fun group ride is the "race ride" which has no traffic lights and a designated finish line. And team tactics come into play. It's basically a 50 mile road race. Every Saturday that I want to do it.
My Tues/Thurs hammerfest is not a race ride. It's just a hammerfest. Too many lights. We will do a paceline of the strongest riders when there is a strong headwind. It happens spontaneously.