[wzdd]

> none of this has anything to do with utilitarianism

"Always go for C (or any strategy)" is not in general a utilitarian strategy, so the mugger would not expect Bentham to employ it.

Your argument assumes that the characters have perfect knowledge, but the point of the parody is that utilitarian choices can change as more information is revealed.

Yes, the mugger could have said something like "if I were to promise to cut off my finger unless you gave me £10, would you do it?", Bentham could have have followed up with "if you knew I would reply no to that question, would you make that promise?", the mugger could have replied "no," Bentham could have responded "In that case, no", and the mugger would have walked away. But Bentham doesn't have all the information until he is faced with the loss of a finger which he can prevent by giving up £10. Bentham is obliged to do so, as it maximises the overall good at that (unfortunate) point.

The idea that Bentham can be "trapped" in a situation where he is obliged to cause some small harm to himself in order to prevent a greater harm is the parody of utilitarianism which is at the heart of the story.