Newsgroups: rec.puzzles
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: Fri, 11 Mar 1994 22:45:06 GMT
Subject: Re: More on Marilyn

With respect to the so-often-repeated problem:

>> Suppose you're on a game show, and you're given the choice of
>> three doors.  Behind one door is a car, the others, goats.  You
>> pick a door, say #1, and the host, who knows what's behind the
>> doors, opens another door, say #3, which has a goat.  He says to
>> you, "Do you want to pick door #2?"  Is it to your advantage to
>> switch your choice of doors?

f...@peregrine.Eng.Sun.COM (Ed Falk) writes:

> ... The original problem states that the host KNOWS what's behind
> which door, and that he DOES give the contestant a choice, not that
> he sometimes give a choice.

I assume you're saying "choice" for "chance to switch", and that the
"original problem" you're talking about is the one above that you
quoted in your post.  You should realize that the problem statement
doesn't include the word "always" any more than it includes the word
"sometimes".  It says the host gave you a chance to switch in the one
observed case.  It does not say he gives this opportunity as a rule.
And since he knows what's behind the door you chose, he may have
decided whether to give you that opportunity based on that knowledge.

If you were on the show,
 and the host offered you a choice of doors,
  and you picked door #2 instead,
   and instead of offering you a chance to switch,
    he opened up door #2
     and said "Ha, ha, loser, take your goat and go home, and here's a
     Spiegel catalog in case you want to buy a car with your own money,"
you wouldn't get anywhere claiming he'd broken the rules.

If you have won money from hosts who did not realize they had this
option, it doesn't mean they didn't have the option.  And if you just
happen to be dealing with a host who takes advantage of this option
when he gets the chance, switching when you get the chance will always
lose.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil