The Scylla of Error and the Charybdis of Paralysis
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I crossposted the particular problem to a forum I frequent:
The conclusion in the thread is that you do best by treating based on the majority of the results at the time, but just sticking with any treatment you've already given the patient three times, on the theory that if it hasn't killed him yet it's probably right.
Unfortunately we reached this conclusion through Monte Carlo simulation, so there aren't any general arguments we can take away from it.