  We consider the unbalanced allocation of $m$ balls into $n$ bins by a
randomized algorithm using the "power of two choices". For each ball, we select
a set of bins at random, then place the ball in the fullest bin within the set.
Applications of this generic algorithm range from cost minimization to
condensed matter physics. In this paper, we analyze the distribution of the bin
loads produced by this algorithm, considering, for example, largest and
smallest loads, loads of subsets of the bins, and the likelihood of bins having
equal loads.
