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beoShaffer comments on What Evidence Filtered Evidence? - Less Wrong
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As long as I don't know his motives (or on what level the host is playing, to put it in HPMOR terms) I can't infer anything from what the host does. He might have opened door 2 because the money isn't behind door 1 and I get another chance. Or because it is behind 1 and he wants me to switch so the company can keep the money. Knowing I should integrate his motives into the equation doesn't mean I can.
Or am I missing something essential here?
Since its a canonical (read most people will have seen it multiple times before) problem the article doesn't go into quite as much detail as it arguably should. Its a well known facet of the standard problem (explicitly stated in many formulations and strongly implied by the context in others) that Monty always opens an empty door that you didn't pick.