The Game Show Problem - Page 2

Wacky · 2003-07-15, 21:58

Quote:

Originally Posted by toferc

hand-waving argument
If you pick the door he didn't open, you win. Switching always wins when you guess wrong the first time.

I think it's fairly obvious that switching always loses when you were right the first time.

So... since your first guess is wrong 2/3 of the time and right 1/3 of the time, switching wins 100% of 2/3 of the time and 0% of 1/3 of the time, for a total of 2/3 of the time.

Rather than hand-waving, I consider this the kind of argument that is appropriate for the puzzle.

PS: Sorry it I upset anyone by being a devil's advocate.

cheesehead · 2003-07-16, 06:31

The "Marilyn is Wrong!" site at http://www.wiskit.com/marilyn.html discusses, among other topics from the "Ask Marilyn" column by Marilyn Vos Savant in Parade magazine, this game show problem. The answer depends on the exact rules about number of contestants, when the host opens a dor, how the host decides which door to open, and so on.

The site says:

"In her Parade Magazine columns of September 9, 1990, February 17, 1991, and July 7, 1991, Marilyn discusses a
gameshow in which the contestant is given a choice of one of three doors, behind one of which is a prize. The reader
asks if, after the contestant chooses a door, the host opens a different door, revealing no prize, and offers the
contestant the opportunity to switch doors, whether the contestant should switch or not. Marilyn replies that the
contest should switch, because the second door has a 2/3 chance of winning."

Later, from a July 21, 1991 article in The New York Times is a confirming quote from Monty Hall: "If the host is required to open a door all the time and offer you a switch, then you should take the switch."

asdf · 2003-07-18, 00:29

At one point in time, I wrote a program to prove this problem because I didn't feel like thinking. After optimizing the code, without thinking, it ended up as something like if(1==1) and if(2==2), giving the switch the better odds.

Kevin · 2003-07-18, 02:54

http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

A simple java applet for the skeptiks.

rogue · 2015-04-28, 14:23

For further discussion: http://puzzling.stackexchange.com/qu...all-over-again

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2003-07-16, 06:31	#13
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 1111000001100₂ Posts	The "Marilyn is Wrong!" site at http://www.wiskit.com/marilyn.html discusses, among other topics from the "Ask Marilyn" column by Marilyn Vos Savant in Parade magazine, this game show problem. The answer depends on the exact rules about number of contestants, when the host opens a dor, how the host decides which door to open, and so on. The site says: "In her Parade Magazine columns of September 9, 1990, February 17, 1991, and July 7, 1991, Marilyn discusses a gameshow in which the contestant is given a choice of one of three doors, behind one of which is a prize. The reader asks if, after the contestant chooses a door, the host opens a different door, revealing no prize, and offers the contestant the opportunity to switch doors, whether the contestant should switch or not. Marilyn replies that the contest should switch, because the second door has a 2/3 chance of winning." Later, from a July 21, 1991 article in The New York Times is a confirming quote from Monty Hall: "If the host is required to open a door all the time and offer you a switch, then you should take the switch."

2003-07-18, 00:29	#14
asdf Sep 2002 2²·3·5 Posts	At one point in time, I wrote a program to prove this problem because I didn't feel like thinking. After optimizing the code, without thinking, it ended up as something like if(1==1) and if(2==2), giving the switch the better odds.

2003-07-18, 02:54	#15
Kevin Aug 2002 Ann Arbor, MI 433 Posts	http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html A simple java applet for the skeptiks.

2015-04-28, 14:23	#16
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	For further discussion: http://puzzling.stackexchange.com/qu...all-over-again