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Monte Hall Paradox

Monte Hall Paradox. Famous game show from the 70's Problem: Three doors One prize (car), 2 goats You chose 1 door Monte Hall (host) opens a door with a goat Asks if you want to switch Should you switch?. Monty Hall Problem. 1 Car, 2 goats Choose door. 1. 2. 3. Monty Hall Problem.

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Monte Hall Paradox

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  1. Monte Hall Paradox • Famous game show from the 70's • Problem: • Three doors • One prize (car), 2 goats • You chose 1 door • Monte Hall (host) opens a door with a goat • Asks if you want to switch • Should you switch?

  2. Monty Hall Problem • 1 Car, 2 goats • Choose door 1 2 3

  3. Monty Hall Problem • Monty Hall reveals goat • Asks if you want to switch • What do you do? 1 2 3

  4. Monty Hall Links • http://www.stat.sc.edu/~west/applets/LetsMakeaDeal.html • http://math.ucsd.edu/~anistat/chi-an/MonteHallParadox.html

  5. Monty Hall Problem 1 2 3 2/3 1/3

  6. Easier Monty Hall • 1000 Doors, 1 car • You chose 1 • Monty opens 998 goats • Should you switch?

  7. Monte Hall Paradox • Famous game show from the 70's • Problem: • Three doors • One prize (car), 2 goats • You chose 1 door • Monte Hall (host) opens a door with a goat • Asks if you want to switch • Should you switch?

  8. Monte Hall 1 3 2 Your Choice

  9. Monte Hall Goat!! 1 3 2 Your Choice Should you switch?

  10. Monte HallProbabilities 1 1/3 3 1/3 2 1/3 Your Choice

  11. Monte HallProbabilities 1 3 1/3 2 2/3 Your Choice Should you switch? Yes

  12. Two Final (difficult) Topics • Time • Chaos/complexity

  13. Time • Horizon • Days, weeks, months, years • Decisions • How effected by new information

  14. Complexity/connections • Interconnection between different variables difficult to predict, control, or understand • System failures • May impact the correctness of our risk model • Model risk

  15. Behavioral Features • Simple rules • Probability/ambiguity • Gambler’s fallacy • Regret/loss aversion • Overconfidence • Choice (information) overload • Under diversification

  16. Choice Overload • Jam samples in supermarket • Consumers sample jam • Can buy with coupon • Case 1: 6 jams • 30 percent redeem coupons • Case 2: 26 jams • 3 percent redeem coupons

  17. Information Overload • Decision makers have lots of information • Need to decide what is relevant • Emergent patterns on irrelevant information • Sunspots

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