TDL 2-7: 3 betting with a 7

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I'll preface this by saying recent experience may be coloring my perception.

How strong of a hand do you need to three-bet the river against a typical player? Generally, I need about an 875 to bet, an 864 to raise and a 76532 to three bet. Obviously, the specific opponent changes things and also how many cards each player drew.

So, what do you need to three bet the river? What other considerations are important when deciding to three bet the river?