Variations of the following probability question have been asked on quant job interviews-
Question- We play a game where I roll a dice up to a maximum of four times. After each roll, you can take the dollar amount of the number showing or you may ask me to roll again. (Once you accept the dollar amount of any roll, the game is over. If you pass three times, you must accept the dollar amount of the fourth roll.)
What is the optimal strategy to follow and what is the expected value of your winnings?
I will post the answer in a blog post later this week.
Hint: The solution to this problem is similar to pricing an option on a multinomial tree.