Math Challenge Problem #1

You are playing a game involving three dice. You can choose to bet on any number from 1 to 6.

I'll roll the three dice. If:
- none shows your number, you lose $1
- one shows your number, you win $1
- two show your number, you win $3
- three show your number, you win $5

What is the expected value of this game? 

Email your answer so as not to ruin the challenge for others.