[roenxi]

> as the probability that the mugger will return with the money is...

That can't be reasonably estimated though. Putting aside the fact that we can't really assert the relation you posit, there is also a finite probability that the mugger is some sort of illuminati member with the ability to create an arbitrary amount of money. Ie, there is some tiny-but-positive probability that he can create an arbitrary amount of money.

At that point, the expected return can be made large compared to the probability that the mugger is lying.

[Dylan16807]

They can't really offer you more than the amount of resources in the entire world, though. Money past some point in the trillions stops being money, because you can't exchange it for anything. So even for an illuminati member, the expected value can only go so high, and I don't know if that value is higher or lower than a dollar.

[maest]

It seems to me that the set of worlds where the mugger can return $X is strictly a subset of the set of worlds where the mugger can return $X+epsilon.

So the probability won't be "inversely proportional" in the strict sense, but it will be decreasing with X increasing.

[roenxi]

At some point it converges to some constant probability. The probability of providing an "almost impossible" - say $9^^^^9 - is almost precisely equal to the probability of providing $9^^^^9+1. This is because any mechanism that can provide the first can also provide the second.

Technically one will be a subset of the other but it will be like the sum of an infinite series where the differences are so small that there is a limiting asymptotic on the value of the sum is 0. The probability will converge to the value of "probability an entity can provide arbitrary compensation".