  The following problem is considered. Two players are each required to
allocate a quota of~$n$ counters among~$k$ boxes labelled~$1,2,\ldots,k$. At
times $t=1,2,3,\ldots$ a random box is identified; the probability of choosing
box~$i$ is~$p_i$. If a player has at least one counter in the chosen box, she
removes one counter from it; otherwise she takes no action. The winner is the
first player to remove all her counters. The game so described may be modified
so that each player simultaneously, but independently, identifies a box at
random.
  This paper analyses this deceptively simple game, which has apparently not
been studied in the literature. Some analytical and numerical results are then
presented, followed by some challenges for further work.
