Monty Hall Dilemma
The Monty Hall Dilemma was discussed in the popular "Ask Marylin" question-and-answer
column of the Parade magazine. Details can also be found in the "Power
of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996.
Marylin received the following question:
|Suppose you're on a game show, and you're given the choice of three
doors. Behind one door is a car, behind the others, goats. You pick a door,
say number 1, and the host, who knows what's behind the doors, opens another
door, say number 3, which has a goat. He says to you, "Do you want to pick
door number 2?" Is it to your advantage to switch your choice of doors?
Craig. F. Whitaker
Marylin's response caused an avalanche of correspondence, mostly from
people who would not
accept her solution. Several iterations of correspondence ensued. Eventually,
she issued a call to Math teachers among her readers to organize experiments
and send her the charts. Some readers with access to computers ran computer
simulations. At long last, the truth was established and accepted.
Below is one simulation you may try on your computer. For simplicity,
I do not hide goats behind the doors. There is only one 'abstract' prize.
You may either hit on the right door or miss it. You make your selection
by pressing small round buttons below input controls that substitute for
the doors. Down below other controls update experiment statistics even
as you progress.
Approximately every second the program clears 'door' controls and is
waiting for your selection. Before you start, set up a desired total
number of experiments. With every selection it will decrease by 1.
You run a simulation. During a simulation you are allowed to make as many
selections as indicated in the "To Go" control before your first selection.
Remember also that after each selection the device needs approximately
1 second to clear up controls. Please wait till it does. To start a new
simulation please press the "Reset" button.
Copyright © 1996-2001 Alexander Bogomolny