Theoretical All-In Call

[Kripke]

I think the problem with your question is that you (maybe purposely) leave out important information. Consider the equity you are giving up if villian is able to do this 1 out of 100 times, maybe 1 out of 25 times or even 1 out of 10 times without the nuts. In that case the situation is entirely different and you are possibly making a horrible horrible fold. Since most people assume that this is a standard game (by the lack of informatio) it would be absurd not to factor in the possibility of a semi-bluff or a worse hand making this move (as crazy as it might seem).

Had you constructed the example so that we knew that villian had e.g. AdKd then the question could be settled by way of simple arithmetic, but it would also be entirely uninteresting.

The question is stupid, because without any information about the particular game or the particular villian, I think most people would consider the possibility of actually having the best hand here (even if it is a very small percentage of the time). And if that is the case, at least as far as I am concerned, I would have to be absurdly deep stacked before considering folding this hand. In other words, I can't really imagine this scenario ever happening and I have no intuitions as regards exactly how deep I would have to be. If people really come up with particular numbers of $ as an answer to your question this will likely reflect how much they could afford (or are willing) to lose in regards to their current BR rather than afford us some real insight into when this is a correct fold.

And btw, your "real life" example is very different from your original example.