The (Almost) Impossible Chessboard Problem

The Problem
You and a friend have been wrongly convicted and sentenced to lengthy prison terms. When you arrive at the prison, the warden greets you and, as a gesture of goodwill, offers you a chance for freedom. He says: 

One of you will come with me into a room in which there's a checkerboard with a coin on each square. I can flip as many coins as I want, creating any pattern of heads and tails I desire. I will then place a key in a compartment under one of the squares. You will see which square I choose. Now you will flip exactly one coin. You'll be led out the back door and your friend will come in. He's been kept far away and knows nothing about what has happened so far. After studying the board, he will guess which square holds the key. If he's correct, you both go free. Before we start, you two can confer and decide on a strategy. I will listen in on your deliberations.

What's your strategy? How often will it work?
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