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What do you do when you probably won't succeed
Shut up and multiply by the payoff, and act on the expected value, not the probability.
but believing that Heaven's army is at your back would increase your chances?
When you have decided what to do, do it 100%. Don't put in 50% effort because you think there's only a 50% chance of success. That is like the fallacy discussed here of guessing whether the red or the blue light will turn on next. If red is more frequent than blue and each event is independent, then you should guess red every time. When you are uncertain what to do, the rational thing to do is to go wholeheartedly for whichever choice seems, however uncertainly, to be the best.
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What should a rationalist do about confidence? Should he lean harder towards
I don't want to falsely construe these as dichotomous. The real answer will probably dissolve 'confidence' into smaller parts and indicate which parts go where. So which parts of 'confidence' correctly belong in our models of the world (which must never be corrupted) or our motivational systems (which we may cut apart and put together however helps us achieve our goals)? Note that this follows the distinction between epistemic and instrumental rationality.
Eliezer offers a decision criterion in The Sin of Underconfidence:
It makes us stronger to know when to lose hope already, and it makes us stronger to have the mental fortitude to kick our asses into shape so we can do the impossible. Lukeprog prescribes boosting optimism "by watching inspirational movies, reading inspirational biographies, and listening to motivational speakers." That probably makes you stronger too.
But I don't know what to do about saying 'I can do it' when the odds are against me. What do you do when you probably won't succeed, but believing that Heaven's army is at your back would increase your chances?
My default answer has always been to maximize confidence, but I acted this way long before I discovered rationality, and I've probably generated confidence for bad reasons as often as I have for good reasons. I'd like to have an answer that prescribes the right action, all of the time. I want know when confidence steers me wrong, and know when to stop increasing my confidence. I want the real answer, not the historically-generated heuristic.
I can't help but feeling like I'm missing something basic here. What do you think?