Optimal Strategy for a Three-Card Game

Three cards with values $n$, $n+1$, and $n+2$ are placed face-down in a random order. You do not know $n$. You flip cards one at a time and make decisions as follows: - Flip the first card. You may **stay** (accept its value as your payoff) or **discard** it and move on. - Flip the second card. You may **stay** or **discard** it, in which case you must take the third card's value. What strategy maximizes your expected payoff? What is the expected payoff under optimal play?