I think the mugger can modify their offer to include "...and I will offer you this deal X times today, so it's in your interest to take the deal every time," where X is sufficiently large, and the amount requested in each individual offer is tiny but calibrated to add up to the amount that the mugger wants. If the odds are a million to one, then to gain $1000, the mugger can request $0.001 a million times.