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

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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 l.jpg

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

Ryan G. Rosandich, Ph.D., University of Minnesota Duluth


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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?


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Game Show Analysis Problems

  • Tests of knowledge or skill

    • Quiz questions

    • Word games

  • Strategy decisions

    • Daily double

    • Lifelines

  • Predictable expected values


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  • Two-party negotiation

  • $1,000,000 top prize

  • Simple yes/no decisions

  • EV can change dramatically each round

  • Case values assigned randomly


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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


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The Game

  • Netherlands 2002

  • U.S. December 2005

  • Data collected

    • 12/2005 through 5/2006

    • Checked and cleaned

    • 32 complete games from 29 episodes


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Game Play

  • Contestant chooses a case

  • Each round:

    • Contestant opens cases

    • Banker makes offer

    • Contestant makes decision

      • Take offer (DEAL)

      • Go on (NO DEAL)


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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


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Banker Target Percentage


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Banker Function

  • First term represents target Rr

  • Second term is luck factor

  • Regression results:

    a=0.93, b=3750, R2=91%


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Banker Function Results


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Banker Function Errors


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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


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Simulation Results (n=10,000)


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32 Games at 0.6 Risk


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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


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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


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Questions?


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