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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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**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**• Monty Hall reveals goat • Asks if you want to switch • What do you do? 1 2 3**Monty Hall Links**• http://www.stat.sc.edu/~west/applets/LetsMakeaDeal.html • http://math.ucsd.edu/~anistat/chi-an/MonteHallParadox.html**Monty Hall Problem**1 2 3 2/3 1/3**Easier Monty Hall**• 1000 Doors, 1 car • You chose 1 • Monty opens 998 goats • Should you switch?**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?**Monte Hall**1 3 2 Your Choice**Monte Hall**Goat!! 1 3 2 Your Choice Should you switch?**Monte HallProbabilities**1 1/3 3 1/3 2 1/3 Your Choice**Monte HallProbabilities**1 3 1/3 2 2/3 Your Choice Should you switch? Yes**Two Final (difficult) Topics**• Time • Chaos/complexity**Time**• Horizon • Days, weeks, months, years • Decisions • How effected by new information**Complexity/connections**• Interconnection between different variables difficult to predict, control, or understand • System failures • May impact the correctness of our risk model • Model risk**Behavioral Features**• Simple rules • Probability/ambiguity • Gambler’s fallacy • Regret/loss aversion • Overconfidence • Choice (information) overload • Under diversification**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**Information Overload**• Decision makers have lots of information • Need to decide what is relevant • Emergent patterns on irrelevant information • Sunspots

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