From nobody@gumbo.valdosta.peachnet.edu Sat Feb 1 10:00 EST 1997
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Date: Sat, 1 Feb 1997 10:00:36 -0500 (EST)
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To: rbarnett@grits.valdosta.peachnet.edu
From: (Travis Welwood-Hreno)
Subject: Submitted Form
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Below is the result of your feedback form. It was submitted by Travis Welwood-Hreno () on Saturday, February 1, 1997 at 10:00:36
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username: threno@julian.uwo.ca
state: Ontario
city: London
country: CANADA
comments: Charles would best maximize his chances
of getting the coffee if he were to switch to Envelope C. The
reason for this is quite straight-forward. In his original choice,
his odds for success were 1 in 3, meaning that his odds for failure
were 2 in 3. There is a much higher probability that the coffee
coupon is in either envelopes B or C. Since envelope B has been
revealed as a non-winner, it can be eliminated as a cntender.
This is now the situation: The original choice still has a 1 in
3 chance of success. But, that means all other likely contenders
have a 2 in 3 chance, and, since B has beem eliminated, THERE
IS ONLY ONE OTHER LIKELY CONTENDER: C.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sat Feb 1 11:39 EST 1997
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Date: Sat, 1 Feb 1997 11:39:40 -0500 (EST)
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To: rbarnett@grits.valdosta.peachnet.edu
From: (Wayne C. Myrvold)
Subject: Submitted Form
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Below is the result of your feedback form. It was submitted by Wayne C. Myrvold () on Saturday, February 1, 1997 at 11:39:38
---------------------------------------------------------------------------
username: wmyrvold@delphi.com
state: MA
city: Sherborn
country: USA
comments: This is, apparently, supposed to be a variant on the old
Monty Hall problem. If so, you've made the same mistake
that Marilyn vos Savant made, in that you've incompletely
specified the problem. (Actually, she responded to an
incompletely specified problem as if it were correctly
posed). Rob Prob's strategy is relevant. If he opened
one of the two remaining envelopes at random (thus risking
revealing the coffee coupon), then one's chances of getting
the coffee coupon are the same whether or not one
switches.
If, however, his strategy is to reveal a water coupon,
whatever envelope Charles chose, then Charles should
switch. I'm assuming that, since you mentioned the Monty
Hall problem, this latter strategy is what you intended.
If the goal is to maximize the chance of getting the coffee
coupon, then the $50 is irrelevant. If the goal is to
maximize expected return, then Charles should switch as
long as the coffee coupon's value is greater than $150,
which (since you said it was worth "many hundreds of
dollars"), it is.
On the other hand, if Rob opened an envelope at random, and
the goal is to maximize his chance of getting the coupon,
then it doesn't matter whether he switches. If
Rob chose randomly and the goal is to maximize expected
return, he should stick with A.
My prediction is that, due to the ambiguities in
presentation, you're going to stir up a lot of contention.
There will be those who take Rob's choice to be random and
the goal to be maximized expected return, who vehemently
insist that Charles should stick with A-- and, on their
interpretation of the problem, they'll be right.
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From people.de!postmaster@mail2.shlink.de Sat Feb 1 20:16 EST 1997
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Subject: E:New Zeno's Puzzle
Date: 01 Feb 1997 02:12:03 +0100
To: rbarnett@grits.valdosta.peachnet.edu
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Ihre Nachricht an: LARS_BECKER@PEOPLE-S.PEOPLE.DE
mit der Message-Id <Pine.SOL.3.95.970131152029.20096A-100000@grits>
und dem Betreff "New Zeno's Puzzle"
ist unzustellbar
User ist in der Box unbekannt!
From nobody@gumbo.valdosta.peachnet.edu Sun Feb 2 10:45 EST 1997
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Date: Sun, 2 Feb 1997 10:45:04 -0500 (EST)
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To: rbarnett@grits.valdosta.peachnet.edu
From: (Robert M. Martin)
Subject: Submitted Form
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Below is the result of your feedback form. It was submitted by Robert M. Martin () on Sunday, February 2, 1997 at 10:45:04
---------------------------------------------------------------------------
username: martin@is.dal.ca
state: NS
city: Halifax
country: Canada
comments: The answer to this question (SWITCH!) is explained brilliantly
on pp. 42-44 of my book, _There are Two Errors in the the
Title of This Book_. (The book is a sourcebook of philosophical
puzzles, paradoxes, fables, thought-experiments, etc. 1995,
Broadview Press.
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From nobody@gumbo.valdosta.peachnet.edu Sun Feb 2 13:20 EST 1997
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Date: Sun, 2 Feb 1997 13:20:43 -0500 (EST)
Message-Id: <199702021820.NAA12339@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Ian Dewar)
Subject: Submitted Form
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Below is the result of your feedback form. It was submitted by Ian Dewar () on Sunday, February 2, 1997 at 13:20:42
---------------------------------------------------------------------------
username: cdewar@is2.dal.ca
state: ON
city: Toronto
country: Canada
comments: Charles should keep envelope A. He
currently has a 50% chance of having
the right env. if he takes A and is right
then he gets free coffe, if he's wrong he
gets $50. if he takes B and is right
he gets free coffee (50%), but if he's
wrong he gets nothing.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sun Feb 2 17:52 EST 1997
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Date: Sun, 2 Feb 1997 17:52:06 -0500 (EST)
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To: rbarnett@grits.valdosta.peachnet.edu
From: (Sergio Tenenbaum)
Subject: Submitted Form
Content-Type: text
Content-Length: 699
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Below is the result of your feedback form. It was submitted by Sergio Tenenbaum () on Sunday, February 2, 1997 at 17:52:05
---------------------------------------------------------------------------
username: sergio@unm.edu
state: NM
city: Albuquerque
url: http://www.unm.edu/~sergio
country: USA
comments: Assuming that the manager would behave
the same way regardless of the content of the envelope that Charles
picked and that Charles is not risk averse regarding money, the
correct answer is "Switch". This choice has an expected
monetary value of 2/3 of hundreds of dollars, which is certainly
more than $50.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Mon Feb 3 01:11 EST 1997
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Date: Mon, 3 Feb 1997 01:11:44 -0500 (EST)
Message-Id: <199702030611.BAA14153@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Charles Howard)
Subject: Submitted Form
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---------------------------------------------------------------------------
username: choward@vt.edu
state: va
city: bLACKSBURG
country: USA
comments: Charles should keep his envelope and take the fifty bucks for it is a fifty-fifty chance that his envelope will have
the coupon or it won't. Plus hey fifty bucks isn't
bad for coffee money.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Mon Feb 3 02:04 EST 1997
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Date: Mon, 3 Feb 1997 02:04:45 -0500 (EST)
Message-Id: <199702030704.CAA14169@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Cathy Legg)
Subject: Submitted Form
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Content-Length: 541
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Below is the result of your feedback form. It was submitted by Cathy Legg () on Monday, February 3, 1997 at 02:04:45
---------------------------------------------------------------------------
username: cathy@coombs.anu.edu.au
state: ACT
city: Canberra
url: http://coombs.anu.edu.au/Depts/RSSS/Philosophy/People/Cathy/Cathy.html
country: Australia
comments: Envelope A, surely????? There's a 50-50 chance with either A or C,
so why not get the $50 as well?
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Mon Feb 3 15:04 EST 1997
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Date: Mon, 3 Feb 1997 15:04:54 -0500 (EST)
Message-Id: <199702032004.PAA01780@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Jamie Dreier)
Subject: Submitted Form
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Below is the result of your feedback form. It was submitted by Jamie Dreier () on Monday, February 3, 1997 at 15:04:54
---------------------------------------------------------------------------
username: James_Dreier@brown.edu
state: RI
city: Providence
country: USA
comments: You say that there is a correct answer. But I think you have
not said enough in the statement of the problem.
I know the intended answer. I am very familiar with this
puzzle.
To conclude that Charles ought to switch, we *must* know something
about Rob Prob's 'strategy'. For instance, we *might* assume,
given your statement of the problem, that Rob Prob would not
offer Charles the opportunity to switch unless Charles got the
good envelope on the first try. Is Rob Prob a tricky sort
of manager? In that case, Charles ought *not* to
switch.
To shore up the problem so that it has a right answer, you
must add that Rob Prob's strategy is always to show the
player an envelope which (a) the player did not choose, and
(b) does not hold the valuable coupon; and furthermore than in
case the player chooses the lucky envelope, Rob will open one
of the other two *at random* (equiprobably).
As you probably know, Marilyn Vos Savant discussed this puzzle
in her column. There ensued 'incorrect' responses from
established mathematicians, statisticians, and so forth. The
amusement and entertainment value of laughing at all those
professionals is vitiated by the fact that Marilyn understated
the problem, just as you have. Since I like this problem, I hope
you will add the material that's needed to have a puzzle with
a single correct answer.
Best wishes,
Jamie Dreier
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Mon Feb 3 15:04 EST 1997
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Date: Mon, 3 Feb 1997 15:04:54 -0500 (EST)
Message-Id: <199702032004.PAA01780@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Jamie Dreier)
Subject: Submitted Form
Content-Type: text
Content-Length: 1736
Status: RO
X-Status:
Below is the result of your feedback form. It was submitted by Jamie Dreier () on Monday, February 3, 1997 at 15:04:54
---------------------------------------------------------------------------
username: James_Dreier@brown.edu
state: RI
city: Providence
country: USA
comments: You say that there is a correct answer. But I think you have
not said enough in the statement of the problem.
I know the intended answer. I am very familiar with this
puzzle.
To conclude that Charles ought to switch, we *must* know something
about Rob Prob's 'strategy'. For instance, we *might* assume,
given your statement of the problem, that Rob Prob would not
offer Charles the opportunity to switch unless Charles got the
good envelope on the first try. Is Rob Prob a tricky sort
of manager? In that case, Charles ought *not* to
switch.
To shore up the problem so that it has a right answer, you
must add that Rob Prob's strategy is always to show the
player an envelope which (a) the player did not choose, and
(b) does not hold the valuable coupon; and furthermore than in
case the player chooses the lucky envelope, Rob will open one
of the other two *at random* (equiprobably).
As you probably know, Marilyn Vos Savant discussed this puzzle
in her column. There ensued 'incorrect' responses from
established mathematicians, statisticians, and so forth. The
amusement and entertainment value of laughing at all those
professionals is vitiated by the fact that Marilyn understated
the problem, just as you have. Since I like this problem, I hope
you will add the material that's needed to have a puzzle with
a single correct answer.
Best wishes,
Jamie Dreier
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Fri Jan 31 14:17 EST 1997
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Date: Fri, 31 Jan 1997 14:17:30 -0500 (EST)
Message-Id: <199701311917.OAA05793@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Stacy L. Prentiss)
Subject: Submitted Form
Content-Type: text
Content-Length: 407
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Below is the result of your feedback form. It was submitted by Stacy L. Prentiss () on Friday, January 31, 1997 at 14:17:30
---------------------------------------------------------------------------
username: stacy.l.sagar@santafe.cc.fl.us
state: FL
city: Gainesville
country: USA
comments: KEEP ENVELOPE "A" & the $50.00
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Feb 4 01:59 EST 1997
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Date: Tue, 4 Feb 1997 01:59:19 -0500 (EST)
Message-Id: <199702040659.BAA05838@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Augusta Era Golian)
Subject: Submitted Form
Content-Type: text
Content-Length: 399
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Below is the result of your feedback form. It was submitted by Augusta Era Golian () on Tuesday, February 4, 1997 at 01:59:19
---------------------------------------------------------------------------
username: aegolian@aol.com
state: Tx
city: Grand Prairie
country: USA
comments: Keep A and $50, a bird in hand...
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Feb 4 14:36 EST 1997
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Date: Tue, 4 Feb 1997 14:36:12 -0500 (EST)
Message-Id: <199702041936.OAA05711@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Marieke Keller)
Subject: Submitted Form
Content-Type: text
Content-Length: 889
Status: RO
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Below is the result of your feedback form. It was submitted by Marieke Keller () on Tuesday, February 4, 1997 at 14:36:11
---------------------------------------------------------------------------
username: marieke_keller@stortek.com
state: CO
city: Louisville
country: USA
comments: I think that Charlie should stay with the envelope he has
now. By staying with 'A' he is guaranteed a minimum of
$50 and a glass of water on May 6, 1997. By switching to
'C', he is guaranteed a minimum of a glass of water. The
$50 could buy coffee for a little while if the coupon in
'A' is for water. You could play a lot of mind games trying
to figure out what Rob (the manager) is thinking by making
the offer. But, I think that it would be a waste of time
and an increase in stress. Stay with 'A', Charlie!!!
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Feb 4 17:41 EST 1997
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Date: Tue, 4 Feb 1997 17:41:13 -0500 (EST)
Message-Id: <199702042241.RAA15213@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Me)
Subject: Submitted Form
Content-Type: text
Content-Length: 338
Status: RO
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---------------------------------------------------------------------------
state: Ca
city: Taft
country: USA
comments: What a unique place!!!!!!
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Wed Feb 5 16:59 EST 1997
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Date: Wed, 5 Feb 1997 16:58:54 -0500 (EST)
Message-Id: <199702052158.QAA01698@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Charner Rouse)
Subject: Submitted Form
Content-Type: text
Content-Length: 443
Status: RO
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Below is the result of your feedback form. It was submitted by Charner Rouse () on Wednesday, February 5, 1997 at 16:58:54
---------------------------------------------------------------------------
username: carouse@grits.valdosta.peachnet.edu
state: GA
city: valdosta
country: USA
comments: Definitely keep A because it is a deliberate
throw-off to choose c
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Wed Feb 5 19:51 EST 1997
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Date: Wed, 5 Feb 1997 19:51:32 -0500 (EST)
Message-Id: <199702060051.TAA01992@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Matt Hoover)
Subject: Submitted Form
Content-Type: text
Content-Length: 511
Status: RO
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---------------------------------------------------------------------------
username: mahoover@mail.datasys.net
state: GA
city: VAldosta
url: http://www.datasys.net/users/stu/mahoover/index.htm
country: USA
comments: A: 50 dollars is better than free water,
or 50 dollars with coffee is better than that!
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Wed Feb 5 20:34 EST 1997
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Date: Wed, 5 Feb 1997 20:34:04 -0500 (EST)
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username: patricia@lanminds.net
state: CO
city: Longmont
country: USA
comments: Of course you should always stick with your first gut instinct,
he should stick with envelope A. Not to matter, even if he
doesn't win at least he won't wave in the wind with his
decisions.
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From nobody@gumbo.valdosta.peachnet.edu Wed Feb 5 22:01 EST 1997
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username: cwilson@bbs.slv.org
state: CO
city: Del Norte
country: USA
comments: I would choose to take envelope c. Because I'm a gambler
and enjoy a risk.
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From nobody@gumbo.valdosta.peachnet.edu Thu Feb 6 02:21 EST 1997
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Date: Thu, 6 Feb 1997 02:21:13 -0500 (EST)
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username: elam@scistud.umkc.edu
state: MO
city: Kansas City
url: http://cctr.umkc.edu/user/eorenick
country: USA
comments: Perhaps I am being naive in choosing to stick with envelope
A, but here are things as I see them:
(1) The chances of the coffee coupon being in either
envelope A or envelope C are equal.
(2) The $50 bonus for choosing A has no ostensible
relationship to the contents of A.
(3) The $50 could be used toward the purchase of coffee
at Zeno's, in which case that coffee, for Charles,
would ultimately be free.
Thus, regardless of Charles' selection of A or C, he would
still be eligible to receive at least $50 worth of free
Zeno's coffee, in which case his choice of envelope A
_guarantees_ him at least $50 worth of free coffee, whereas
the choice of envelope C has no such guarantee.
Now, it may be that envelope A carries the coupon for water
and that Rob Prob, knowing this, baited A with the $50,
thinking that he would lose less money if he were only out
$50 worth of coffee, rather than $500 worth. But as
indicated above, we have no evidence to this affect. So,
given that envelope A carries the only guarantee of any free
coffee at all, it seems that A would be the best choice, in
light of the evidence we have to work from.
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From nobody@gumbo.valdosta.peachnet.edu Thu Feb 6 08:28 EST 1997
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username: yael@radview.com
city: Tel-Aviv
country: Israel
comments: Keep A
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From nobody@gumbo.valdosta.peachnet.edu Thu Feb 6 20:12 EST 1997
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username: ejplondk@grits.valdosta.peachnet.edu
state: GA
city: Valdosta
url: http://www.freenet.tlh.fl.us/~plonk
country: USA
comments: Assuming random assortment, there are 3! ( or 6) different
ways that the doors could be arranged: Water1, Water2, Java;
W1, J, W2; W2, W1, J; W2, J, W1; J, W1, W2; or J, W2, W1.
We know that J cannot be in slot 2, so there are
4 choices. Half have J in slot A, so go with door A.
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From nobody@gumbo.valdosta.peachnet.edu Fri Feb 7 18:49 EST 1997
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From: (Sue McCalden)
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username: mccalden@unixg.ubc.ca
city: Vancouver
country: Canada
comments: Charles should switch to envelope C. Although it would
appear that Charles should keep envelope A, so that he receives
at least $50 regardless of the envelopes' contents, this is
not the case.
There are two principles which could be applied to this
challenge: Maximum Expected Utility (MEU) or the Dominance
Principle (DP).
The MEU principle is the best choice for the following reasons.
Assume that the probability of one envelope over the other
is conditional. That Rob Prob (the Predictor) has predicted
that Charles will keep envelope A due to the incentive
of gaining $50.
This rules out the D.P. since this principle relies upon
there being only independent probabilities (i.e. making
Charles' choice random).
Therefore, by using MEU, Charles should switch to envelope
C. The following illustrates the sol'n to this problem.
The Predictor (Rob Prob) has predicted that Charles will
act "rationally" and keep envelope A with the addtional $50
since he will get something even if the java coupon isn't
in envelope A. Because of this, the expected utility is
some high ratio close to 1, call it 'x', measuring the
likelihood of its predicted outcome, multiplied by the
value of the coffee (assume its value is $500), measuring
the utility.
The utility of any outcome can be represented by the
probability of that outcome multiplied by the value of it.
So, whatever 'x' may be, 50 x 'x' is much less than 500 x 'x',
MEU recommends choosing envelope C.
Let 'x'=.8 For EA the MEU formula is:
'x' x 50 + 1-'x' x 550
.8 x 50 + 1-.8 x 550 = 40 + 110
= 150
Then for the E.C., the MEU formula is:
'x'-1 x 0 + 'x' x 500
.8-1 x 0 + .8 x 500= 0+400
= 400
Since 400 is > than 150, Charles should most definately
switch to envelope C.
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From nobody@gumbo.valdosta.peachnet.edu Fri Feb 7 20:09 EST 1997
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From: (deb whitewolf cox)
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username: dcox@mail.datasys.net
state: ga
city: valdosta
country: USA
comments: To MAXIMIZE the chances-keep the envelope
and accept the $50. However, being the adventurous person that
I am, I'd probably choose the other envelope on a whim. Psychologically
and from the law enforcement mind set(my field and background),
Rob is probably telling the patron this to make him think the
envelope he has is not the winning envelope, thus saving the owner
money. In reality, knowing the patron's love of coffee, the envelope
in hand is probably the winner. Does the owner psych out the
patron? See future soap opera chapters for further insights!
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From nobody@gumbo.valdosta.peachnet.edu Sat Feb 8 15:28 EST 1997
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Email: powerj@ocps.k12.fl.us
Name: Judy Power
Rating: Friendly
Text: Dear Ron,
You will not remember me but I was in your Phiolosphy 101 class many years ago. I was also the clerk for the department (work study). Mostly I made coffee and flirted. It was many years ago. My fellow student, Barabara Meehan, and I often discussed topics that we heard in your class. I hope you're fine. I still remember your class with fondness and I am glad that I had just a touch of philosphy.
Yours Truly,
Judy Power aka Judy McDonald
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From nobody@gumbo.valdosta.peachnet.edu Mon Feb 10 22:37 EST 1997
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username: jparsly@usit.net
state: TN
city: Knoxville
url: http://www.public.usit.net/jparsly/
country: USA
comments: He should switch. At the beginning of the game A had a
1/3 chance of being the big winner and B & C TOGETHER had
a 2/3 chance that one of them was the winner. Now that
B has been revealed, we know that C is the only potential
winner in the BC set. Thus C has a 2/3 chance of being the
big winner. In terms of expected value, if you stay
with A your expected winnings are $50 plus 1/3 the value
of the coffee. If you pick C the expected value is 2/3 the
value of the coffee. Since the value of the coffee is
'many hundreds' of dollars, C has a higher expected
value.
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From nobody@gumbo.valdosta.peachnet.edu Tue Feb 11 17:13 EST 1997
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From: (JOhn Trombetta)
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username: jtrombet@grits.valdosta.peachnet.edu
state: GA
city: Valdosta
country: USA
comments: I choose A, The $50 will at least get him
some free coffee and of course I am assuming because I have not
been told otherwise (fallacy of false assumption I know) that
$50 will by 365 cumps of Zeno's Best!
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From nobody@gumbo.valdosta.peachnet.edu Tue Feb 11 21:08 EST 1997
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From: (Emma Osman)
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username: eosm@cybergraphic.com.au
city: Melbourne
url: www.civag.unimelb.edu.au/~eosm
country: Australia
comments: Change!
At the point of decision, Charles has a 2/3 probability of
holding a water-coupon. So, obviously, the thing to do would
be to change envelopes, giving himself a 2/3 probability of
getting the coffee ... if it weren't for the $50 which he
gives up by this decision. The question is, is $50 enough to
compensate him for the lower chance of winning if he holds onto
envelope A?
If he keeps A, he has a 1/3 chance that it was the coffee, and he
gets the coffee and the money, and a 2/3 chance it was the water,
and he only gets the money. So his expected winning from
keeping it are
1/3($50 +$coffee) + 2/3($50)
On the other hand, if he changes he's more likely to win the
coffee, but he might win nothing - expected winnings
are
2/3($coffee)
By simple algebra, these two expressions are equal to each other
when $coffee = $150. So if the coffee is worth more than this
(which it is, being 'many hundreds' of dollars worth) Charles
should maximise his chance of minning it and forget about the
$50. So - change
(PS, I think your box needs to be bigger.......:-)
Emma
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From nobody@gumbo.valdosta.peachnet.edu Thu Feb 13 18:15 EST 1997
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username: brazilla@mscd.edu
state: DCO
city: Denver
url: http://mosquito.frcc.cccoes.edu/~abrazill
country: USA
comments: Envelope C
Since the argument implies choice, and the choice is related to coffee
and Charles is the one making the choice, hence notice the repetition of
C...thus C provides that which would make Charles happy when
making his choice...coffee.
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From nobody@gumbo.valdosta.peachnet.edu Fri Feb 14 11:43 EST 1997
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From: (Mark Hartswood)
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username: mjh@dcs.ed.ac.uk
city: Edinburgh
country: Scotland
comments: A switch would maximise Charles' chances of getting the
coffee because...
The vouchers might be organised in the envelopes as
shown below:
A B C
1 Coffee Water Water
2 Water Coffee Water
3 Water Water Coffee
If Charles selects A (or any other envelope) then
if situation 1 is true - then Charles will lose by switching.
If situation 2 or 3 is true, then Charles will win by switching.
Thus Charles has a 2/3 chance of winning if he switches. But if
he decided to keep envelope A - then he only has a 1/3 chance
of winning. By opening an envelope containing a water voucher -
Rob Prob effectively gives Charles more information about the
problem.
However, personaly I would have kept envelope A, and the $50
dollars - I can't abide coffee...
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From nobody@gumbo.valdosta.peachnet.edu Fri Feb 14 13:17 EST 1997
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From: (Mark Young)
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username: Mark.Young@AcadiaU.CA
state: NS
city: Wolfville
country: Canada
comments: Switch.
Charles had a one-in-three chance of selecting the coffee
coupon. Nothing that happens afterward can change that
probability. That means a one-in-three chance that B and
C are *both* water coupons. Two thirds of the time B and
C will be one of each. We know B is a water coupon, so
that means that C will be the coffee coupon two times out
of three. Strange, but true.
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From nobody@gumbo.valdosta.peachnet.edu Fri Feb 14 16:22 EST 1997
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From: (leah)
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username: rowlan_L@denison.edu
country: USA
comments: always switch.
Parade magazine had a good explanation of this in one of "Ask Marilyn"'s columns--
it might be worth checking out!
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From nobody@gumbo.valdosta.peachnet.edu Sat Feb 15 12:26 EST 1997
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username: jheath@dtatsys.net
state: GA
city: Valdosta
url: http://www.valdosta.peachnet.edu/~jhheath/index.htm
country: USA
comments: keep envelope A
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From nobody@gumbo.valdosta.peachnet.edu Mon Feb 17 06:28 EST 1997
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Date: Mon, 17 Feb 1997 06:28:24 -0500 (EST)
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From: (joni hietala)
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username: JONI@MODEEMI.CS.TUT.FI
city: tampere
url: modeemi.cs.tut.fi/~joni
country: Finland
comments: He should keep the envelope A with 50$,
because whichever envelope he chooses, he cannot be sure to choose
correctly. Therefore it's better to pick A so even if it's not
the 'coffee' envelope, he'll get some coffee with that extra 50$.
If he picks C, and it's not the right one, he'll get nothing.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Feb 18 00:44 EST 1997
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From: (tom)
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username: tomdrag@geocities.com
state: nj
country: USA
comments: switch choice, the envelope in his possession was chosen
when the odds were 1 out of three. if he switches his
choice his odds will be 1 out of two, which are much
better.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Thu Feb 27 09:25 EST 1997
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Date: Thu, 27 Feb 1997 09:25:47 -0500 (EST)
Message-Id: <199702271425.JAA16846@gumbo.valdosta.peachnet.edu>
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From: (Allan Simonsen)
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username: allans@daimi.aau.dk
city: Aarhus
url: http://www.geocities.com/Athens/3347
country: DK
comments: If he chooses A and the coffeecoupon is there he will have earned several hundred dollars
If he chooses A and the coupon is not there he will have earned 50 dollars
If he chosses C and the coupon is there he will have earned 50 dollars less than if he had chosen A and it was there
If he chooses C and the coupon is not there he will not have earned anything
Therefore choose A
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Thu Feb 27 13:57 EST 1997
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Date: Thu, 27 Feb 1997 13:57:45 -0500 (EST)
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From: (jim hite)
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username: jimhiute@brawleyonline .com
state: CA
city: Brawley
country: USA
comments: Switch to Envrelope C if you really want that coffee.
A was chosen with a 1 in 3 chance of being correct.
C has a 1 in 2 chance of being correct.
Learning that B is not the free coffee doesn't change the
chance that A had originally, but does change the chance
that C has then. Plus years of watching Monte has given
me the insight that he always tries to tempt you with a
reverse psychology bribe to keep a bad choice.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Mar 4 15:57 EST 1997
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Date: Tue, 4 Mar 1997 15:57:18 -0500 (EST)
Message-Id: <199703042057.PAA26915@gumbo.valdosta.peachnet.edu>
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From: (jim hite)
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username: jimhite@brawleyonline.com
state: CA
city: Brawley
country: USA
comments: Choose C, My earlier explanation wasn't good. the way to think
of the answer is to consider that choosing C is really the
same as having chosen B and C in the first place. One or the
other must be worthless, but you still have a 2 in 3 chance
that way. Imagine if there were 100 envelopes and you chose
the first one, then they said that all of the envelopes but
the one you chose and envelope number 40 were worthless. Most
of us would trade then in a second.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Wed Mar 5 23:58 EST 1997
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Date: Wed, 5 Mar 1997 23:58:24 -0500 (EST)
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From: (Ryan Earehart)
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username: ryanearehart@juno.com
state: AZ
city: LHC
country: USA
comments: Chuckie should keep the envelope and get
the $50 bucks - -initial guess is right more than wrong
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Thu Mar 6 14:13 EST 1997
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From: (Douglas Pashakarnis)
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username: diogenes@oeonline.com
state: MI
city: Hazel Park
country: USA
comments: Keep (A) plus the fifty dollars.
There is 50% chance that Charles has the right envelope
with the opening of envelope (B). The offer of $50 simply
acts as an additional free coupon...since it can be expended
upon Zeno's java.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sat Mar 8 11:10 EST 1997
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From: (Lisa)
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username: Crimsum98@aol.com
state: Fl
city: Jacksonville
country: USA
comments: I think Charley should keep envolope "A"
because he has a fifty-fifty chance of getting the coffee with
either of the left-over envolopes. Also, he will get the extra
$50. He could use that for java-money if he gets the water.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sun Mar 9 09:53 EST 1997
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From: (wolfgang winter)
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username: wolfgang.winter@rz.unibw-muenchen.de
city: Munich
url: http://www.rz.unibw-muenchen.de
country: Germany
comments: The answer is: switch to envelope C.
The reason is: in the first choice the chances of
winning the coupon was one third. After envelope had been taken
away he has a second choice. This the chances of winning the coupon
is 50%, but only if he chooses again and this means he must switch
to envelope C.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sun Mar 9 15:27 EST 1997
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Message-Id: <199703092027.PAA05674@gumbo.valdosta.peachnet.edu>
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From: (Mike Hajba)
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username: s019mjh@discover.wright.edu
state: oh
city: dayton
country: USA
comments: If he stays with A and the $50 then he has a 100% chance of
free coffee, even if only $50 worth. If he goes with C he
has only a 1 in 2 chance of free coffee. So, to maximize
his chance of free coffee he should go with A and
the $50.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sun Mar 9 20:28 EST 1997
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From: (Ken Zeno)
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username: Kzeno@earthlink.net
state: MA
city: Peabody
country: USA
comments: Go for the 'A' because according to Zeno's
paradox the more steps you take the less progress you make.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Mar 11 17:12 EST 1997
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Message-Id: <199703112212.RAA09791@gumbo.valdosta.peachnet.edu>
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From: (Tike Trepanier)
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username: tikey@total.net
state: Que
city: Montreal
country: Canada
comments: With envelope A you can win $50 worth
of coffee, regardless of whether the coupon for the free coffee
is in the envelope or not.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Fri Mar 14 13:03 EST 1997
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Message-Id: <199703141803.NAA16128@gumbo.valdosta.peachnet.edu>
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From: (Roy Baker)
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username: baker_rl@acadmn.mercer.edu
state: GA
city: Macon
country: USA
comments: Switch to envelope C. Rob Prob probably
knows which is the correct envelope. He is trying to get Charles
to switch so he won't get the free coffee. Sure Charles can buy
a lot of coffee with 50 bucks, but the goal is to win the free
coffee.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sat Mar 15 01:45 EST 1997
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From: (Jessica)
Subject: Submitted Form
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username: kmille45@cybertrails.com
state: AZ
city: Holbrook
country: USA
comments: I think that Charles will pick envelope
A because regardless of what is inside he will still get $50 giving
him enough money to buy coffee.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sun Mar 16 10:40 EST 1997
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From: (Frank)
Subject: Submitted Form
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country: USA
comments: Keep A and the $50
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Sun Mar 16 12:23 EST 1997
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From: (Frank Belluccia)
Subject: Submitted Form
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username: frankb@icubed.net
state: FL
city: Tampa
country: USA
comments: Envelope A.
Maybe I'm missing something, but unlike some of the other
challenges (I have not read them all yet); I see no greater
benefit in C when compared to A.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Mon Mar 17 12:57 EST 1997
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Message-Id: <199703171757.MAA19843@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Billy Ray Wagenseller)
Subject: Submitted Form
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username: wag@heald.edu
state: CA
city: San Francisco
country: USA
comments: Take envelope A & the $50. His chances that the 2 for 1 offer
is in A (or C) is 50%. By keeping A he is "guaranteed" to win
(at least $50) and has the same probability of winning more
if he chooses C rather than keeping A.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Tue Mar 18 01:03 EST 1997
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From: ()
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country: USA
comments: switch to envelope C.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Wed Mar 19 03:06 EST 1997
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Date: Wed, 19 Mar 1997 03:06:51 -0500 (EST)
Message-Id: <199703190806.DAA26380@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Lauri Kultti)
Subject: Submitted Form
Content-Type: text
Content-Length: 845
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---------------------------------------------------------------------------
username: lauri.kultti@helsinki.fi
city: helsinki
country: Finland
comments: Charles should be indifferent between A
and C. So he should keep A (why to bother changing?).
I guess there is a trick. The question states that Charles is maximizing only his chance for the free coffee - the mentioned free 50$ along with A should not have effect on his choice.
And still, if there is some train of thought recommending
changing from A to C the same train of thought propably gives
reasons for switching back from C to A, and so forth. So, Charles
should keep envelope A.
---------------------------------------------------------------------------
From nobody@gumbo.valdosta.peachnet.edu Thu Mar 20 00:52 EST 1997
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Date: Thu, 20 Mar 1997 00:52:45 -0500 (EST)
Message-Id: <199703200552.AAA28535@gumbo.valdosta.peachnet.edu>
To: rbarnett@grits.valdosta.peachnet.edu
From: (Ravi Ramkissoon)
Subject: Submitted Form
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Below is the result of your feedback form. It was submitted by Ravi Ramkissoon () on Thursday, March 20, 1997 at 00:52:44
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username: ravir@mit.edu
url: web.mit.edu/ravir/www/
country: Trinidad
comments: He should definitely switch.Drawing a simple tree diagra
shows that switching increases his chances from 1/3 to 2/3.
And 2/3 chance is good enough to give up the coupon
for $50.
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From nobody@gumbo.valdosta.peachnet.edu Sun Mar 23 16:18 EST 1997
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Date: Sun, 23 Mar 1997 16:18:15 -0500 (EST)
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To: rbarnett@grits.valdosta.peachnet.edu
From: (Alexei Marcoux)
Subject: Submitted Form
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username: amarcou@bgnet.bgsu.edu
state: OH
city: Bowling Green
country: USA
comments: He should switch to C. The probability that his
initial choice, A, is correct, is 1/3. The probability
that not-A (i.e., B or C) is correct is 2/3. As B
is eliminated from consideration and the probability
that A is coirrect remains only 1/3, the probability that
C is correct is 2/3. Yes, I have read the rich
literature on the Monty Hall paradox ...
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From nobody@gumbo.valdosta.peachnet.edu Tue Mar 25 12:17 EST 1997
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username: BMAssey733@aol.com
state: PA
city: Pittsburgh
country: USA
comments: This one was solved definitely at the University
of Pittsburgh. One ought to switch to envelope C because that
will give 50-50 chance of victory. If not switch then the odds
are one third for victory. This was much discussed at the Center
for Philosophy of Science at Pitt several years ago. It's the
MOnty Hall problem.
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From nobody@gumbo.valdosta.peachnet.edu Tue Apr 1 03:43 EST 1997
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Date: Tue, 1 Apr 1997 03:43:53 -0500 (EST)
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From: (R.A. Johnson)
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username: ajohnson@cyberspace.org
state: wa
city: seattle
url: http://internetcafe.allyn.com
country: USA
comments: he should choose envelope A. if envelope
A contains the certificate, he gets free coffee and 50$, if it
doesn't he still gets 50$ of coffee (if he chose to buy coffee
with it). The former would maximise the coffee because he would
get free coffee for himself and another for a year AND beable
to buy coffee for even another with the 50$ extra (probably not
all year considering his and probably his freinds java habit).
C leaves the possibility of nothing...the opposite of maximum...thus
is ruled out.
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From nobody@gumbo.valdosta.peachnet.edu Tue Apr 1 15:26 EST 1997
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Date: Tue, 1 Apr 1997 15:26:35 -0500 (EST)
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To: rbarnett@grits.valdosta.peachnet.edu
From: (Maria Karekla)
Subject: Submitted Form
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username: mkarekla
state: GA
city: Valdosta
country: USA
comments: I believe, he should go with envelope A
and the $50 dollars.Usually our first choice is the best one.
Even if there is water in the envelope, he will still get the
$50.
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