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)

Message-Id: <199702011500.KAA06856@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Travis Welwood-Hreno)

Subject: Submitted Form

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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.

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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)

Message-Id: <199702011639.LAA06944@gumbo.valdosta.peachnet.edu>

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)

Message-Id: <199702021545.KAA12174@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Robert M. Martin)

Subject: Submitted Form

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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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Content-Length: 616

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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

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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.


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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)

Message-Id: <199702022252.RAA13729@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Sergio Tenenbaum)

Subject: Submitted Form

Content-Type: text

Content-Length: 699

Status: RO

X-Status:

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.

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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.

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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?

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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


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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

Status: RO

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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

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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...

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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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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!!!

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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

X-Status:

Below is the result of your feedback form. It was submitted by Me () on Tuesday, February 4, 1997 at 17:41:12

---------------------------------------------------------------------------

state: Ca

city: Taft

country: USA

comments: What a unique place!!!!!!

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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

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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!

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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)

Message-Id: <199702060134.UAA02129@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Patricia Donaldson)

Subject: Submitted Form

Content-Type: text

Content-Length: 560

Status: RO

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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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To: rbarnett@grits.valdosta.peachnet.edu

From: (Cathy Wilson)

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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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To: rbarnett@grits.valdosta.peachnet.edu

From: (Elam O'Renick)

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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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From: (Yael Brahms)

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username: yael@radview.com

city: Tel-Aviv

country: Israel

comments: Keep A

---------------------------------------------------------------------------

From nobody@gumbo.valdosta.peachnet.edu Thu Feb 6 20:12 EST 1997

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From: (Erich Plondke)

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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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To: rbarnett@grits.valdosta.peachnet.edu

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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To: rbarnett@grits.valdosta.peachnet.edu

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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From: (James Parsly)

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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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Message-Id: <199702112213.RAA10526@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (JOhn Trombetta)

Subject: Submitted Form

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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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To: rbarnett@grits.valdosta.peachnet.edu

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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To: rbarnett@grits.valdosta.peachnet.edu

From: (Amy Braziller)

Subject: Submitted Form

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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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Message-Id: <199702141643.LAA04426@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Mark Hartswood)

Subject: Submitted Form

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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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Message-Id: <199702141817.NAA04734@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Mark Young)

Subject: Submitted Form

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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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Message-Id: <199702142122.QAA05444@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (leah)

Subject: Submitted Form

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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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From: (me)

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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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From: (joni hietala)

Subject: Submitted Form

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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.

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From nobody@gumbo.valdosta.peachnet.edu Tue Feb 18 00:44 EST 1997

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Date: Tue, 18 Feb 1997 00:44:44 -0500 (EST)

Message-Id: <199702180544.AAA10009@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

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.

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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>

To: rbarnett@grits.valdosta.peachnet.edu

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

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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)

Message-Id: <199702271857.NAA17461@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (jim hite)

Subject: Submitted Form

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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.

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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>

To: rbarnett@grits.valdosta.peachnet.edu

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.

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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)

Message-Id: <199703060458.XAA29586@gumbo.valdosta.peachnet.edu>

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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

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From nobody@gumbo.valdosta.peachnet.edu Thu Mar 6 14:13 EST 1997

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To: rbarnett@grits.valdosta.peachnet.edu

From: (Douglas Pashakarnis)

Subject: Submitted Form

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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.

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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.

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From nobody@gumbo.valdosta.peachnet.edu Sun Mar 9 09:53 EST 1997

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Date: Sun, 9 Mar 1997 09:53:19 -0500 (EST)

Message-Id: <199703091453.JAA05444@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

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.

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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>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Mike Hajba)

Subject: Submitted Form

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Below is the result of your feedback form. It was submitted by Mike Hajba () on Sunday, March 9, 1997 at 15:27:33

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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.

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From nobody@gumbo.valdosta.peachnet.edu Sun Mar 9 20:28 EST 1997

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Message-Id: <199703100128.UAA05951@gumbo.valdosta.peachnet.edu>

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From: (Ken Zeno)

Subject: Submitted Form

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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.

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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>

To: rbarnett@grits.valdosta.peachnet.edu

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.

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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>

To: rbarnett@grits.valdosta.peachnet.edu

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.

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From nobody@gumbo.valdosta.peachnet.edu Sat Mar 15 01:45 EST 1997

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To: rbarnett@grits.valdosta.peachnet.edu

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.

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From nobody@gumbo.valdosta.peachnet.edu Sun Mar 16 10:40 EST 1997

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From: (Frank)

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country: USA

comments: Keep A and the $50

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From nobody@gumbo.valdosta.peachnet.edu Sun Mar 16 12:23 EST 1997

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Message-Id: <199703161722.MAA18281@gumbo.valdosta.peachnet.edu>

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From: (Frank Belluccia)

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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.


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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.

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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.

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From nobody@gumbo.valdosta.peachnet.edu Wed Mar 19 03:06 EST 1997

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Message-Id: <199703190806.DAA26380@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Lauri Kultti)

Subject: Submitted Form

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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.

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From nobody@gumbo.valdosta.peachnet.edu Thu Mar 20 00:52 EST 1997

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Message-Id: <199703200552.AAA28535@gumbo.valdosta.peachnet.edu>

To: rbarnett@grits.valdosta.peachnet.edu

From: (Ravi Ramkissoon)

Subject: Submitted Form

Content-Type: text

Content-Length: 540

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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)

Message-Id: <199703232118.QAA06035@gumbo.valdosta.peachnet.edu>

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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Date: Tue, 25 Mar 1997 12:17:20 -0500 (EST)

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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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To: rbarnett@grits.valdosta.peachnet.edu

From: (R.A. Johnson)

Subject: Submitted Form

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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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