In another thread I recommended Quacks. It's a push your luck game where you play as a quack doctor. It's a good game for all levels of experience, at least imo. It's not complicated to explain to new players, yet with all the permutations of rulesets there's a lot of emergent complexity for more experienced players. I think the push your luck aspect also adds to this, as I've had first timers beat me just cause I drew poorly. Some people may really hate that though, but I think it's more fun for newer players to have a chance even at my expense. It's also really fun to peer pressure your friends into drawing too much.