# Re: Monty Hall

From: Taylor, Karl (krt196@soton.ac.uk)
Date: Fri Feb 21 1997 - 11:40:53 GMT

The first thing I would like to say about the Monty
Hall problem is that it seems to me that it is a good
example of cognitive penetrability, because a good example

a) catches you out first time around because you
just don't get it (it appears inpenetrable),
b) slowly becomes penetrable and solvable after some
thought.

The more inpenetrable it seems and the longer it
takes to penetrate, the better. So don't feel bad if you
don't get it yet.
Another indication that it is a good example is that even if
you have penetrated the problem, it still doesn't become
very easy to explain. All the penetration has to happen in
It is important to realise that the two stages of
the problem (ie. first there's three doors and then there's
two) are not independent of one another. The insight you
gain from knowing that there were orignally three doors (ie.
you had a one in three chance of being right) is what helps
you solve it.
This is how I think of the Monty Hall problem:

Imagine you are in a game show on T.V. with
uncomfortable bright lights and a cheap and nasty set
design. You have done so well that you are through to the
big FINAL ROUND. You're playing for the money (or the car,
or the cruise, or whatever).
Your host (Monty Hall?) with a fake tan and offensive taste
in clothes takes you by the arm and turns you to face three
doors.
"Behind one of these doors," he says to the camera
"is tonights star prize!"
The audience (who aren't really there, it's all on
tape) go "Ooh!" and Monty smiles his whiter-than-white
smile.
"Contestant...you've got a one in three chance. Take
The audience start shouting numbers at you.
"Number one!" "Number three!" "NUMBER TWO!"
You feel hot, excited, and nauseas. You say:
"I'll have door number... one, please Monty."
Monty takes a big gold star and hanges it on door number
one.
"Now," says Monty, after the applause has died down.
"Because I'm feeling generous, I'm going to show you what's
behind one of the doors you didn't pick!" He says that every
week.
Monty opens door number three, to reveal that there is
nothing behind it.
"Now, will you stay with door number one? Or would
you like to change your mind and take door number two?"
Now you have to really try and think. You try to
ignore the hot studio lights, the hysterical audience that
aren't really there, and Monty's stupid grin, and try to
remember what you learnt about probabilty in the fourth year
at school.
You know you had a one in three chance of being
right when you picked door number one. Now Monty has
eliminated door number three. What should you do? Should you
change? Should you stay with door number one, or should you
pick door number two?
Slowly, you run everything over in your mind. What
it comes down to is this:

The chances are that your first choice was wrong. You had a
one in three chance of picking the star prize, that's a two
in three chance of getting nothing at all.
Now you know that Monty is always going to open one of the
empty doors.
That means there's two doors left: one empty door, and one
suitcase full of money.
BUT, and this is where it clicks, if one door has to be
right, and one door has to be wrong, AND you know that the
chances are you picked an empty door the first time around
(ie. chances are that you've got the wrong door), then THE
OTHER DOOR is more likely to be the winner!

You turn confidently to your host and say:
"I think I'll have door number two please, Monty."

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