You are a risk-neutral investor and you have a fair six-sided dice (numbered 1-6) and you are

asked to participate in the following gamble. You are allowed to throw the dice a maximum of

three times, after each throw you have two choices:

A: To throw the dice again

B: To stop and receive $5 per point showing on the dice.

Obviously, if you throw the dice for the third time you must choose B.

a) What is your optimal strategy, i.e what scores would lead you to stop on the first and

second rolls?

b) What is the fair price (assume that you are risk neutral) to pay to enter into this particular

gamble?

c) What would be the impact on your answers to parts a) and b) if the number of throws was

increased to 5? (You do not need to calculate anything here, although you can if you

want)