Okay, after thinking for a good 30 minutes this is what I came up with. I promise I didn't cheat and google it.
The flop is:
334
The turn is:
4
Which makes a board of: 3344
You have:
27 (7 high)
Your opponent has:
56
You are currently leading with seven high. But no matter what card comes next you cant win, you can only tie or lose.
If the next card is a 2 your opponent will make a straight (23456)
If the next card is a 3 or 4 you and your opponent will make a fullhouse and it would be split.
If the next card is a 5 or 6 your opponent will make a higher 2 pair (55446, 66445)
If the next card is a 7 your opponent will make a straight (34567)
If the next card is an 8-Ace it would be a split pot (3344X)
I am pretty sure this is the correct answer. I actually feel pretty smart now.