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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

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
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?
game show analysis problems
Game Show Analysis Problems
  • Tests of knowledge or skill
    • Quiz questions
    • Word games
  • Strategy decisions
    • Daily double
    • Lifelines
  • Predictable expected values
slide4
Two-party negotiation
  • $1,000,000 top prize
  • Simple yes/no decisions
  • EV can change dramatically each round
  • Case values assigned randomly
goals
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
The Game
  • Netherlands 2002
  • U.S. December 2005
  • Data collected
    • 12/2005 through 5/2006
    • Checked and cleaned
    • 32 complete games from 29 episodes
game play
Game Play
  • Contestant chooses a case
  • Each round:
    • Contestant opens cases
    • Banker makes offer
    • Contestant makes decision
      • Take offer (DEAL)
      • Go on (NO DEAL)
banker behavior
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
banker function
Banker Function
  • First term represents target Rr
  • Second term is luck factor
  • Regression results:

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

contestant behavior
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
conclusions
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
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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