  The game of plates and olives was originally formulated by Nicolaescu and
encodes the evolution of the topology of the sublevel sets of Morse functions.
We consider a random variant of this game. The process starts with an empty
table. There are four different types of moves: (1) add a new plate to the
table, (2) combine two plates and their olives onto one plate, removing the
second plate from the table, (3) add an olive to a plate, and (4) remove an
olive from a plate. We show that with high probability the number of olives is
linear as the total number of moves goes to infinity. Furthermore, we prove
that the number of olives is concentrated around its expectation.
