The FontAwesome random is pretty awkward. I wouldn't use it. The idea of rolling dice is the best one to play off of. But, I don't like giving it a discrete value. To me that represents that actual value. Just as the FontAwesome icon, seems to mean discretely switching two items. Which is far from what you want.
My best idea is to use a question mark and dice to properly represent the idea of random. The thing you need to avoid is making it look like help. So making it cocked a bit to the side, to avoid the insinuation of posing a question.
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And a fluke that looked nice, kinda like you're rolling the dice and getting "?":
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