"We start a random process with Nb blue balls and Nr red balls such that N=Nr+Nb. In each step we divide all these N balls into groups of size 4 at random and in each group if the number of blue balls is 3 or 4, then all balls in that group change their color to blue, unless they all change to red. If we denote the number of blue balls in step t by Nb(t), then what is the expectation of Nb(t)?"

Thank you so much in advance.