1. ECONOMIC ANALYSIS OF EXPECTED VALUE AND RISK MANAGEMENT IN A HIGH- STAKES GAME SHOW Ryan G. Rosandich, Ph.D., University of Minnesota Duluth

2. Risky Decisions Low-income experiments India and China (rural) Reward still low, extreme situation Game show analysis Jeopardy! Lingo Who wants to be a millionaire? Deal or No Deal?

3. Game Show Analysis Problems Tests of knowledge or skill Quiz questions Word games Strategy decisions Daily double Lifelines Predictable expected values

4. Two-party negotiation $1,000,000 top prize Simple yes/no decisions EV can change dramatically each round Case values assigned randomly

5. 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

6. 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 $1.00 $5.00 $10.00 $25.00 $50.00 $75.00 $100.00 $200.00 $300.00 $400.00 $500.00 $750.00 $1,000.00 $5,000.00 $10,000.00 $25,000.00 $50,000.00 $75,000.00 $100,000.00 $200,000.00 $300,000.00 $400,000.00 $500.000.00 $750,000.00 $1,000,000.00

7. Game Play Contestant chooses a case Each round: Contestant opens cases Banker makes offer Contestant makes decision Take offer (DEAL) Go on (NO DEAL) RoundCases Opened Unopened Cases 1620 2515 3411 438 526 615 714 813 912 1020

8. Banker Behavior Target percentage Percent of EV increases each round Builds excitement Luck factor “Lucky” contestants encouraged to continue with lower offers “Unlucky” contestants encouraged to stop with higher offers

9. Banker Target Percentage

10. Banker Function First term represents target R r Second term is luck factor Regression results: a=0.93, b=3750, R 2 =91%

11. Banker Function Results

12. Banker Function Errors

13. 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

14. Simulation Results (n=10,000)

15. 32 Games at 0.6 Risk Average Case Amount Average Winnings GamesSource $79,650$105,00032Data Set $78,700$104,80032Simulation $78,250$106,15032Simulation

16. 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

17. 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

18. Questions?