Originally posted by Sparko
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http://educ.jmu.edu/~lucassk/Papers/MHOverview2.pdf
(High-Numbered Monty). As before, we have three identical doors
concealing one car and two goats. The player chooses a door which remains
unopened. Monty now opens a door he knows to conceal a goat. This time,
however, we stipulate that Monty always opens the highest-numbered door
available to him (keeping in mind that Monty will never open the door the
player chose.) Will the player gain any advantage by switching doors?
For reasons of concreteness, we will assume once more that the player
initially chooses door one. Any time door one conceals a goat, Monty has no choice regarding which
door to open. He can not open door one (since the player chose that door),
and he can not open the door that conceals the car. This leaves only one
door available to him.
The interesting cases occur when door one conceals the car. Unlike Classic
Monty, who now chooses randomly, High-Numbered Monty will always open
door three when he can. It follows that if we see him open door two instead
we know for certain that the car is behind door three.
And if High-Numbered Monty opens door three? Since Monty is certain
to open door three whenever the car is behind door one or door two, we now
have no basis for deciding between them. It really is a fifty-fifty decision in
this case.
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