Fifteen

Two players take turns choosing one of the whole numbers 1 to 9. Each number can only be chosen once — once someone takes it, it's gone. The first player to hold any three numbers that add up to exactly 15 wins. If all nine numbers get taken and nobody has three that add to 15, it's a draw.

Here's a secret: this is actually the exact same game as Noughts and Crosses in disguise! (1 through 9 can be arranged in a 3×3 grid where every row, column, and diagonal adds up to 15 — a “magic square.”) That's also why the computer opponent below never makes a mistake: since it's really tic-tac-toe, perfect play always ends in at least a draw. Can you force one?