# Monte Hall Paradox - PowerPoint PPT Presentation

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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

• 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

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?

1

3

2

### Monte Hall

Goat!!

1

3

2

Should you switch?

1

1/3

3

1/3

2

1/3

### Monte HallProbabilities

1

3

1/3

2

2/3

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

• 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