Consider a relatively small fleet of only 4 boats, each of which is equally likely to win any given race.

a) If there are only two races, the boat that wins the regatta will have a score of 2, 3, 4 or possibly even 5. What is the expected value of the winning score?

b) If there are three races, what is the expected value of the winning score? (I found even this simple case hard to calculate exactly, and I am hoping that somebody will come up with a better method than mine. And yes, I know that it is easy to simulate.)

c) If there is a large number of races, how might I approximate the expected winning score? (Among other things, I think I'd welcome a simulation here)