The Die With No Six

A carnival booth lays out two dice that look identical. One is fair; the other has had its six ground off and can never show a 6. Nobody tells you which is which. Each roll costs $\$1$: you pick up either die (switching between rolls is free and unlimited), roll it, and collect $\$20$ if it shows a 6. You may quit whenever you like. How should you play, and is the game worth playing?