Question: Decided to travel to Las Vegas to bet on the next Series.
For $100, he bought a certificate from a casino, which allows him to stake that $100 on whether the Red Sox will win the 2008 series. The casino is offering four-to-one odds for the Red Sox not to win a second time consecutively. That is, if Shantanu declares that the Red Sox will win, he will receive $500 if he is correct, and if he declares that they will not win, he will receive $125 if he is correct. In either case, if he is incorrect, he gets nothing.
Assume that to Shantanu, any dollar amount one year from now is worth as much as any dollar amount today. Now suppose Shantanu thinks that the Red Sox do have a four-to-one chance of losing their title next year; that is, he agrees with the casino's assessment of the odds and believes that there is a 0.8 chance that the Red Sox will lose next year. Unfortunately, you do not know whether Shantanu follows the delta property, and you don't even know what his initial wealth is-you just know that he follows the five Rules of Actional Thought and prefers more money to less. How should Shantanu bet?
a. There is not enough information to answer this question.
b. He should bet on the Red Sox winning if he is risk-averse and on their losing if he is risk preferring.
c. He should bet on the Red Sox losing if he is risk-averse and on their winning if he is risk preferring.
d. No matter what his risk attitude is, he should be indifferent between the two alternatives.