[math-fun] simple curves on punctured planes

What's the simplest example of a simple closed curve in the triply-punctured plane that has winding number 0 around each of the punctures but is not contractible? (Back when I was in grad school in Berkeley in the '80s, there was a painting of one such curve on the wall, along with the associated word in the fundamental group of the surface.) Also, what's the simplest way to prove that no analogous curve exists for the doubly-punctured plane? Jim Propp