At a monthly "casino night," there is a game called Chuck-a-Luck: three dice are rolled, and you place a $1 bet on any number from one to six. If your number comes up on any of the dice, you get your $1 back as well as $1 for each time your number is facing up. For example, you choose six. The dice are rolled, and there are two sixes and a four. You would receive your original bet of $1 plus an additional $2 ($1 for each six). If instead, the dice showed a one, a three, and a five, you would lose your dollar. The dice are certified to be fair dice, and you certainly can consider the value on each die independent of the other dice.
On average, how much would you expect to win (or lose) each time you play this game?