Dicey Trickies

There are two requirements in order for rolling a die and multiplying the result by n to yield an odd number. The number rolled on the die must be odd (50% chance), and n must be odd (we can assume there's a 50% chance of n being odd). When you multiply the two probabilities together, the there is a 25% chance of the final number being odd.

In order for rolling n dice to yield an odd number, there must be an odd amount of odd number outcomes. The probability that one roll will yield an odd number is 50%, so there is a 50% chance of there being an odd amount of odd number outcomes.

Let's suppose n is an odd number.

Then the final result of rolling n dices has a 50% chance of being odd, and a 50% chance of being even. The result of rolling 1 dice also has a 50% chance of being odd, and a 50% chance of being even. So when you multiply the result by n, the final result might be odd or even.

Hence, in both cases when n is odd, there is an equal chance of having an odd final result number.

But what if n is an even number?

Rolling n dices will still have a 50-50 chance of odd and even, but when you roll 1 dice and multiply by n, it must be even! Hence, the result of rolling n dices must be odd.

Hence, in both cases when n is even, rolling n dices will have a higher chance of having an odd final result number.

In the 4 cases, 3 of them gives rolling n dices an odd result, while only 1 of them give rolling 1 dice and multiply by n an odd result.

So the answer is rolling n dices.