Dice Payoff: Product of Two vs. Square of One

You can play one of two games: - **Game 1:** Roll two fair six-sided dice. Your payoff is the product of the two outcomes. - **Game 2:** Roll one fair six-sided die. Your payoff is the square of the outcome. (a) Without any calculation, argue intuitively which game has the higher expected payoff. (b) Verify your answer with explicit calculations.