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:

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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city: Exeter

country: U.K.

comments: I choose Box B

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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state: WI

city: Milwaukee

country: USA

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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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state: MI

city: Roseville

country: USA

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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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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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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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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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state: que

city: Montreal

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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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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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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state: MO

city: Blue Springs

country: USA

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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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city: helsinki

country: FINLAND

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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

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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state: AB

city: Red Deer

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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state: MN

city: Minneapolis

country: USA

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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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state: GA

city: Atlanta

country: USA

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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state: QC

city: Montreal

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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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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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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state: NS

city: Wolfville

'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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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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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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state: Ont

city: Waterloo

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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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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state: PA

city: Phoenixville

country: USA

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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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state: OH

city: Dayton

country: USA

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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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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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state: CA

city: Goleta

country: USA

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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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state: on

city: Toronto

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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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

---------------------------------------------------------------------------Below 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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