I'm either gonna win $130 with 47% chance or lose $130 with 53% chance. My $250 bill is sunk and completely independent of this decision and outcome. Otherwise any time I have an expensive bill to pay and will be left with only about $130 why not gamble it save the amount I need to pay in the long run. This is the start of a gambling problem.No, you're missing the point: the $250 is, indeed, a sunk cost. The $100 fee that's going to add on if it's not paid on time, however, is not.
Stripping away all the irrelevant details of the problem, the (completely contrived and artificial, indeed) choice is between:
A) Certainly losing another $100,
B) A near 50/50 shot (minus a single-digit house edge) of either winning $130, or losing $230 (lose the $130 bet, plus have to pay the $100 "late fee")
The $250 owed is irrelevant to the problem except to trigger the late fee and set up this payoff structure.
Firstly the concept of expected value only make sense over repeated trials of the same experiment and using it here on a one off is a misapplication.
Whether or not expected value calculations are valid for single shot deals, are you really saying you'd choose option A in this situation, which loses you twice as much as the expected loss in option B?