Suppose that the choice is offered to you out of the blue and for a brief moment, during which you cannot exchange with anyone. So for example, you cannot ask your wealthy friend to bankroll your roll of the dice. The choice is yours and yours only.
Resolves by poll created after closure.
I think that is a good example where some people would not choose by expected value. Myself, for example. I do not see significant difference between effects on my life if i get 1 million or 10 million. The size of the second option prize is not important. So instead of picking highest expected value i would go for lowest probability of not recieving anything (because for my life there would be difference between 0 and 20k).
@KongoLandwalker Excellent comment. Indeed the expected value is only the first-order moment. It captures very little information about a random variable or a probability distribution. Therefore, its usefulness for decision-making is correspondingly limited.