Harold plays a game in which he starts with $2. Each game has 2 rounds; in each round, the amount of money he starts the

Harold plays a game in which he starts with $2. Each game has 2 rounds; in each round, the amount of money he starts the round with is randomly either added to or multiplied by a number, which is randomly either 1 or 0. The choice of arithmetic operation and of numbers are independent of each other and from round to round. If Harold plays the two-round game repeatedly, the long-run average amount of money he is left with at the end of the game, per game, is between

A. $0 and $0.50
B. $0.50 and $1
C. $1 and $1.50
D. $1.50 and $2
E. $2 and $2.50

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT