Suppose in a tournament with only three players left, first place receives $6,000, second place receives $3,000, and third place receives $500. You have a 32% chance of winning first place, 30% chance of winning second place, and 38% chance of winning third place.
a. What would be your expected winnings in this tournament?
b. The tournament organizer gives you the option to continue playing or stop and split the total prize money, proportional to your current standings. If you currently have 700 of the 1800 chips currently in play, how much would you win if you stopped playing and split the winnings?
c. Based on parts a and b, should you continue playing or stop and split the money? Why?