The problem is to find E 1 . At this point it starts to get less obvious what the probabilities are to advance closer to a yahtzee.
Lets assume the two of a kind is of the number a.
Below are the number of ways to advance closer and the number of corresponding combinations. So there are 15 ways to progress to a four of a kind. There is obviously only 1 way to progress to a five of a kind. Next solve for E 1 . Lets assume that the one of a kind is already an a.