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Play the game 50 times using paper cups as doors, a scrap of
red paper as a car and two scraps of white paper as goats. Being
the host (Monty) do not "follow any predictable patter", except
for one rule. That implied rule is that "the door hiding a car can
not be open before the second selection is made by the guest."
You will discover a significant difference between the outcomes
of two strategies: (a) switching the original selection and (b)
not switching the original selection. The first strategy, for a
large number of games, will yield twice as many winnings
as the second one.
You can also play the applet game but that would not be
convincing because we do not know if the underlying code
is a true simulation designed to validate (or invalidate) a
theory or a fake simulation designed to illustrate what is
"expected according to that theory." I did write codes for
true simulations of (a) and (b) strategies; they confirm the
theoretically expected 1/3 and 2/3 limits. It takes a second
to play more than 10,000 games on my six years old
computer. I will be happy to e-mail (or post) these easy
to follow True Basic codes, if somebody is interested.