> if my loans are $50k, and I or my lawyer think that the odds of getting them eliminated are <1%, then based on the expected value, I should spend less than $500 of time and effort on it.

Leaving the probability aside, this assumes that expected values of money are linear. The negative value of debt grows faster than linear; a debt of $50000 is not exactly 10 times worse than a debt of $5000, if you can arrange your finances to pay the $5000 but could never successfully pay $50000 (for instance if the amount you can afford to pay down regularly would cover a large part of the principle on the former but almost entirely interest on the latter).

That's true, but then the amount I'm willing to pay in the example above should be even less than the expected value of $500.

The cost, time and effort is the bankruptcy itself. Once that step is taken it would be the equivalent of omitting any other debts because the cost, time and effort it listing them.

I think maybe your hypothetical is assuming the cost/benefit of a bankruptcy purely for a student loan as opposed to multiple debts, and I am addressing my desire to see 100% of those already filing bankruptcies to list student loans, and as you will see another comment listed the statistics, it is a tiny percentage of filers who list student loans, but of those who do nearly 40% are successful.