Chess
You play White against the computer. Castling, en passant, pawn promotion (always to a queen), and checkmate and stalemate detection are implemented. Draws by repetition, the fifty-move rule, and insufficient material are not.
The computer looks three half-moves ahead (its move, your reply, its answer) using the negamax algorithm with alpha-beta pruning, which skips branches that cannot beat a move it has already found. At the depth limit it keeps following captures so it never stops in the middle of an exchange.