Repeated singleton-removal allocation

In repeated uniform balls-in-bins allocation, remove each ball that is alone in its bin and independently reallocate all remaining balls in the next round. If $B_j$ balls remain, the conditional expectation of the next count is $B_j[1-(1-1/n{)}^{B_j-1}]$ for $B_j\ge 2$, and zero for $B_j\le 1$. The surviving-ball indicator random variables need not be independent. For two balls and two bins, both remain with probability $2^{-j}$ after $j$ rounds, so $\mathbb{E}{B}_j=2^{1-j}$.