Re: TT multiway
If you'd feel comfortable laying down to a raise, then bet the river. Otherwise, check/call is good. What you don't want to do is bet the river and call a raise.
If you're behind, both check/call and bet/fold are the same result: you lose an extra bet.
If you're ahead, check/call risks missing bets from hands like lower pairs that may call, and bet/fold risks an inferior hand pushing you out of the pot with a raise.
You've got to gauge how often an inferior hand raises on the river versus it checking all the way through to see if the relative gain of 1-3BB versus a relative loss of up to 12-15BB is worth it.
EDIT: Guess I better give a straight answer: if you are very comfortable with your loose-passive read, bet/fold the river. If you were in the pot with a tricky or aggressive player check/call.
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