The Mathematics of Game Shows - Patterns in Practice

Good Plin

Where you drop Plinko

Drop Above Chip EV

$10,000 $2,558
$0 $2,266
$1,606
$1,000 $1,009
$500 $780
$100

nko Advice

o chips matters a lot!

(Did they build the board
this way on purpose?)

Good Plin

Where you drop Plinko

Drop Above Chip EV

$10,000 $2,558
$0 $2,266
$1,606
$1,000 $1,009
$500 $780
$100

nko Advice

o chips matters a lot!
If you ever get on…
DROP IT IN
THE MIDDLE!!!
Actual average
winnings:
$1,805 per chip

($753 lost per chip…
1,227 times)

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(Let’s get back to
the games already…)

y… Gold Bond
d Powder

The #2 Game

ANY NU

We don’t need a
Plinko board to play
this one.

Who wants
to play??

e on TPIR is…

UMBER!

3CHEESE

BUS

PIGGY BANK

3207
695

K184

Any Nu

Assuming the player is
(which seems about ri
probability that they wi

This is a ha

umber

s just picking randomly
ight), what is the
in the big prize?

ard question!

Any Nu

Assuming the player is
what is the probability
prize?

This question would be
prize had 3 digits inste

The probability of w
must be le

umber

s just picking randomly,
that they win the big

e a lot easier if the big
ead of 4…

winning the big prize
ess than 1/3.

Solving by

There are 10! = 3,628,
player can pick numbe
10! is a much bigger n
enumerating by hand i
One option is to simula
large number of times.

Cheese: 2,
Bus

Piggy B

Simulation

,800 different ways the
ers.
number than 24, so
is impractical.
ate running the game a
. Here’s 10,000 trials:

,605 (26.05%)
s: 3,682
Bank: 3,713

Solving by T

Solve a simpler versio
number in each prize l
chance of winning the
If there’s two numbers
one in each of the sma

2/4 x 1
chance of winning the
coordinate system: P(2
Continue and “build ou
answer at P(4,3,3). (B

Tree Diagram

on! If there’s one
left, there is a 1/3
big prize.
s left in the big prize and
all prizes, there is a
1/3 = 1/6
big prize. This is like a
2,1,1) = 1/6.
ut” until you find the
Build a 3-D model!)

Solving by E

For computers, 3.6 mi
around the number of
A computer can try all
could be played:

Cheese: 933,12
Bus: 1,347,840
Piggy Bank: 1,347,

This is different from w
found; its probability is

Enumeration

illion isn’t that big, it’s
5-card poker hands.
10! ways the game

20 (25.71% = 9/35)
0 (37.14% = 13/35)
,840 (37.14% = 13/35)

what the simulation
s an estimate.

Solving by B

Let’s play a different ga
But That One.
You pick a number; if it’
explodes. You win the
Say you pick 3… chees

What’s the pro
cheese stan

Being Clever

ame called Any Number
’s in a prize, that prize
last prize standing.
se explodes! (Oops.)

obability of the
nding alone?

Solving by B

This game doesn’t last
On the first pick, 6 of th
one of the two small pri
After you blow up one s
pick is decisive: 3 of the
the other small prize, a

6/10 x 3/7 = 9

Hey, it’s the sam

Being Clever

nearly as long…
he 10 numbers explode
izes. (Which is good.)
small prize, the next
e 7 numbers explode
and then it’s all cheese.
9/35 (25.71%)

me probability…

Solving by B

Imagine being forced, b
Number, to write down
you plan to call them. H
up with Any Number Bu
•  The first exploding nu
final digit that you neve
•  The second exploding
in the other prize you d
In long games, it is ofte
doesn’t happen instead

Being Clever

before playing Any
all 10 digits in the order
Here’s how it matches
ut That One:
umber you pick is the
er plan to pick.
g number is the last one
didn’t complete.
en easier to look at what
d of what does.

Historic

Players win Any Numbe
predicted by chance.

2000
257 p
Big prize (A New C
Small p
Piggy B

Players often guess the
Also, 0 and 5 are more

cal Data

er more often than

0-2011
plays
Car!): 92 (35.80%)
prize: 91
Bank: 74

e first digit of the car.
e likely to appear there.

(Our last commercial break…)

Classroom

In my teaching, I found
worked better than oth
games for test review,
wrap-ups.

Good

Press Your Luck
Card Sharks
Millionaire
High Rollers

m Interlude

d some game shows
hers. Mostly I used
, but also for openers or

Bad

Jeopardy! (yes, bad)
Deal or No Deal
Twenty-One
Newlywed Game

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hematical Practice
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A Quick

Who’s got a #2 pencil?
Now roll this die numb
do, pick one:
•  Try to roll a 1 through
•  Try to roll a 6 to win $

You must pic
What’s it g

Game…

? Stand up.
ber cube, but before you

h 5 to win $2, or
$20.

ck in advance!
gonna be???

The Same

Let’s raise the stakes…
Now roll this die numb
do, pick one:
•  Try to roll a 1 through
•  Try to roll a 6 to win $

Why is this
How do play

e Game…?

… hypothetically.
ber cube, but before you

h 5 to win $25,000, or
$250,000.

so different?
yers behave?

It’s National

NBN was The Price is
Right with bingo instead
of shopping.

(It only lasted six
episodes. Wonder why…
Its games were
interesting probability
problems, but usually no
strategy. Except for
Bingo 365…

Who wants to play?

Bingo Night!

d
…)
o

?

Get Out Your B

The final game of the s
If you complete a bing
wins, you win all rema

(Ties will be broken
Important: if you are o
bingo, STAND UP so w
away.

Bingo Cards…

show is Bingo 365.
go before the contestant
aining prizes!
n by a math problem.)
one number away from a
we can tell you are one

Bingo

For each bingo ball, th
whether the next ball w
than the one that just c

If they are right, the ba
their score. 75 is bette

The first ball doesn’t s

o 365

he contestant guesses
will be higher or lower
came out.

all number is added to
er than 23.

score any points.

Bingo

The contestant wins if
they get a total of 365
points or more before
anyone in the audienc
completes a bingo.

TV Show audience: 20
players, one card each
This audience: 100
players, two cards eac

o 365

ce

00
h.
ch.

I swear this was actually
on network TV.

Bingo

42

o 365

Bingo balls go from
1 to 75.

Is the next ball higher
or lower than 42?

Bingo

42 60

o 365

Is the next ball higher
or lower than 60?

Bingo

42 60 5

o 365

Is the next ball higher
or lower than 5?