# Here's The Winner In Our Pick-A-Number Game

This is a guessing game. To play, pick a number between 0 and 100. The goal is to pick the number that's closest to half the average of all guesses.

So, for example, if the average of all guesses were 80, the winning number would be 40.

Thanks very much to the 15,322 people who entered.

We'll get to the winning number (and the winners) in a minute. But first, here's why we were interested in this game in the first place.

What's fun about this game is it forces you to think about how everybody else thinks. And then it forces you to think about how everybody else thinks about how everybody else thinks. Etc.

If you assume everybody else is just picking a number at random, you would expect the average guess to be 50. In that case, the winning number would be 25 — half of 50.

But if everybody is thinking that way, and everybody guesses 25, then then answer should be half of that — somewhere around 12.

Why stop there? You can use this kind of logic to keep cutting the number in half. So eventually you get down near zero.

You can see each of these strategies play out in the entries in our contest. We graphed all of the responses, and you see big spikes around 25, 12 and near zero.

Jess Jiang/NPR
Jess Jiang/NPR

(Here's a spreadsheet with every single guess.)

I talked with Ben Polak, a Yale economist who plays this game each year with his intro to game theory class. He said he likes the game because it shows the importance of strategic thinking — to think about not only what others are thinking, but what others think that you're thinking. (Like in Keynes's beauty contest, or this Friends episode.)

Polak guessed that the answer to our contest would be somewhere around 10. In other words, he's saying Planet Money readers think other Planet Money readers are rational — but not that rational.

Over at Cheap Talk, the economist Jeff Ely has a very nice discussion of this sort of experiment. He does a little math, a little handwaving, and guesses 16.

Ok. Here's the moment you've been waiting for:

The winning number in our experiment is 11.53

Five people guessed 11.5. They are our winners.

BJ
Amanda
Jami L. Bennett
Greg Cunningham

A few people gave decimal answers that were also pretty close — Bolivia Red, Spencer J Padilla, Steven Burt, Aaron Chinn, and Jasen.

Finally, an honorable mention goes to all 772 people who guessed 12 — the closest integer to the correct answer. Here's the full list:

61north
Aaron
Aaron
Aaron Couch
Aaron Rouby
ababcoc
Abbie
Abby
Abby Brody
Abby Thomas
Aimee
Al Good
Al Lopez
Alan Goos
Alanna Turner
Alex
Alex Barrett
Alex Chaice
Alex Hopmann
Alex MacDonald
Alexa Squire
Alexander Vennebush
Aliotsy Andrianarivo
Alison
Alison Klejna
Alissa Browning-Couch
Alix Grabowski
Allison
Alyssa
Amanda
Amanda Hannan
Amanda Holmes Duffy
Amanda Yates
Amber Huff
Amos
Amy Bitner
Amy Brandenburg
Amy Rossello
Amy S.
Amy Stroth
Amy Taylor
Andrea
Andrea Palmer
Andrew
Andrew
Andrew Conner
Andrew Hodges
Andrew J
Andrew McDaniel
Andrew Payzant
Andrew Peterson
Andrew Ramirez
Andy Cohen
Angie Boyter
Anissa Core
Anne
Annie Clement
Anurag Saxena
Apple Kabob
April Neigut
April Stevenson
Armando Duran
Arnold Fox
Art Ryel-Lindsey
Ash Haeger
Ashley Trimble
Audrey
Avi
Avi
Barb C,
Barb Kilgust
Barbara Berkley
Barbara Gooby
Barbara Langstaff
Barbara Targum
Becky LaFlamme
becky nelson
Beki S.
Ben A
Ben B
Ben Luippold
Ben Thompson
Benjamin Morrill
Benjamin Reichstein
Beth
Beth Forbes
beth h.
Beth Meredith
Beth Ruedi
BHC
bill
Bill
Bill Palkowsky
Bill Siderski
Billie
Bobby!
Boris Mindzak
Brandon
Brandon Leung
Bredan McGovern
Brenda Cooper
Brendan Simons
Brian
Brian Archibald
Brian Exelbierd
Brian Francis
Brian Hilburn
Brian Jacoby (Tallahassee, if there's more than one)
Brian Landberg
Brian Roberg
Brian Schermerhorn
brian weindling
britt
Britt Smith
Brittany Burkett
Brittany-Renee
Bronislava Lee
Bryan Newman
Buck
Byron Combs
Caitlin Rohrer
Calvin Gosla III
Cameron Gilroy
Cao Jingshu
Cara McClintock-Walsh
carina
Carl
Carla Kilgore
Carly Baxendale
Carole
Carolyn K.
CarterB
Casey Primel
cassandra lenhard
Cassia
Cassie
Catherine Merrbach
Catie
CB Jarvis
Charles Borgerding
Charlie
Chase P S
Chelan
Chelsea Paice
CHris
chris
Chris
Chris Benham
Chris Burnett
chris hardee
chris moore
Chris Morin
Chris S.
Chrissy
Christie Jarrio
Christie Jett
Christina Hevko
christina steen
Christine Gunsaullus
Christopher Coleman
Christopher Wheat
Cindie Carroll-Pankhurst
Cindy
Cindy
Clark
Clayton Kinsler
Clifford Beshers
Clint
Collin
Corina Jaisle
Cory Erlandson
Courtney Cudlip
Craig R.
Cris Whetstone
cucumber17
Cynthia
Cynthia Beard
Dale Borgeson
Dale Howard
Dali
Dan
Dan Cieplinski
Dan S
Daniel Fletcher
Daniel Michelson-Horowitz
Danny A
Danny Swan
Darryn
Dave Cooper
Dave Grace
Dave Hagen
Dave Kramberg
david
David Bauer
David G.
David Hilson
David Lakin
David Myer
David Onder
David Palchak
David Roberts
David robertson
David Schiffrin
David Tuman
Davis
Dawn
Dawn Leavy
denise
Derek Martinez
Destin perrin
Diana Hellman
Diane
Diane Carlson
diane h. james
Diane Johnson
Dori Kempin
Dorothy
Doug Berry
Doug Cornelius
drew woods
Duane Wilkey
Duncan
Duncan Ellis
dustin skarda
Dusty Reed
Dylan J.J.
Ed Briscoe
Ed Gulczynski
Elizabeth
Elizabeth Fahs
elizabeth impossible
Ella
Emily Bull
Emily Shelton
Emily Watts
emma
Eric Kitterman
Eric McCormick
Eric The Awesome Nord
Eric Werner
Erik Johnsgard
Erin Richey
Erin Stutelberg
Evan N
Farid
Fernando Miranda-Mendoza
Francisco Melli-Huber
Frank McD
frank newell
fuzzless
Gabriel Martin
Gary Oshust
Genesis Ponce
Geoff Harrison
George
George Hamzik
Gianna Borkhuis
Gordon
Gorg Huff
gough.bob
greg
Greg Koeser
Greg Mohler
Greg Sand
Greg Schaeffer
Greg T
Gregory Lobo Jost
Guilhem Flouzat
Guy Yedwab
Gwynne Ash
Hannah Brown
Hannia
Harlyn Pacheco
Harris Kalat
Heather Dowding
hiramlevy
Hoang
Holly
Holly Burke
Hy Schwartz
ian smith
Isaac_Mtz_12
Isabelle
Isaiah Oliver
Ismael
Issam
J.D. Hewitt
Jackie
Jackie Julien
Jackline Lasola
Jacob
Jacob Heidenreich
Jake Langlois
James Brucker
James C. Lee
James Eliot C
James Pace
Jamie Tisdale
Janet Riessman
Janice Bossart
Jared Smith
jason
Jason
Jason
Jason
Jason Baek
Jason Blanchard
Jason Bribitzer-Stull
Jason Clark
Jason F
Jason Mayer
Jason Robles
Jay Bonci
Jay Feldman
Jayanth Rangaraju
Jean
jean coggan
Jeff Agnew
Jeff Boyle
Jeff Carrier
jeff f
Jeff Myers
Jenn Mercer
Jennifer
Jennifer Jula
Jennifer Little
Jennifer M
Jennifer Marzullo
Jennifer Page
Jennifer Perrine
Jennifer Scheper
Jennifer Taransky
Jenny Brundage
jenny hall
Jenny Landry
Jenny Zhang
Jeris Sunneberg
Jesse
Jesse
Jessica
Jessica
Jessica Fletcher
Jessica Hoskins
Jessica Williams-Holt
Jewel Kjellberg
Ji12
Jim Felt
Jim Kopeny
Jim Pacek
Jimmy Hogan
jjulich
Joan
Joanna Green
joaoagn
Jodi MacNeal
Joe
Joe Ducey
Joe Frollo
Joe Pallas
Joe Shouldice
Joe the Listless Activist
Joe Traynor
Joel Mejiano
Joel Ramirez
Joel Van Diepenbos
Johanna
John
John
John BIgelow
John Cooper
John Robertson
John Roney
John S
John Wanek
Johnathan Hughes
Johnny Wyskiel
Jon Baumgartner
Jon D
Jonas
Jonathan Korman
Jose A. Fajardo
Joseph Burke
Joseph Giddens
Joseph Lalli
Joseph Lamoree
josh
Joshua Moody
Joshua Thurmond
Joy Washington
Judy Caplan
Judy Gordon
Julian
Julianne
Julie Hubbard
Juliet
Juni Gloves
Juno Farnsworth
Justin Ropella
Kahini
Kara Sarchet
Karen
Karen Croghan
Karen Hamilton
Karin Todd
Karin Winters
Kate
Kathi Griffin
Kathy
katie
Katie Vojtko
Kattie
Kaylem Carter
KC
Keil Drescher
keith
Keith M
Keith Williams
Kelly
Kelly Chisholm
Kelly Watson
Kelly Zorzi
Ken Jones
Kerry
Kevin
Kevin Hunt
Kim
Kim
Kim Fenton
Kim Gorman
KimPossible
Kirsten
kismet_doo
Krissy Kirlin
Kristen
Kristen
Kristin Dawson
Kristina Stredwick
Lacy Ward
Laura
Laura
laura
Laura Thomson
laurel
Lauren M.
Laurie
Laurie Kilfoy
lchiang
Leah McDermott
Len Sharp
Lena
Lena Koschmann
Liam Foley
Lily Kirby
Linda
Linda Nielsen
Lindsey
Linus W.
Lisa
Lisa
Lisa Holl
Liz
Liz Anderson
liz finlay
Lola Fields
Louis Shell
Luke
Luke Duff
Lulzasaur
Lydia
Lyn Drennan
Lynn
Lynn
M
Manja
Marci Kirchberg
Margaret
Margot Vigeant
Marguerite Kenner
Marja Engel
Mark
Mark
Mark Anthony
Mark Landman
Mark Q.
Martha
Martin
Martin Fisher
Mary Stephens
marybeth
MaryBeth
Matt
Matt
Matt Bingay
Matt Jung
Matt Lane
Matt McQueen
Matt Romano
Matthew Andersen
Matthew Louwrens
Matthew Slaven
Mavin Giss
Max
Max Corchin
Max Greenheck
MB Lapis
Megan Geerdts
Megan Hasenwinkel
Megan Johnson
MeiMei
Melinda McLaughlin
Mette Weis
Micah
Michael
Michael Baer
Michael Greenfield
Michael Sanchez
michael yeiter
Michelle Buccini
Michelle Terry
Mike
Mike Daly
Mike davis
Mike davis
Mike Erbes
MIke Johanson
Mike Lynn
Mike Robertson
Mike Van Treese
Mike_L
Mildy
Min Lee
Mindy P
Missy Gibson
Mitzi Levy
MJ Kiran
mofoblaster
Mohammed Syed
Molly
molly countermine
Molly McGriff
Mosin
Natalie Mora
Nate Reeves
Nathaniel Carroll
Nathaniel Irons
Ned Ryersen
Ned Zimmerman
Nicholas
Nick Marshall
Nick Rile
Nick White
Nicole Craig
Nicole Faby
Nina Stull
nora
Nora Kuster
Ohanes
Ohanes
oliviakraus
Orion Delwaterman
Orkilein
P.Roach
Pam Schmidt
Pamela Salata
Parks
pat
Patricia Atkinson
Patricia LoCascio
Patricia Robertson
Patrick
Patrick Connaughton
Patrick Fleury
Patrik Antich
Patriot
Patt Hull
Patty Lee
patty munson
Paul
Paul De Waard
Paul Ludlow
Paula M.
Peter Axel Komistra
peter b
Peter K
Peter N
Peter Ravn Rasmussen
Phil Canuto
Phil Wellington
Phillip Green
pilar stewart
pj
PMurphy
quizzigal
Rachel
Rachel
rachel
Rachel Brown
Rachel Farley
Rachel Skipper
Randi
Raymond
Raymond
Raymond Jowdy
Rebecca Bar
Rebecca Calvo
Rebecca Tassoni
Regan
Richard Rothblatt
Riley Hyle
Rina Huettner
Risa RS
Rob Chew
Rob Duffy
Rob Engar
Rob Killian
Rob Ledbetter
Rob M
Robert Paynter
Roger Hinze
Ron Miller
Rose Spinoza
Ryan
Ryan Abman
Ryan Dietrich
Ryan Freeberg
Ryan Guyer
Ryan Hagglund
Ryan Rilea
Ryan Tabaldi
S Willis
Sam
Sam Felder
Sam Margulies
Samantha Klinger
Samer
Sandeep
Sarah
Sarah
Sarah Brewer
Sarah Kingsbery
Sarah Ross
Sarah W
Scot Rogers
Scott Fiero
Scott M
Scott Telfer
Scott van Pletzen-Rands
Scott Ward
sean
Senja
Serdar Ince
Sergio M.
Shannon M. Smith
Shay
Shea Goff
shon forsyth
Simeon Kang
simona
Sittha Sukkasi
Skip Jackson
Sophie
Søren
Søren
sriram
stacey tannenbaum
Stacey Willis-Center
Stefanie
Stefanie G
Stephanie
Stephanie Helgeson
Stephanie Settimi
Stephanie Thirtyacre
Stephanie Waite
Stephen Tsai
Steve
Steve Benedetti
Steve Colvett
Steve Muller
Steve Rylander
Steve Urich
SteveI
Steven G. Blank
Steven Green
StevenG
Sue
Sue Papin Sears
Susan
Susan
susan
susan
Susan Chemey
Susan Hutchins
Susan Segura
Suzanne
Tamar E Cohen
Tara
TC
Ted Kolberg
Terry Walsh
Theresa
Theresa Yaukey
TheTwelveGuy
Thom Blanton
Thomas
Thomas Medina
tim
Tim Carolan
Tim Evans
Tim Gagne
Tim jackson
tim park
Tinkerhell
TM Ricker
Todd Dulaney
ToddB
Tom
Tom Kraikit
Tommy Ratliff
toxie
Traci
Tracy Gorelick
Tracy J Spencer
trd
Twelve Thetwelthiest
Tyler
Tyler Van Brunt
Upendra
urmila
Vail Gardner
Vernon
Vic Schubert
Wally Bugg
Wanda
Wendy
Wendy Krause
Wes Merchant
Wesley
Whit
Will Rusk
William
William Freeman
William Oetting
Zhuo H.
Zora Law