1. More is expected from Expected Value
Jim Friedrich

2. Which would you prefer?
A B
$60 $5
100%
10%
90% $0

3. An A B preference every minute means
60 minutes X 24 hours X 365 days
525,600 minutes in a year
1,000,000,000 divided by 525,600 is
NEARLY 2000 years
A preference every second is OVER 30 years

4. A B $5 10% for $60 otherwise $0 100% 0.1% for $6,000

5. A B $5 100% 10% for $60 otherwise $0 0.1% for $6,000
60%
40%
46%
54%
24%
76%
Expected Value = $5
Expected Value = $6

6. $5
100% A B
20% for $50 and 80% for $-5
10% for $105 and 90% for $-5

7. $5 A B 100% 20% for $50 and 80% for $-5 10% for $105 and 90% for $-5
48%
52%
53%
47%
Expected Value = $5
Expected Value = $6

8. $-5
100% A B
30% for $-50 and 70% for $-3

9. $-5 A B 30% for $-50 and 70% for $-3 100% 17% Expected Value = $-5

10. Is it possible to design two preferences so that all students would choose a preference with a smaller expected value?
Hint: It may require using an unfamiliar term

11. B $5
100% A
“lifetime of debt”
90%
10%
$10
100%

12. Two ideas when teaching expected value
1. State the assumptions
Are you playing once?
2. Psychology may have a greater influence than mathematics

13. References Priceless by William Poundstone
Rational Decision Making Models
St. Petersburg paradox
Game Theory