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Wei_Dai comments on Advancing Certainty - Less Wrong
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If we follow your suggestion and obtain E(A) < 0, then compute from that the probability of winning the lottery, we end up with P(will win lottery) < 1e-8. But what if we want to compute P(will win lottery) directly? Or, if you think we shouldn't try to compute it directly, but should do it in this roundabout way, then we need a method for deciding when this indirect method is necessary. (Meta point: I think you might be stopping at the first good answer.)
The parallel calculation would be
I don't put P_typical very high.
Okay, I'll grant you that one. I'm still promoting my original idea to a top-level post.
Edit: ...in part because I would like more eyes to see it and provide feedback - I would love to know if it has some interesting faults.
Edit: Here it is.