re: Marilyn vos Savant and the history of the Montel Hall question

quote:

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What am I missing here?

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I'm guessing it has to do with the fact that you are considering 4 options instead of focusing on only 3 doors/options.

If you pick the right door initially, the host has 2 options on doors to open. As you basically noted, if you pick wrong initially, the host only has 1 door to open.

In your test, you are allowing the contestant to pick the correct door twice. In reality, there are 3 doors and he gets 1 initial pick, regardless which of the 2 goat doors the host decides to open next. So 1 and 2 in your test is really 1 OR 2 so ONE win, not two.