More is expected from Expected Value Jim Friedrich

More is expected from Expected Value Jim Friedrich

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

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

A 100% $5 B 10% for $60 otherwise $0 0. 1% for $6, 000 0. 0001% for $6, 000

A 100% $5 B 10% for $60 otherwise $0 40% 60% 0. 1% for $6, 000 46% 54% 0. 0001% for $6, 000 24% 76% Expected Value = $5 Expected Value = $6

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

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

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

A B 100% 30% for $-50 and 70% for $-3 $-5 17% Expected Value = $-5 Expected V = $-3. 60

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

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

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

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