The Mathematics of Game Shows - Patterns in Practice

The Math
Game

Bowen
Research Sc

(and part-time g

bkerins@

hematics of
e Shows

n Kerins
cientist, EDC

game consultant)

@edc.org

Over

Game shows are filled
•  Contestants

•  How do I play best
•  How much is enou
•  Producers
•  How do I build a fu
•  How will contestan
•  How much money

rview

d with math problems…

t?
ugh?

un game to watch?
nts behave?
y are we giving out?

PRIZ

Want t
We’ll need some vo
You may leave here

(Warning: definition o

ZES!

to win?
olunteers for games.
with fabulous prizes!

of fabulous may vary.)

Personal E

February 2000: Million

(for $1000: How many

Encounters

naire (episode #49)

degrees in a right angle?)

Personal E

February 2000: Million

(I got the next

Encounters

naire (episode #49)

t question wrong.)

Personal E

April 2004: The Price I

(Double overbid on t

Encounters

Is Right

the showcase! Bummer.)

Personal E

July 2007: National Bin

(I also worked on “Show Me T
Bee”… which, four years later

Encounters

ngo Night

The Money” and “The Singing
r, is still on the air.)

Personal E

Since Then…

Recent work: “in-developmen
and Ryan Seacrest Productio

Encounters

nt” shows for Endemol, Gurinco,
ons. (He’s older than me.)

Expected V

$.01 Better kn
$1 Deal or N
$5
$10
$25
$50
$75
$100
$200
$300
$400
$500
$750

Value Hour

nown as $1,000
No Deal $5,000
$10,000
$25,000
$50,000
$75,000
$100,000
$200,000
$300,000
$400,000
$500,000
$750,000
$1,000,000

Expected V

$.01 The “fair
$1

$5

$10 Multiply
$25 outcome
$50
$75 probabi

$100

$200 Total: $41
$300

$400

$500

$750 Fair deal: ~$

Value Hour

r deal”: $1,000
each $5,000
e by its $10,000
ility… $25,000
10,210 $50,000
$102,500 $75,000
$100,000
$200,000
$300,000
$400,000
$500,000
$750,000
$1,000,000

Expected V

$.01 The “bank
$1

$5

$10 Guarantee
$25 always less
$50
$75 valu

$100

$200 Fair deal: ~$
$300

$400 Offer: $8

$500

$750 Deal or No

Value Hour

k offer”: $1,000
$5,000
e, almost $10,000
s than fair $25,000
ue $50,000
$75,000
$102,500 $100,000
82,000 $200,000
o Deal? $300,000
$400,000
$500,000
$750,000
$1,000,000

Expected V

$.01 What’s the
$1 value of th
$5
$10 boar

$25

$50 How does it
$75 to the firs
$100

$200

$300 How does it
$400
$500 to how muc
$750 players actu

Value Hour

expected $1,000
he initial $5,000
rd? $10,000
$25,000
t compare $50,000
st offer? $75,000
$100,000
t compare $200,000
ch money $300,000
ually win? $400,000
$500,000
$750,000
$1,000,000

Expected V

$.01 Initial bo
$1

$5 Fair deal: $

$10

$25

$50 First of
$75

$100 ~$8,000-$
$200

$300

$400 The first of
$500 terrible!

$750

Value Hour

oard… $1,000
$131,477 $5,000
$10,000
ffer: $25,000
$20,000 $50,000
$75,000
ffers are $100,000
Why? $200,000
$300,000
$400,000
$500,000
$750,000
$1,000,000

Expected V

$.01

$1 Actual av
$5 winnings p

$10

$25 $122,

$50

$75 Initial bo
$100 expected
$200

$300 $131,
$400

$500

$750 (Close! Why th

Value Hour

verage $1,000
per player: $5,000
,500 $10,000
$25,000
oard’s $50,000
d value: $75,000
,477 $100,000
$200,000
he difference?) $300,000
$400,000
$500,000
$750,000
$1,000,000

Expected V

$.01

$1 Offer perce

$5 (compared
$10 value, by
$25
$50 11%, 21%

$75 50%, 62%
$100
$200 88%, 92%

$300

$400

$500 (Commercial
$750

Value Hour

entages $1,000
d to fair $5,000
round): $10,000
%, 36%, $25,000
%, 73%, $50,000
%, 98% $75,000
$100,000
l break…) $200,000
$300,000
$400,000
$500,000
$750,000
$1,000,000

Sponsored by…

•  Four-year, NSF-funded cu
•  Published in 2008 by Pea
•  25,000+ students use it n

Chicago, Pittsburgh,

Fundamental Organ
The widespread utility
mathematics come no
specific skills, topics, a
more importantly, from
of thinking—the habits
create the results.

… CME Project

urriculum written by EDC
arson Education
nationally: Boston,
Des Moines… and more

nizing Principle
y and effectiveness of
ot just from mastering
and techniques, but
m developing the ways
s of mind—used to

CME Projec

By focusing on habits

•  Coherent curriculum, fewer
•  Closely aligned to Common

Mathematical Practice (sev
•  Closely aligned to NCTM’s

Making goals (several exam
•  General-purpose tools help

Summer sessions

June 27-29, July 1

(we also do house calls…

ct Overview

s of mind…

r chapters
n Core’s Standards of
veral ideas come from CME)
Reasoning and Sense-
mples come from CME)
p students get the big ideas

s in New England!

18-20, August 1-5

but now, back to the show)

The Price

•  Now in its 39th yea
•  Lots of good math
• Also a huge sampl

played games (
visit http://tpirsu

Who wan

e Is Right

ar
problems!
le size of repeatedly-
(for agonizing detail,
ummaries.8m.com)

nts to play??

Four Pri

Place a price next to e
right price, you w

Slumdog Millionaire

Glee: The Game

Word Wear

Jenga

ice Tags

each item. If it’s the
win the prize!

Four Pri

Place a price next to e
right price, you w

Slumdog Millionaire

Glee: The Game

Word Wear

Jenga

ice Tags

each item. If it’s the
win the prize!

Good luck…
you’ll need it.

$9.99
$10.00
$10.09
$10.59

Audience, any advice?

Four Pri

So, how did you do…?

Slumdog Millionaire
Glee: The Game
Word Wear
Jenga

ice Tags

?

$10.00
$10.59
$9.99
$10.09

The Produce

If I keep offering this g
many prizes will I give

Answer by calculating
the number of prizes p

There are 24 different
place the price tags. (W

ers’ Question

game repeatedly, how
e away, on average?

the expected value for
per game.

ways the player can
Why?)

24 Ain’t T

Here are the 24 ways

ABCD BACD
ABDC BADC
ACBD BCAD
ACDB BCDA
ADBC BDAC
ADCB BDCA

That Many

to place the price tags:

CABD DABC
CADB DACB
CBAD DBAC
CBDA DBCA
CDAB DCAB
CDBA DCBA

Gotta Sco

For each of the 24 way
of price tags placed co

ABCD 4 BACD 2
ABDC 2 BADC 0
ACBD 2 BCAD 1
ACDB 1 BCDA 0
ADBC 1 BDAC 0
ADCB 2 BDCA 1

ore ‘Em All

ys, count the number
orrectly.

CABD 1 DABC 0
CADB 0 DACB 1
CBAD 2 DBAC 1
CBDA 1 DBCA 2
CDAB 0 DCAB 0
CDBA 0 DCBA 0

The expecte

This frequency chart s
ways to get each resu

# prizes # ways
4
2 1
1 6
0 8
9
TOTAL 24

ed value is…

shows the number of
ult.