Results of Zeno's Challenge #20
ORIGINAL PROBLEM
The Ever-so-Bold Charles!
It seems that our man Charles has kept his eye on Zeno's players, and has done some calculating--at least to his own satisfaction. After the earlier challenge #13, Charles has now agreed to put his money where his mouth is! He has assured respondents that he will ACTUALLY PAY winners, if there are any, for any winnings in the latest Coffeehouse challenge...So let's get busy and see if we can outsmart Charles in this decision-scenario. Here's the challenge:
You are to choose either Box A, B, or C, and only one.
Choose Box A and you will win $1 if 1/3 of those playing choose A also; otherwise, you win nothing;
Choose Box B and you win $10 if 3/4 of those playing choose B also; otherwise, nothing;
Choose Box C and you win $5 if 1/2 of those playing choose C also; otherwise, nothing.
So there it is--think about the best choice, and submit your entry. Charles is getting nervous!!!
Well, folks, the results are in!! As you will see from the comments and responses below, the best choice wasn't obvious, at least to these Zeno's players. Some example comments: Weill didn't like the repeated challenge, and asked that it be stopped!! (Don't worry, no more reruns of this!) Weill chooses B, a response that Valter Sorana analyzes as the optimal one, using a Pareto function. J.P. Holohan, however, thinks that A is the "only choice with a cat in hell's chance of winning!" HHmmm. And according to Ross Cameron, choice C is the best one--although Ross predicts that nobody will win anything!! Could he be right? With FREE MONEY and NO RISK on the line?? Indeed he IS correct, for
NOBODY WINS ANYTHING!!
Reasons: Since there were 39 resonses, winnings for A ($1), B ($10), and C
($5), respectively, required votes of at least 13, 29, and 19. But, these were the votes
cast: A=8, B=23, and C=8. So, each possible FREE MONEY win was not satisfied!! And Charles
is so happy!! Enjoy thinking about the implications of this decision-scenario, with the
same results as the earlier Zeno's Challenge, repeated here...remember Louis Marinoff's
fine "Tragedy of the Coffeehouse" article, available from Zeno's Coffeehouse
website? I wonder what Louis would say about THIS result!!...........Cheers! Ron Barnette,
Zeno's Proprietor
RESPONSES:
username: Weill
state: NY
city: New York
url: matweill@aol.com
country: USA
comments: I choose Box B. I wish everyone would realize that there is no reason not to do
so. Of course, people will over-analyze the situtation, as proven by your earlier versions
of this problem, and come up with silly explanations for choosing other boxes (most likely
A). The truth is we, the respondents, are in control. If we could talk, we could all agree
to pick B. Also, I've noticed that the number of respondents is rather small. So, I could
enlist 50 or so people I know to answer as I have and get the result I want. However, I
would rather not waste that much time for $10. Please stop giving this problem.
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username: S.A.Wardell@ex.ac.uk
city: Exeter
country: U.K.
comments: I choose Box B
username: j.p.holohan@student.derby.ac.uk
city: Derby
country: UK
comments: I don't live in America, and even if I did I wouldn't really be interested in
the $1 prize. however I still go for box A because that is the only one with a cat in
hells chance of actually winning anything.
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username: confuzed_bob@yahoo.com
state: WI
city: Milwaukee
country: USA
comments: Box B
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Below is the result of your feedback form. It was submitted by Seth Johnston ()
on Sunday, January 17, 1999 at 21:25:36
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city: london
country: England
comments: I choose Box c
Below is the result of your feedback form. It was submitted by Anna
D'Alessandro () on Wednesday, January 20, 1999 at 22:10:36
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username: axd05845@cca.munet.edu
state: MI
city: Roseville
country: USA
comments: I choose box B, please!!!
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Below is the result of your feedback form. It was submitted by Ross P Cameron
() on Monday, February 1, 1999 at 09:49:19
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username: 9705789c@student.gla.ac.uk
city: Glasgow
country: Scotland
comments: I choose Box C
My reason for choosing so is that box A does not offer a large
enough incentive to gamble on, and box B requires too large
a proportion of the voters to choose it.
I still don't think anyone will win.
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Below is the result of your feedback form. It was submitted by Wilson Potter ()
on Tuesday, February 2, 1999 at 17:02:57
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state: FLA
city: Jacksonville
country: USA
comments: I choose C
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Below is the result of your feedback form. It was submitted by rand mace () on
Thursday, February 4, 1999 at 22:41:34
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username: rmace@ns.net
state: ca
city: camino
country: USA
comments: i chose box C
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Below is the result of your feedback form. It was submitted by Valter Sorana ()
on Friday, February 5, 1999 at 00:22:15
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username: vsorana@leland.stanford.edu
state: CA
city: Stanford
country: USA
comments: I choose B.
I assume that "if 3/4 of those playing" means "at least 3/4 of those
playing".
The Pareto dominant Nash equilibrium for the players is such that everyone chooses B.
(Nash equilibrium = everyone is making the best choice given the other players' choices;
Pareto dominant = there is no other Nash equilibrium in which everyone is (weakly) better
off)
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Below is the result of your feedback form. It was submitted by Karen Haines ()
on Sunday, February 7, 1999 at 16:34:03
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username: kazzy@canoemail.com
state: que
city: Montreal
country: canada
comments: I choose Bow B because I am a gambler altough it has the highest pay, it also
has the worst odds. I am hoping other gamblers are out there.
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Below is the result of your feedback form. It was submitted by Vinny () on
Thursday, February 11, 1999 at 01:06:19
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username: vinny@pro-ns.net
state: mn
city: minnetonka
country: USA
comments: Box B. If everyone is smart they would choose box b. maximum winning to the the
mximum winners
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Below is the result of your feedback form. It was submitted by Wendy () on
Sunday, February 14, 1999 at 17:54:59
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username: WeninLB@aol.com
state: CA
city: Long Beach
country: USA
comments: Surely after seeing the results from the last game, everyone will choose B this
time!
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Below is the result of your feedback form. It was submitted by Kyle S.C. Vogel
() on Thursday, February 18, 1999 at 00:19:44
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username: kvogel@cysource.com
state: MO
city: Blue Springs
country: USA
comments: Box B
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Below is the result of your feedback form. It was submitted by lauri kultti ()
on Thursday, February 18, 1999 at 03:30:35
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username: lauri.kultti@helsinki.fi
city: helsinki
country: FINLAND
comments: B. Shouldn't need any comments.
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Below is the result of your feedback form. It was submitted by James Mavrodes
() on Thursday, February 18, 1999 at 08:43:43
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state: CA
city: Stockton
country: USA
comments: I choose Box C
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Below is the result of your feedback form. It was submitted by Amy Irvine () on
Thursday, February 18, 1999 at 08:44:51
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state: PA
city: Philadelphia
country: USA
comments: I go for Box A
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Below is the result of your feedback form. It was submitted by Jay Davis () on
Thursday, December 31, 1998 at 14:37:54
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username: jay-27@home.net
state: AB
city: Red Deer
country: Canada
comments: I chose box "C"
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Below is the result of your feedback form. It was submitted by Kyle Calderhead
() on Monday, January 4, 1999 at 10:15:19
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username: chead@math.umn.edu
state: MN
city: Minneapolis
country: USA
comments: Box C
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Below is the result of your feedback form. It was submitted by Greg Ferro () on
Thursday, January 7, 1999 at 22:02:32
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username: gferro@mindspring.com
state: GA
city: Atlanta
country: USA
comments: B
Below is the result of your feedback form. It was submitted by Sissa Tyson ()
on Saturday, January 9, 1999 at 17:22:59
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city: Sidney
country: Australia
comments: I select C
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Below is the result of your feedback form. It was submitted by marika
hadzipetros () on Monday, January 11, 1999 at 17:30:22
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username: mhadzi@hotmail.com
state: QC
city: Montreal
country: Canada
comments: I choose box B.
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Below is the result of your feedback form. It was submitted by John Pormann ()
on Wednesday, January 13, 1999 at 10:21:21
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username: jpormann@ee.duke.edu
state: NC
city: Durham
country: USA
comments: I choose Box C - it seems to have the best balance of risk
and reward (you get 5x the reward vs. Box A for a little
increase in risk, while Box C only gives 2x the reward of B
with a significant increase in risk). Given past results,
it's seems useless to do any more thorough an analysis than
this :)
Below is the result of your feedback form. It was submitted by Nick Terzi () on
Thursday, January 14, 1999 at 14:00:55
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username: nicholas_terzi@publicis-usa.com
state: NY
city: New York
country: USA
comments: I pick B.
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Below is the result of your feedback form. It was submitted by Mark Young () on
Thursday, January 14, 1999 at 14:26:46
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username: Mark.Young@AcadiaU.CA
state: NS
city: Wolfville
country: Canada
comments: Choice: A
'A' came pretty close to winning last time, and neither of
the others did. My guess is that you'll see a drop in C,
spread between A and B. Given that A was only 5 people
away from paying last time, there's a reasonable chance
that enough will go over to make it pay this time. Too
bad the same can't be said about B....
Below is the result of your feedback form. It was submitted by Fredrick Harris
() on Thursday, January 14, 1999 at 16:44:33
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username: fbharris@valdosta.edu
state: ga
city: valdosta
country: USA
comments: I would like to pick box A!!!
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Below is the result of your feedback form. It was submitted by Bill Welsch ()
on Thursday, January 14, 1999 at 18:19:28
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state: CA
city: Stockton
country: USA
comments: I'll go for Box A
From: Douglas Guthe <Douglas Guthe>
To: rbarnett@valdosta.edu <rbarnett@valdosta.edu>
Subject: Submitted Form
Date: Friday, January 22, 1999 10:21 AM
Below is the result of your feedback form. It was submitted by Douglas Guthe () on Friday, January 22, 1999 at 10:21:28
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username: dbgrlc@aol.com
state: NC
city: Chapel Hill
country: USA
comments: I choose B.
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Y‘€ Œ˜CBelow is the result of your feedback form.
It was submitted by MrCoffee () on Friday, January 22, 1999 at 21:41:59
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username: cmckinno@artsmail.uwaterloo.ca
state: Ont
city: Waterloo
country: Canada
comments: Box A is obviously out of the question. Real $ equates to people taking risks.
Afterall, we have nothing to lose. Therefore, who would waste their time choosing box A?
Box C seems logical if you are indecisive or in my mind the type of person that a
relativist is. This crowd is filled with die hards. I can feel it. I select Box B!
Below is the result of your feedback form. It was submitted by Curtis Hoffman
() on Sunday, January 24, 1999 at 00:33:01
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username: pchoffm@clemson.edu
state: SC
city: Clemson
country: USA
comments: I'll take box B. These are not considerably large sums of money and I would
willingly risk the opportunity for one or five dollars for the chance for ten.
Below is the result of your feedback form. It was submitted by Patrick Hoffman
() on Sunday, January 24, 1999 at 00:36:05
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username: hoffmonster@hotmail.com
state: PA
city: Phoenixville
country: USA
comments: Box B, please
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Below is the result of your feedback form. It was submitted by Roger Wilcox ()
on Sunday, January 24, 1999 at 00:36:47
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username: rogerman25@hotmail.com
state: OH
city: Dayton
country: USA
comments: Box B
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Below is the result of your feedback form. It was submitted by Susan Poncey ()
on Monday, February 1, 1999 at 14:14:17
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city: London
country: England
comments: I select A
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Below is the result of your feedback form. It was submitted by Brandon Cooke ()
on Wednesday, February 3, 1999 at 10:11:40
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username: blc@st-andrews.ac.uk
city: St. Andrews
country: Scotland
comments: High rollin', got to pick "B".
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Below is the result of your feedback form. It was submitted by Maggie Long ()
on Thursday, February 4, 1999 at 12:00:13
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state: PA
city: Pittsburgh
country: USA
comments: Box C will be a winner for me!!
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Below is the result of your feedback form. It was submitted by Elizabeth
Collier () on Thursday, February 4, 1999 at 21:41:02
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city: Oxford
country: England
comments: I choose Box a!!
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Below is the result of your feedback form. It was submitted by Dean Mitchell ()
on Saturday, February 6, 1999 at 04:20:49
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username: umcbrm00@umail.ucsb.edu
state: CA
city: Goleta
country: USA
comments: Box $10
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Below is the result of your feedback form. It was submitted by Chris () on
Wednesday, February 10, 1999 at 14:21:11
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username: chris@creativetechnology.on.ca
state: on
city: Toronto
country: Canada
comments: I chose box B
Below is the result of your feedback form. It was submitted by Chris Winter ()
on Thursday, February 11, 1999 at 16:08:38
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username: chris.winter@asu.edu
state: AZ
city: Chandler
url: http://www.public.asu.edu/~bujin
country: USA
comments: I choose box B
From: Robert Brighton <Robert Brighton>
To: rbarnett@valdosta.edu <rbarnett@valdosta.edu>
Subject: Submitted Form
Date: Thursday, February 11, 1999 5:49 PM
Below is the result of your feedback form. It was submitted by Robert Brighton () on Thursday, February 11, 1999 at 17:49:40
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state: NY
city: New York
country: USA
comments: I choose box A
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is the result of your feedback form. It was submitted by Kat Gordon () on Wednesday,
February 17, 1999 at 17:22:48
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username: moondreamer17@hotmail.com
state: MN
city: Bloomington
country: USA
comments: I pick box B.
peace,
kat