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ECONOMIC ANALYSIS OF EXPECTED VALUE AND RISK MANAGEMENT IN A HIGH-STAKES GAME SHOW

ECONOMIC ANALYSIS OF EXPECTED VALUE AND RISK MANAGEMENT IN A HIGH-STAKES GAME SHOW. Ryan G. Rosandich, Ph.D., University of Minnesota Duluth. Risky Decisions. Low-income experiments India and China (rural) Reward still low, extreme situation Game show analysis Jeopardy! Lingo

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ECONOMIC ANALYSIS OF EXPECTED VALUE AND RISK MANAGEMENT IN A HIGH-STAKES GAME SHOW

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  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

  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)

  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 Rr • Second term is luck factor • Regression results: a=0.93, b=3750, R2=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

  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?

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