X-Message-Number: 7063 Date: Wed, 23 Oct 1996 21:01:37 -0700 (PDT) From: John K Clark <> Subject: Winning the Deal -----BEGIN PGP SIGNED MESSAGE----- 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 -----BEGIN PGP SIGNATURE----- Version: 2.6.i iQCzAgUBMm7j1H03wfSpid95AQH9XgTwtOIu0R7QgPlOiFH0TOkPYAs9DTz9TQSO ZgByuacNeHyFEfpYBhg1fCElf0ttrWoZFcOvcIiVU2E5YQWQO1Q7cUDNOK0tZ0IM BEKsXIvQ0AAoG8JVp+xlo5m02SKUG4EQ2KbjqMauy5RhnqPaAYzjRKrHaugVT/42 Eb9DXpcWc/4bIo2Kl8m6II2/wCEJR/aUs6dUW19uQBYmLaYpHE0= =BO+H -----END PGP SIGNATURE----- Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=7063