I have some set $S_1,\ldots,S_k$ ($k \geq 3$) of bins, each initially with $N_0(S_i)$ balls ($N_t(S_i)$ denotes the number of balls in $S_i$ at time $t$). A bin can contain a negative number of balls. Now I apply the following rule: at time $t$, I choose 3 bins uniformly at random, say $S_{i_1}, S_{i_2}, S_{i_3}$, and $N_{t+1}(S_{i_1}) = N_t(S_{i_1}) - 1,$ $N_{t+1}(S_{i_2}) = N_t(S_{i_2}) + N_{t}(S_{i_3}) + 1,$ $N_{t+1}(S_{i_3}) = 0.$ Can anything reasonably be said about the distribution of balls as $t\to \infty$?
Edit: I should also say, the 3 bins are chosen among the $\binom{k}{3}$ 3-sets of bins; they are always distinct.