From Richard Peto, University of Oxford
Oxford
Your review (12 April, p 42) and correspondence (3 May, p 55) discuss only
the trivial form of the Monty Hall problem, where the game show host himself has
no strategy.
Monty has concealed £10 000 in one of three boxes, A, B or C. After you
have nominated box A as your choice, he shows you that C is empty and invites
you to switch your choice to B. If you know that, irrespective of whether you
were right or wrong, Monty was bound to open another box that does not contain
the prize, then switching has a 2/3 probability of success. This is the trivial
form of the problem.
If, however, you know that he is malevolent and would have opened an empty
box only if you were right in your first choice, then you should certainly not
switch. If, conversely, you know he is benevolent, and would have opened an
empty box only if you were wrong in your initial choice, then you should
obviously switch.
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As you don’t know for certain whether his strategy is neutrality,
malevolence, benevolence or something more complex, your response has to depend
on some “guesstimate” of the probabilities of his different possible
strategies.
see Biteback section at http://www.nsplus.com for much more on
this
