1 research outputs found
An exponential limit shape of random -proportion Bulgarian solitaire
We introduce \emph{-random -proportion Bulgarian solitaire}
(), played on cards distributed in piles. In each pile, a
number of cards equal to the proportion of the pile size rounded upward
to the nearest integer are candidates to be picked. Each candidate card is
picked with probability , independently of other candidate cards. This
generalizes Popov's random Bulgarian solitaire, in which there is a single
candidate card in each pile. Popov showed that a triangular limit shape is
obtained for a fixed as tends to infinity. Here we let both and
vary with . We show that under the conditions and as , the
-random -proportion Bulgarian solitaire has an exponential limit
shape