Mathematics

The key is recognizing that expectation is linear, so $E(X)$ factors nicely across independent dice, while $E(Y)$ requires you to account for how products behave—they're not linear. For $X$, you can use symmetry: each die contributes equally to the average sum. For $Y$, you must sum over all 36 outcomes since the product of independent random variables doesn't factor as simply as their sum does. Computing both directly reveals which dominates.

The key is recognizing that expectation is linear, so $E(X)$ factors nicely across independent dice, while $E(Y)$ requires you to account for how products behave—they're not linear. For $X$, you can use symmetry: each die contributes equally to the average sum. For $Y$, you must sum over all 36 outcomes since the product of independent random variables doesn't factor as simply as their sum does. Computing both directly reveals which dominates.