Your preferences actually can be captured by expected utility maximization. But if you have the standard preference, here's sort of how the reasoning goes. The worst I can do in that gamble is get a million dollars. So maybe said in another way, there is a rational way of behaving under which the introduction of even a tiny chance of a super bad outcome weighs very, very heavily in your decision process. And so if you're the kind of person that weighs worse cases heavily, you don't even have to weigh them that heavily. You just have to weighing them sort of more than you weigh best cases.

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