you will achieve a net gain of $4950*p(x) over a non-committer (a very small number admittedly given that p(x) is tiny, but for the sake of the thought experiment all that matters is that it’s positive.)
Given that someone who makes such a precommitment comes out ahead of someone who doesn’t—shouldn’t you make such a commitment right now?
Right now, yes, I should precommit to pay the $100 in all such situations, since the expected value is p(x)*$4950.
If Omega just walked up to me and asked for $100, and I had never considered this before, the value of this commitment is now p(x)*$4950 - $100, so I would not pay unless I thought there was more than a 2% chance this would happen again.
Right now, yes, I should precommit to pay the $100 in all such situations, since the expected value is p(x)*$4950.
If Omega just walked up to me and asked for $100, and I had never considered this before, the value of this commitment is now p(x)*$4950 - $100, so I would not pay unless I thought there was more than a 2% chance this would happen again.