Carnival Game Math Puzzle

In years gone by, there was a carnival game where the player would place his bet on a number from 1-6. He would then roll 3 dice. The payout was his bet plus 1, 2 or 3 times the bet, depending on how many times his number came up. Of course, if it didn't come up at all, he got nothing.

If the player bets $1, what is the expected gain or loss per game?

From Mathematical Puzzles of Sam Loyd

Click to find the answer to this math puzzle.