  We consider a stochastic version of Bulgarian solitaire: A number of cards
are distributed in piles; in every round a new pile is formed by cards from the
old piles, and each card is picked independently with a fixed probability. This
game corresponds to a multi-square birth-and-death process on Young diagrams of
integer partitions. We prove that this process converges in a strong sense to
an exponential limit shape as the number of cards tends to infinity.
Furthermore, we bound the probability of deviation from the limit shape and
relate this to the number of rounds played in the solitaire.
