Raashan, Sylvia, and Ted play the following game. Initially, Raashan has $2, Sylvia has $1, and Ted has $0. A bell rings every 15 seconds, at which time each of the players who currently have money simultaneously chooses one of the other two players independently and at random and gives $1 to that player. What is the probability that after the bell has rung 2019 times, each player will have $1?
