Re: monty hall problem
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if the host randomly picks the door between the two unchosen doors without knowing where the prize is. and if the host opens the unchosen door with the prize.. then the contestant lose.
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*Under these conditions*, 1/3 of the time you will lose automatically when the host exposes the prize, and the rest of the time you have the same chance whether you switch or not.
Note that those *aren't* the conditions that applied to the classical Monty Hall problem - in which the host DID know where the prize was, and ALWAYS exposed a goat. Under those conditions, your chance was indeed 1/3 if you stayed and 2/3 if you switched. If you play bridge, see also "Principle of Restricted Choice" for the same phenomenon at work.
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