Just as in your second poll, the results should be statistically equal.

In the first case, I'm 100% sure I'll make $100.

In the second, I have a 50% chance of getting nothing, and a 50% chance of making $200. That's an average of $100.

So it shouldn't matter. But in reality 50%/50% flips of a coin probably aren't really 50/50. One side of the coin is likely heavier than the other, and should land down more often than the other. So if you knew which side that was, you'd want to bet against it.

That's the case with dice, where the 1 and 6 are opposite each other. The additional dimples on the 6-side make that side of the die lighter. So, if the die is rolled a million times, that side will show slightly more often.

Boring data, I know...