Start with the blue L in the bottom center.
Use the top image of
to find out which tile Stauf responded with.
Take that corresponding letter from the bottom picture, and reply with a piece of the same letter. If there are two tiles to choose from, and one of them has an apostrophe, choose that one, otherwise it doesn't matter.
No matter what stauf does you can now either win with one move, or can easily force a win with the next 2 moves.
Explanation: If the perfect response to Stauf's choice of tile X is tile Y, then, for symmetry reasons, the perfect response to Stauf's choice tile Y is tile X, because if the first three tiles chose are L, X, Y or L, Y, X, the remaining board is the same. Furthermore, when L is chosen first, two of the bottom left tiles are identical, as they have the same remaining neighbours, signified by the "=" sign. Apparently Stauf chooses randomly after you pick the L, probably because he knows it doesn't matter, much like with the 4-in-a-row trilobyte cake puzzle.
Example: Start with L. Stauf chooses the long red at the top. It's a D, so you reply with the other "D"-Tile, the white piece on the top left. No matter what Stauf chooses next, you can either win on the next move by filling everything in, or force a 3 step win.
