An exponential limit shape of random $q$-proportion Bulgarian solitaire

Kimmo Eriksson, Markus Jonsson abd Jonas Sjöstrand

We introduce \emph{$p_n$-random $q_n$-proportion Bulgarian solitaire} ($0<p_n,q_n\le 1$), played on $n$ cards distributed in piles. In each pile, a number of cards equal to the pro…