Card Game (Expected Value)

The Problem

A deck has cards numbered 1 through $n$, shuffled randomly. You turn over cards one at a time. At any point you may say "stop"; you win \k$where$k$ is the value of the last card turned over. If you don't stop before the deck runs out, you must take the last card.

For $n=3$ (cards 1, 2, 3), what is the expected payoff under optimal play? What is the optimal strategy?