Tic-Tac-Toe is the classic example of a game that is mathematically impossible to win if both players play perfectly (check out the movie War Games).
Connect three X ’s or O ’s. Place one piece per turn in the 3 by 3 grid.
Calculation - Determine all the possible moves and responses and so forth. This is a great exercise in simple calculation and visualization, and will help your math abilities in general.
Control the middle. The center piece is critical. After the center piece, just find a way to set up two in a row in two different directions. This is the classic way to win this game. On defense, just guard against this tactic and you’ll tie every time.