ECONOMIC ANALYSIS OF
EXPECTED VALUE AND RISK
MANAGEMENT IN A HIGHSTAKES GAME SHOW
Ryan G. Rosandich,
Ph.D., University of
Minnesota Duluth
Risky Decisions

Low-income experiments

Game show analysis
• India and China (rural)
• Reward still low, extreme situation
• Jeopardy!
• Lingo
• Who wants to be a millionaire?
• Deal or No Deal?
Game Show Analysis Problems

Tests of knowledge or skill

Strategy decisions

Predictable expected values
• Quiz questions
• Word games
• Daily double
• Lifelines





Two-party negotiation
$1,000,000 top prize
Simple yes/no decisions
EV can change dramatically each
round
Case values assigned randomly
Goals





Collect and organize data
Determine banker behavior
Simulate games
Find a good contestant strategy
Compare actual and simulated
games to determine actual
contestant strategies
The Game



Netherlands 2002
U.S. December 2005
Data collected
•
•
•
12/2005 through
5/2006
Checked and cleaned
32 complete games
from 29 episodes
$0.01
$1,000.00
$1.00
$5,000.00
$5.00
$10,000.00
$10.00
$25,000.00
$25.00
$50,000.00
$50.00
$75,000.00
$75.00
$100,000.00
$100.00
$200,000.00
$200.00
$300,000.00
$300.00
$400,000.00
$400.00
$500.000.00
$500.00
$750,000.00
$750.00
$1,000,000.00
Game Play


Contestant chooses
a case
Each round:
•
•
•
Contestant opens
cases
Banker makes offer
Contestant makes
decision
• Take offer (DEAL)
• Go on (NO DEAL)
Round
Cases
Opened
Unopened
Cases
1
6
20
2
5
15
3
4
11
4
3
8
5
2
6
6
1
5
7
1
4
8
1
3
9
1
2
10
2
0
Banker Behavior

Target percentage

Luck factor
• Percent of EV increases each round
• Builds excitement
• “Lucky” contestants encouraged to
•
continue with lower offers
“Unlucky” contestants encouraged to stop
with higher offers
Banker Target Percentage
120.0%
100.0%
80.0%
60.0%
40.0%
20.0%
0.0%
1
2
3
4
5
6
Round
Banker
Prediction
7
8
9
Banker Function



First term represents target Rr
Second term is luck factor
Regression results:
a=0.93, b=3750, R2=91%
 Er

Br  aRr Er  b  1.00 
 E0

Banker Function Results
$400,000.00
Prediction
$300,000.00
$200,000.00
R2 = 91%
$100,000.00
$0.00
$0.00
$100,000.00
$200,000.00
Bank Offer
$300,000.00
$400,000.00
Banker Function Errors
100
90
80
Frequency
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
Bins
10
11
12
13
14
15
16
Contestant Behavior

Reward/Risk ratio
• Reward is difference between best
•
•
possible outcome of the next round and
current offer (contestant opens lowest
valued cases)
Risk is difference between current offer
and worst possible outcome of the next
round (contestant opens highest valued
cases)
Low number is high risk, 1.0 is neutral,
high number is low risk
Simulation Results (n=10,000)
120%
100%
Winnings
80%
60%
40%
20%
0%
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
Risk Threshold
0.4
0.3
0.2
0.1
0
32 Games at 0.6 Risk
Average
Case Amount
Average
Winnings
Games Source
$79,650
$105,000
32
Data Set
$78,700
$104,800
32
Simulation
$78,250
$106,150
32
Simulation
Conclusions



Banker behavior is over 90%
predictable
Contestants exhibit an average
reward/risk threshold of 0.60
Only a high-risk strategy will result in
the initial average expected winnings
of $131,478
How much should I win?



Risk neutral contestants (1.0) can
easily win about $65,000
Risk taking contestants will average
about $131,000 in winnings with
much variation
The only way to win big is to take
risks and be lucky
Questions?