= 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 $B_j\geq2$, and zero for $B_j\leq1$. 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 $\mathbb E B_j=2^{1-j}$.
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