A stranger threatens infinite harm for five dollars — do the math anyway

Nick Bostrom's thought experiment: a mugger claims he'll harm an astronomical number of people unless you hand over five dollars, and swears he has the power to do it. The odds of that being true are tiny, but the claimed harm is so vast that pure expected-value math says pay him anyway. It exposes a breakdown in weighing tiny probabilities against unbounded stakes.

— Nick Bostrom, Pascal's Mugging: Tiny Probabilities of Vast Utilities — Analysis, 2009