More is expected from Expected Value Jim Friedrich

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

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

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

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

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

$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

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

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

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

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