X-Message-Number: 7063
Date: Wed, 23 Oct 1996 21:01:37 -0700 (PDT)
From: John K Clark <>
Subject: Winning the Deal
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I must respectfully disagree with Art Quaife on his analysis of the
"Winning the Deal" puzzle. I don't think it makes the slightest difference
if you stick with your original choice or switch.
>Host Monty Hall knows which [of 3] door hides the car. You
>have no way of knowing, so for you each choice is equally
>likely. Your initial guess of door #1 had 1/3 chance of
>winning.
I agree, so far.
>the goats are indistinguishable for the purposes of this
>puzzle
But in your table you act like there is only one goat. As long as you're
just interested in getting the car I don't see how it would change the logic
of the puzzle a bit if you had a trash can and a goat or a black goat and a
white goat, distinguishable but equally worthless.
>Monty's opening another door to reveal a goat, as he
>previously promised to do, does not change that probability.
Why not? Probability is not an objective static quality, but a function of the
individual and the amount of information he has. To me there is one chance in
3 that I can correctly guess which door the car is behind, so the probability
is .333 . Monty has more information than I do, for him there is one chance in
1 that he can correctly guess which door the car is behind, so the probability
is 1.0. If Monty gives me a little more information and shows me one door the
car is definitely not behind, then my chances of guessing correctly changes
from 1 in 3 to 1 in 2. If Monty always shows you a goat after you pick a door
then there are really only 2 doors on the show, the third door is just a sham
and you would know from the start that you have a 50% of wining the car.
The car and the goats can be arranged 6 different ways behind the doors, I
can pick one of 3 doors and Monty can show me either goat, that gives me 24
possibilities in my table, not just 3 as in yours. In 12 of the possibilities
you would do better sticking with your original choice, in 12 possibilities
you'd be better off switching. I agree with you that Monty could try to
influence the outcome by allowing me to switch or denying me that privilege
as he saw fit, but even in that case, unless I knew if he was trying to help
or hurt me, I would have no way of knowing if it would be better to stick or
switch and might as well flip a coin when he gave me that choice.
Possi- Car Goat Goat You Monty Winning
bility Black White choose opens choice
__________________________________________________
D O O R #
A 1 2 3 1 2 Stick
B 1 2 3 1 3 Stick
C 1 2 3 2 3 Switch
D 1 2 3 3 2 Switch
E 1 3 2 1 2 Stick
F 1 3 2 1 3 Stick
G 1 3 2 2 3 Switch
H 1 3 2 3 2 Switch
I 2 1 3 1 3 Switch
J 2 1 3 2 1 Stick
k 2 1 3 2 3 Stick
L 2 1 3 3 1 Switch
M 2 3 1 1 3 Switch
N 2 3 1 2 1 Stick
O 2 3 1 2 3 Stick
P 2 3 1 3 1 Switch
Q 3 1 2 1 2 Switch
R 3 1 2 2 1 Switch
S 3 1 2 3 2 Stick
T 3 1 2 3 1 Stick
U 3 2 1 1 2 Switch
V 3 2 1 2 1 Switch
W 3 2 1 3 2 Stick
X 3 2 1 3 1 Stick
Possi- Car Goat Goat You Monty Winning
bility Black White choose opens choice
___________________________________________________
John K Clark
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