If you think you have a definitive solution, please show your work, in math.

Irrelevant, because the original thread started with my reply to:

It would seem rational to accept any argument that is not fallacious; but this leads to consideration of problems such as Pascal's mugging and other exploits.

to which I pointed out that it is not rational to simply accept any argument that does not appear fallacious, not in the way EY defines rationality (as winning). If you apply the maxim "extraordinary claims require extraordinary evidence" (e.g. requesting to show at least a simulated amoeba before you consider the mugger's claims of simulating people any further), you win whether the mugger bluffs or not. WIN!