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jsteinhardt comments on A Thought on Pascal's Mugging - Less Wrong Discussion
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The OP is not living in the least convenient possible world. In particular, let X be the worst thing that could happen. Suppose that at the end of the day you have calculated that X will occur with probability 10^(-100) if you don't pay the mugger $5. Assuming that you wouldn't pay the mugger, then by definition of the utility function it follows that u($5) > 10^(-100) u(X). So u(X) < 10^(100) u($5) and is therefore bounded. Since u(X) is the worst thing that could happen, this means that your entire utility function is bounded.
See also my reply to wedrifid where this argument is slightly expanded.
If your utility function is not bounded (below), then there is no "worst thing that could happen."
See my reply to komponisto in the comment above.