Don't play the lottery. And don't go to Harvard.

Every once in a while when I'm trying to persuade someone that from a monetary perspective it's irrational to buy lottery tickets, I hear the following response: But someone wins it. In this particular context, that response is a trivial mistake of not differentiating between conditional and unconditional probabilities: sure the probability of someone winning is close to one (not quite one but almost there), but what you should be concerned with is the conditional probability of that someone being you, which is, well, pretty close to zero.

Is the same mistake responsible for the popularity of the "American dream" (as in: surely, a story of "from rags to riches" will happen every once in a while, but what makes you think it'll happen to you)? And if so--is this mistake evolutionarily deliberate, in that if we knew the true odds, we'd all just stop trying?

I think the answer is yes and no, respectively. Yes, it is the same mistake; but the reasons we're making it are not uniform. We are able to recognize some conditional probability situations (i.e. poker hands or SAT problems) as such, while others (like the lottery or the American dream), we are not. Different context fools us into thinking those things are different in essence. Whereas if the mistake were evolutionarily selected for, we just wouldn't be able to deal with conditional probabilities at all, ever.