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Tyrrell_McAllister comments on An Intuitive Explanation of Solomonoff Induction - Less Wrong
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Yes. But the point is that this number should be negligible if you haven't seen how the tiger behaves in the absence of the pills. (All of this assumes that you do not have any causal model linking pill-presence to tiger-absence.)
This case differs from the use of antihistamine against anaphylaxis for two reasons:
There is some theoretical reason to anticipate that antihistamine would help against anaphylaxis, even if the connection hasn't been nailed down with double-blind experiments.
We have cases where people with anaphylaxis did not receive antihistamine, so we can compare cases with and without antihistamine. The observations might not have met the rigorous conditions of a scientific experiment, but that is not necessary for the evidence to be rational and to justify action.
Absolutely. The precise thing that matters is the probability tigers happen if you don't use the pills. So, say, I wouldn't recommend doing the experiment if you live in areas with high densities of tigers (which you do if there's one showing up every day!) and you weren't sure what was going into the pills (tiger poison?), but would recommend doing the experiment if you lived in London and knew that the pills were just sugar.
Similarly, I'm more likely to just go for a herbal remedy that hasn't had scientific testing, but has lots of anecdotal evidence for lack of side-effects, than a homeopathic remedy with the same amount of recommendation.